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Two funds

13.3.3 Two funds Lazy portfolios


31Lug2022

Information
Andrea Gonzali Lazy portfolios 878 hits
Prima pubblicazione: 05 Aprile 2022

«The shortest distance between two points is a straight line».

Archimede

Il Two funds portfolio è composto da 2 ETF ed è un portafoglio bilanciato: la percentuale di azionario e obbligazionario dipende dalla versione scelta .

Nella versione in USD, il Two funds è composto dai seguenti ETF:

  • VTI: replica il mercato azionario statunitense (è un ETF di Vanguard dal TER eccezionalmente basso: 0,03%).
  • BND: replica il mercato obbligazionario statunitense (anche questo è un ETF di Vanguard dal TER bassissimo: 0,035%).

Nella versione in EUR, abbiamo utilizzato i seguenti ETF (descrizione e caratteristiche):

Descrizione degli ETF che compongono il Two funds portfolio
TickerISINNomeSocietà  emittenteDescrizione
CSEMU IE00B53QG562 iShares Core MSCI EMU UCITS ETF EUR (Acc) iShares Replica i titoli azionari ad alta e media capitalizzazione dei paesi dell'unione monetaria ed economica europea
EYLD IE00BD49RB39 WisdomTree EUR Aggregate Bond Enhanced Yield UCITS ETF EUR Acc WisdomTree Replica la performance di obbligazioni a tasso fisso, denominate in euro, includendo obbligazioni del tesoro, governative, societarie e cartolarizzate (Investment Grade)
Caratteristiche degli ETF che compongono il Two funds portfolio
TickerTERReplicaHedgingPROCONTRO
CSEMU 0.12% Fisica (Replica totale) No Ampia diversificazione Niente di rilevante
EYLD 0.18% Fisica (Campionamento) No Ampia diversificazione Niente di rilevante

Il two fund portfolio può avere diverse asset allocation: data la sua semplicità, basta alzare o abbassare la percentuale di uno dei due ETF per modularne la rischiosità.

I più conosciuti two fund portofolios americani sono i seguenti:

  • Rick Ferri Two funds portfolio. È composto dal 40% di obbligazionario (US Bond market) e dal 60% di azionario (Total World market).
  • John Bogle Two funds portfolio. Esistono 4 versioni: 20/80, 40/60, 60/40 e 80/20 (percentuali di obbligazionario e azionario). Bogle suggerisce la replica di obbligazioni a medio termine e del mercato azionario statunitensi.
  • Warren Buffett Two funds portfolio. Questo portafoglio è uno di quelli che abbiamo analizzato e i suoi risultati verranno approfonditi nel capitolo 13.3.4.

Asset allocation dei Two funds Lazy portfolios

03 Two fund all merged

Per verificare meglio il comportamento del Two funds portfolio, abbiamo deciso di backtestare tutte le possibili combinazioni di pesi tra i due ETF che lo compongono (con variazioni pari al ± 10%).

Gli ETF utilizzati nei backtest dei portafogli in EUR potrebbero essere sostituiti da quelli elencati nelle due tabelle seguenti (descrizione e caratteristiche degli ETF). Alcuni ETF che replicano lo stesso indice (o un indice simile) potrebbero essere stati esclusi.

Gli ETF seguenti sono possibili alternative dell'ETF: CSEMU
La lista è orientativa e non pretende di essere esaustiva
TickerISINNomeSocietà emittenteDescrizione
ACWIE IE00BYM11K57 UBS ETF (IE) MSCI ACWI SF UCITS ETF (hedged to EUR) A-acc UBS Replica i titoli azionari di molti paesi sviluppati ed emergenti di tutto il mondo. La copertura valutaria in euro è relativa ai soli titoli dei paesi sviluppati
SWDA IE00B4L5Y983 iShares Core MSCI World UCITS ETF USD (Acc) iShares Replica i titoli azionari di circa 25 paesi sviluppati di tutto il mondo
VWCE IE00BK5BQT80 Vanguard FTSE All-World UCITS ETF (USD) Acc Vanguard Replica i titoli azionari dei paesi sviluppati ed emergenti di tutto il mondo
TickerTERReplicaHedgingPROCONTRO
ACWIE 0.21% Sintetica (Basata su swap) - Amplissima diversificazione
- Copertura valutaria e rischio di cambio limitato
Replica sintetica
SWDA 0.20% Fisica
(Campionamento ottimizzato)
No - Amplissima diversificazione, anche se inferiore agli ETF che replicano anche i titoli azionari dei paesi emergenti
- Dimensione del fondo molto grande
Rischio di cambio
VWCE 0.22% Fisica
(Campionamento ottimizzato)
No Amplissima diversificazione Rischio di cambio
Gli ETF seguenti sono possibili alternative dell'ETF: EYLD
La lista è orientativa e non pretende di essere esaustiva
TickerISINNomeSocietà emittenteDescrizione
AGGH IE00BDBRDM35 iShares Core Global Aggregate Bond UCITS ETF EUR Hedged (Acc) iShares Replica le obbligazioni emesse nei mercati emergenti e sviluppati di tutto il mondo (Investment Grade)
XG7S LU0908508731 Xtrackers Global Government Bond UCITS ETF 5C DWS Replica il mercato dei titoli di debito fisso emessi da governi di paesi sviluppati (Investment Grade)
XGSH LU0378818131 Xtrackers II Global Government Bond UCITS ETF 1C EUR Hedged DWS Replica il mercato mondiale delle obbligazioni governative emesse da nazioni sviluppate (Investment Grade)
TickerTERReplicaHedgingPROCONTRO
AGGH 0.10% Fisica (Campionamento) - Amplissima diversificazione
- Copertura valutaria e rischio di cambio molto limitato
- TER basso
Niente di rilevante
XG7S 0.20% Fisica (Campionamento) No Amplissima diversificazione Rischio di cambio
XGSH 0.25% Fisica (Campionamento) - Amplissima diversificazione
- Copertura valutaria e rischio di cambio molto limitato
Niente di rilevante

Qual è la correlazione lineare tra i rendimenti degli ETF che compongono il portafoglio?

Vediamola graficamente, sia per i portafogli in USD che per quelli in EUR e per tutte e 3 le durate analizzate:

12 Two Fund correlazione ETF

Nel portafoglio in USD, la correlazione lineare tra gli ETF VTI e BND è 0,03, −0,05 e −0,10; in quello in EUR, la correlazione lineare tra gli ETF CSEMU e EYLD è −0,01, −0,12 e −0,10.

Il primo livello di diversificazione offerto dagli ETF che compongono il Two funds portfolio è ottimo.

Una nota a parte la merita il Two funds Lazy portfolio dinamico.

Nel Two funds dinamico il peso standard non è fisso, ma varia in base alla volatilità del mercato. Lo scopo è quello di garantire una maggiore conformità col contesto di mercato: cavalcare il trend azionario nelle fasi di crescita e viceversa.

L’indicatore utilizzato per la scelta del contesto di mercato è il VIX: esso misura la volatilità implicita dell’indice S&P 500 e permette di quantificare le aspettative del mercato sulla volatilità nei prossimi 30 giorni.

Senza entrare troppo nei dettagli, ci basta osservare che il VIX è inversamente correlato con lo S&P 500: se il VIX è alto, l’aspettativa è di una decrescita dello S&P 500 e viceversa.

Nei momenti di crisi più intensa dei mercati azionari, proprio durante le fasi di “panic selling”, il VIX raggiunge i suoi valori massimi.

Per questo motivo, il VIX è stato ribattezzato “indice della paura” (“the fear index”).

Nel Two funds dinamico, in fase di ottimizzazione dei pesi si può verificare uno dei seguenti scenari:

  • Mercato azionario volatile (VIX > 24): il peso standard utilizzato è 10/90 (azionario = 10% e obbligazionario = 90%).
  • Mercato azionario poco volatile (VIX ≤ 18): il peso standard utilizzato è 90/10 (azionario = 90% e obbligazionario = 10%).
  • Mercato azionario mediamente volatile (18 < VIX ≤ 24): il peso standard utilizzato è 50/50 (azionario = 50% e obbligazionario = 50%).

Nei modelli vincolati, il peso standard selezionato in base al contesto di mercato potrà variare ulteriormente nel processo di ottimizzazione (± 5%).

I valori del VIX pari a 18 e 24 non sono il prodotto di un’artificiale calibrazione finalizzata a massimizzare la performance del Two funds portfolio dinamico in fase di backtest: sono valori che hanno una logica, ovviamente, ma che sono stati scelti prima di verificare i risultati dei backtest, eseguiti soltanto utilizzando queste soglie del VIX.

La stessa cosa può essere detta dei pesi scelti nei vari 3 scenari: perché 10-90, 50-50 o 90-10?

Queste tre opzioni non derivano da alcun processo di fine tuning applicato ai backtest: non c’è stato alcun Look-back bias.

L’unica motivazione è la logica associata alla creazione di un portafoglio aggressivo quando ci sono prospettive di una crescita dei mercati azionari, di un portafoglio prudente quando ci sono prospettive di una crisi finanziaria o di una decrescita dei mercati azionari e di un portafoglio equidistribuito tra componente azionaria e obbligazionaria quando ci si trova in una situazione di incertezza.

La scelta di pesi pari al 20-80/80-20 oppure 30-70/70-30 avrebbe potuto generare risultati molto diversi: dato che, in fin dei conti, si tratta di una scelta soggettiva, ognuno è libero di selezionare le soglie che ritiene più corrette.

La cosa da evitare è effettuare una scelta sulla base di multipli backtest eseguiti con lo scopo di verificare la combinazione che avrebbe massimizzato le performance passate: non c’è alcuna garanzia che essa produca risultati simili in futuro.

Equity lines, rendimenti e drawdown

Come per i Lazy portfolios precedenti, mostreremo:

  • Le equity lines ottenute dalle nostre analisi nei periodi 1985-2020, 2000-2020 e 2010-2020.
  • I grafici dei rendimenti giornalieri.
  • I grafici dei drawdown.

Per non riempire decine di pagine di grafici, li accorperemo in modo da farne entrare 6 in ogni pagina (ogni Two funds ha 3 grafici, uno per ognuno dei 3 periodi di analisi).

Seguiranno le nostre considerazioni.

 

Two funds 10/90 e 20/80
03 1 Two fund 10 90 20 80

 

Two funds 30/70 e 40/60

03 2 Two fund 30 70 40 60

 

Two funds 50/50 e 60/40

03 3 Two fund 50 50 60 40

 

Two funds 70/30 e 80/20

03 4 Two fund 70 30 80 20

 

Two funds 90/10 e dinamico03 5 Two fund 90 10 dinamico

 

Two funds 90/10

Esaminiamo il Two funds 90/10 più attentamente.

Vediamo il grafico delle equity lines che copre il periodo 1985-2020:

11 two fund 90 10 1985

La parte superiore rappresenta l’equity line del Two Fund 90/10 in USD, USD→EUR e EUR (medie degli 11 modelli di ottimizzazione backtestati).

La parte centrale del grafico misura il rendimento giornaliero del Two Fund 90/10 in USD. Il rendimento medio del Two Fund 90/10 in USD è stato 0,0368% e la deviazione standard dei rendimenti giornalieri è stata 0,6882%.

Vediamo di quanto si discosta la conformazione del grafico a barre dei rendimenti giornalieri da quella di un white noise.

Il grafico sottostante rappresenta un white noise generato in modo che abbia una media approssimativamente pari a 0, 0368% e una deviazione standard dell’0,6882%:

 03 Barplot White noise Two fund 90 10

Il grafico a barre dei rendimenti del World Stocks in USD è il seguente:

03 Barplot rendimenti Two fund 90 10 USD 1985

Non proprio un white noise. Sono visibili in maniera chiara i picchi di volatilità del Black Monday del 1987, della crisi dei subprime del 2008/2009 e di quella del COVID-19 del 2020.

Vediamo le distribuzioni degli pseudo-rendimenti white noise e quelli del Two funds 90/10 in USD:

03 Frequenze rendimenti white noise Two fund 90 10

Come ci aspettavamo, la distribuzione con le frequenze più vicine a 0 e con le code più spesse è quella dei rendimenti del Two funds 90/10 in USD; l’altra è quella degli pseudo-rendimenti white noise che, come ormai sappiamo, sono distribuiti normalmente.

Il grafico situato nella parte inferiore raffigura l’andamento del drawdown: diminuzioni di rendimento calcolate dai livelli massimi di rendimento cumulato della equity line.

Lo visualizziamo di nuovo:

03 Drawdown Two fund 90 10 1985

I massimi drawdown del Two funds 90/10 sono stati contrassegnati dai cerchietti neri:

  • In USD, il massimo drawdown è stato del 32,11%.
  • In EUR, il massimo drawdown è stato del 33,34%.
  • In USD→EUR, il massimo drawdown è stato del 43,84%.

Stavolta, i drawdown del portafoglio in EUR non sono molto più ampi di quelli del portafoglio in USD, come era avvenuto per il World Stocks.

Nel Two funds in USD gli ETF utilizzati – un azionario e un obbligazionario – replicano il mercato statunitense. In quello in EUR, replicano il mercato dell’area euro.

Questo è il motivo per cui i risultati del World Stocks (100% azionario) e del Two funds 90/10 (90% azionario) sono così diversi, al di là di quel 10% in più di componente azionaria del World Stocks: tutte le tipologie di Two funds analizzate azzerano il rischio di cambio.

Le misure di rischio calcolate per questi portafogli quantificano soltanto il rischio di mercato.

I drawdown del Two funds 90/10 in USD→EUR sono invece decisamente superiori. Oltre al rischio di mercato, l’investitore dell’area euro che avesse scelto questo portafoglio si sarebbe assunto anche una grossa porzione di rischio di cambio.

Vediamo il grafico relativo al periodo 2000-2020:

11 two fund 90 10 2000

L’andamento non è molto diverso da quello del periodo più lungo: le considerazioni fatte in precedenza sono valide anche per il periodo 2000-2020.

Vediamo infine il grafico del periodo 2010-2020:

11 two fund 90 10 2010

Nel decennio 2010-2020, il rischio di cambio avrebbe favorito l’investitore dell’area euro.

Un ultimo commento sul Two funds dinamico: i suoi risultati sono molti simili a quelli del Two funds 50/50. Questo significa che l’asset allocation utilizzata è stata il 50% azionario e il 50% obbligazionario per quasi tutto il periodo di analisi.

Probabilmente la scelta del livello del VIX pari a 24 non è stata ottimale e non ha creato quella dinamicità nell’asset allocation che ci aspettavamo.

La reazione automatica – ma sbagliata – sarebbe quella di abbassare la soglia VIX da 24 a 20, 18 o a un valore ancora inferiore e verificare i cambiamenti che si sarebbero prodotti nei risultati dei backtest, fino a trovare quelli che avrebbero reso i risultati ottenuti attraenti per un investitore.

Non è quello che faremo. Come abbiamo più volte ripetuto in questo stesso capitolo e nei capitoli 7 e 9, non ci interessa ottimizzare il valore del VIX sui dati passati per poter presentare un Lazy portfolio di nostra creazione che abbia sovraperformato tutti gli altri Two funds.

Sarebbe un esercizio inutile, perché quelle performance sarebbero dovute a un overfitting del VIX e il Two funds dinamico così costruito non avrebbe modo di ripetere quei risultati in futuro.

Avremmo però fatto un figurone e, forse, proprio i bei risultati di quel Two funds dinamico ci avrebbero permesso di ottenere molte sottoscrizioni in più al nostro sito.

È quello che consciamente o inconsciamente fanno la stragrande maggioranza dei fornitori o venditori di trading system.

È, nella stragrande maggioranza dei casi, anche ciò che fanno i trader, gli analisti tecnici o gli analisti fondamentali.

È, probabilmente, quello che fanno alcuni gestori attivi nel management dei loro stessi fondi, credendo di fare la cosa giusta mentre stanno in realtà spalancando le porte all’inevitabile disastro o, nella migliore delle ipotesi, a una gestione che nel lungo termine non farà altro che sottoperformare sempre di più il benchmark che avrebbe l’obiettivo di battere.

Arrivati a questo punto, cosa dovremmo fare con il nostro Two funds dinamico?

Ripartire con l’analisi da zero. Il VIX dovrebbe essere abbandonato.

Le azioni da seguire dovrebbero più o meno essere le seguenti:

  • Pensare a qualcosa di nuovo; ipotizzare una diversa variabile connessa ai mercati replicati dagli ETF del Two funds Lazy portfolio, che abbia con essi una qualche relazione economico-statistica: un possibile nesso di causalità che sia sfruttabile (la semplice correlazione lineare non basta e non garantisce niente).
  • Una volta trovata, dovremmo modificare l’algoritmo scritto in linguaggio R – il motore delle nostre analisi – per renderlo compatibile con la nuova ipotesi.
  • Effettuare un nuovo backtest e analizzare i risultati ottenuti per valutare se il Two funds dinamico ribilanciato secondo il nuovo algoritmo abbia o meno delle chance di successo.

Non è facile e non è come la maggior parte degli analisti risponde agli insuccessi: il comportamento corretto è controintuitivo.

Performance del Two Fund

Presentiamo qui di seguito tutti i risultati dei backtest, suddivisi per modelli statici, dinamici vincolati e dinamici non vincolati (l’ordine seguito sarà Two funds portfolio 10-90, Two funds portfolio 20-80, …, Two funds portfolio 90-10 e Two funds portfolio dinamico).

Two funds 10/90

Two funds 10/90: Modelli dinamici vincolati e modello statico standard
Performance delle 12 misure statistiche calcolate sulla base di ciascun modello di ottimizzazione
Misura statisticaModello StaticoModelli dinamici
vincolati
StandardBoudt SD ROIBoudt SD RandomBoudt CVaR ROITCOV ROBNaif
USD 1985-2020
Return 5.68% 5.69% 5.63% 5.83% 5.72% 5.69%
Standard Deviation 8.14% 7.93% 7.91% 7.96% 7.93% 7.93%
Sharpe Ratio 0.6973 0.7182 0.7120 0.7319 0.7205 0.7176
Cumulative Return 628.76% 632.87% 616.97% 667.22% 638.20% 631.00%
Worst Drawdown 22.63% 20.79% 20.85% 21.10% 20.81% 20.85%
Average Drawdown 1.11% 1.02% 1.04% 1.00% 1.02% 1.02%
Average Length 24.2849 22.2182 22.9811 21.5646 22.2943 22.2260
Average Recovery 12.8148 11.5325 12.0566 11.0861 11.6745 11.5818
Hurst Index 0.3321 0.3385 0.3384 0.3367 0.3387 0.3383
VaR −0.73% −0.70% −0.70% −0.71% −0.70% −0.70%
CVaR −1.00% −0.92% −0.91% −1.00% −0.93% −0.92%
Sortino Ratio 1.0494 1.0774 1.0690 1.0955 1.0802 1.0764
USD 2000-2020
Return 3.16% 3.20% 3.14% 3.22% 3.28% 3.19%
Standard Deviation 6.09% 5.94% 5.92% 6.10% 5.98% 5.93%
Sharpe Ratio 0.5196 0.5388 0.5296 0.5274 0.5485 0.5367
Cumulative Return 89.48% 90.72% 88.45% 91.55% 93.76% 90.25%
Worst Drawdown 22.35% 20.89% 20.81% 22.47% 21.29% 21.00%
Average Drawdown 0.63% 0.60% 0.63% 0.64% 0.59% 0.61%
Average Length 22.4037 21.2087 22.5787 22.6111 20.3473 21.6756
Average Recovery 13.6422 12.5522 13.5000 13.6250 12.1004 12.8756
Hurst Index 0.3875 0.3908 0.3909 0.3905 0.3914 0.3908
VaR −0.48% −0.45% −0.45% −0.46% −0.45% −0.45%
CVaR −0.48% −0.45% −0.45% −0.46% −0.45% −0.45%
Sortino Ratio 0.7616 0.7893 0.7763 0.7731 0.8018 0.7865
USD 2010-2020
Return 4.76% 4.80% 4.70% 4.88% 4.85% 4.79%
Standard Deviation 4.00% 4.02% 3.96% 4.07% 4.03% 4.01%
Sharpe Ratio 1.1895 1.1938 1.1862 1.1987 1.2014 1.1925
Cumulative Return 61.16% 61.79% 60.19% 63.14% 62.57% 61.60%
Worst Drawdown 9.51% 9.43% 9.29% 9.50% 9.37% 9.42%
Average Drawdown 0.41% 0.40% 0.41% 0.40% 0.39% 0.40%
Average Length 12.9722 11.9538 12.7486 11.5594 11.7085 12.1458
Average Recovery 7.5833 6.6769 7.3443 6.3366 6.3417 6.8281
Hurst Index 0.4745 0.4732 0.4729 0.4719 0.4718 0.4732
VaR 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
CVaR −0.66% −0.66% −0.66% −0.66% −0.66% −0.66%
Sortino Ratio 1.6128 1.6195 1.6076 1.6305 1.6333 1.6176
USD → EUR 1985-2020
Return 4.67% 4.80% 4.79% 4.96% 4.75% 4.75%
Standard Deviation 15.46% 15.18% 15.18% 15.22% 15.14% 15.14%
Sharpe Ratio 0.3020 0.3160 0.3157 0.3257 0.3135 0.3136
Cumulative Return 416.39% 439.65% 438.49% 470.04% 429.95% 430.03%
Worst Drawdown 51.95% 52.04% 51.80% 50.40% 51.52% 51.48%
Average Drawdown 4.01% 3.96% 3.98% 3.76% 3.87% 3.86%
Average Length 67.6439 68.5846 68.0611 63.6714 66.5746 66.0889
Average Recovery 32.7424 34.2385 32.6794 31.6857 33.3507 32.8296
Hurst Index 0.2706 0.2717 0.2712 0.2750 0.2720 0.2721
VaR −1.48% −1.45% −1.45% −1.46% −1.45% −1.45%
CVaR −2.11% −2.08% −2.08% −2.10% −2.07% −2.07%
Sortino Ratio 0.5403 0.5576 0.5570 0.5710 0.5536 0.5537
USD → EUR 2000-2020
Return 1.73% 1.65% 1.73% 1.86% 1.68% 1.68%
Standard Deviation 12.23% 12.06% 12.05% 12.16% 12.02% 12.02%
Sharpe Ratio 0.1416 0.1372 0.1437 0.1533 0.1398 0.1399
Cumulative Return 42.21% 40.01% 42.23% 46.07% 40.77% 40.76%
Worst Drawdown 51.74% 51.90% 51.35% 51.39% 52.01% 51.55%
Average Drawdown 3.05% 3.04% 2.92% 2.95% 3.02% 2.96%
Average Length 93.2727 93.2909 90.0351 90.0000 93.2545 89.9825
Average Recovery 45.6727 45.9091 44.0526 43.9123 45.7455 43.9123
Hurst Index 0.3053 0.3042 0.3040 0.3061 0.3066 0.3055
VaR −1.22% −1.20% −1.20% −1.21% −1.20% −1.20%
CVaR −1.82% −1.80% −1.80% −1.83% −1.80% −1.79%
Sortino Ratio 0.2871 0.2794 0.2885 0.3025 0.2827 0.2828
USD → EUR 2010-2020
Return 5.49% 5.39% 5.38% 5.54% 5.53% 5.48%
Standard Deviation 8.82% 8.60% 8.60% 8.75% 8.62% 8.61%
Sharpe Ratio 0.6218 0.6262 0.6260 0.6338 0.6411 0.6366
Cumulative Return 73.03% 71.37% 71.26% 74.01% 73.73% 72.95%
Worst Drawdown 13.73% 14.42% 14.48% 13.87% 13.80% 13.80%
Average Drawdown 1.83% 1.72% 1.76% 1.70% 1.67% 1.71%
Average Length 34.8889 33.5333 34.4247 32.6753 32.6234 33.4800
Average Recovery 19.9028 18.8133 19.2877 18.4156 18.2597 18.7733
Hurst Index 0.3742 0.3734 0.3738 0.3700 0.3731 0.3737
VaR −0.80% −0.78% −0.78% −0.81% −0.78% −0.78%
CVaR −1.19% −1.16% −1.16% −1.24% −1.17% −1.16%
Sortino Ratio 0.9497 0.9551 0.9547 0.9655 0.9759 0.9692
EUR 1985-2020
Return 5.01% 5.03% 5.05% 5.10% 5.04% 5.06%
Standard Deviation 4.94% 4.84% 4.79% 4.95% 4.87% 4.83%
Sharpe Ratio 1.0137 1.0388 1.0536 1.0286 1.0343 1.0474
Cumulative Return 480.40% 484.24% 487.79% 497.32% 485.55% 489.91%
Worst Drawdown 18.55% 18.23% 18.23% 18.26% 18.26% 18.26%
Average Drawdown 0.99% 0.98% 0.97% 1.02% 1.00% 0.98%
Average Length 28.9865 28.4884 28.3543 29.0949 28.2970 28.0000
Average Recovery 13.9122 14.4186 14.1755 13.7898 14.2376 14.0131
Hurst Index 0.3025 0.3036 0.3008 0.3052 0.3073 0.3037
VaR −0.46% −0.46% −0.45% −0.47% −0.46% −0.46%
CVaR −0.71% −0.72% −0.70% −0.73% −0.73% −0.72%
Sortino Ratio 1.4990 1.5298 1.5528 1.5171 1.5216 1.5411
EUR 2000-2020
Return 3.12% 3.18% 3.13% 3.19% 3.20% 3.18%
Standard Deviation 4.77% 4.62% 4.59% 4.86% 4.69% 4.63%
Sharpe Ratio 0.6549 0.6892 0.6819 0.6567 0.6832 0.6880
Cumulative Return 87.86% 90.24% 88.13% 90.40% 90.86% 90.18%
Worst Drawdown 11.51% 10.82% 10.88% 10.98% 10.75% 10.82%
Average Drawdown 1.16% 1.05% 1.07% 1.11% 1.11% 1.05%
Average Length 41.2149 38.6822 39.9120 40.9262 39.2992 38.6822
Average Recovery 20.6364 19.9767 20.6880 21.7459 20.2835 19.9767
Hurst Index 0.3055 0.3067 0.3059 0.3071 0.3078 0.3068
VaR −0.46% −0.45% −0.45% −0.47% −0.45% −0.45%
CVaR −0.74% −0.71% −0.71% −0.75% −0.72% −0.71%
Sortino Ratio 0.9709 1.0180 1.0070 0.9719 1.0101 1.0164
EUR 2010-2020
Return 3.68% 3.56% 3.57% 3.40% 3.54% 3.57%
Standard Deviation 4.94% 4.76% 4.75% 4.96% 4.78% 4.76%
Sharpe Ratio 0.7444 0.7491 0.7503 0.6857 0.7398 0.7494
Cumulative Return 44.91% 43.28% 43.29% 40.97% 42.90% 43.30%
Worst Drawdown 11.60% 10.18% 10.09% 10.24% 10.55% 10.18%
Average Drawdown 1.12% 1.21% 1.20% 1.08% 1.16% 1.21%
Average Length 39.9839 41.3833 41.3833 43.7193 39.4921 41.3833
Average Recovery 25.5161 27.9667 27.9667 29.8070 26.5556 27.9667
Hurst Index 0.3279 0.3289 0.3284 0.3278 0.3292 0.3289
VaR −0.49% −0.47% −0.47% −0.50% −0.48% −0.47%
CVaR −0.89% −0.83% −0.83% −0.86% −0.84% −0.83%
Sortino Ratio 1.0792 1.0867 1.0887 0.9960 1.0727 1.0872
Two funds 10/90: Modelli dinamici non vincolati e modello statico 1/N
Performance delle 12 misure statistiche calcolate sulla base di ciascun modello di ottimizzazione
Misura statisticaModello StaticoModelli dinamici non vincolati
1/NBoudt SD No-boxHRPBoudt Random MVPBoudt Random HS
USD 1985-2020
Return 8.15% 7.01% 6.73% 6.82% 8.51%
Standard Deviation 9.71% 7.54% 7.43% 7.50% 9.94%
Sharpe Ratio 0.8389 0.9297 0.9064 0.9081 0.8561
Cumulative Return 1,572.92% 1,042.09% 940.62% 971.06% 1,785.92%
Worst Drawdown 26.04% 19.80% 20.05% 20.26% 23.62%
Average Drawdown 1.18% 0.96% 1.04% 0.99% 1.38%
Average Length 17.8962 18.5793 20.7115 19.6799 19.2255
Average Recovery 9.2839 9.7621 11.5623 10.8972 9.5786
Hurst Index 0.3720 0.3481 0.3391 0.3461 0.3166
VaR −0.85% −0.68% −0.68% −0.67% −0.96%
CVaR −1.06% −1.03% −1.11% −0.99% −1.80%
Sortino Ratio 1.2038 1.3536 1.3230 1.3277 1.2441
USD 2000-2020
Return 5.61% 3.67% 3.32% 3.42% 3.95%
Standard Deviation 9.73% 5.92% 5.91% 5.89% 10.55%
Sharpe Ratio 0.5763 0.6205 0.5615 0.5813 0.3741
Cumulative Return 206.22% 109.50% 95.41% 99.48% 121.19%
Worst Drawdown 27.89% 18.92% 19.70% 19.33% 41.82%
Average Drawdown 1.07% 0.60% 0.70% 0.65% 1.53%
Average Length 18.5211 18.3409 22.0404 20.5485 31.5190
Average Recovery 9.5862 10.8750 13.2466 12.4810 20.9937
Hurst Index 0.3735 0.3941 0.3886 0.3929 0.3947
VaR −0.82% −0.43% −0.46% −0.43% −0.47%
CVaR −0.82% −0.43% −0.46% −0.43% −0.47%
Sortino Ratio 0.8579 0.9024 0.8204 0.8479 0.5834
USD 2010-2020
Return 8.73% 5.12% 4.33% 4.69% 5.91%
Standard Deviation 8.61% 4.29% 4.03% 4.03% 7.57%
Sharpe Ratio 1.0142 1.1929 1.0750 1.1621 0.7805
Cumulative Return 136.12% 66.96% 54.52% 60.06% 80.30%
Worst Drawdown 19.33% 9.43% 8.96% 9.38% 17.94%
Average Drawdown 0.80% 0.43% 0.47% 0.43% 0.83%
Average Length 10.8774 12.2158 15.0633 13.2443 13.9763
Average Recovery 5.4151 6.9263 8.6329 8.0568 8.0414
Hurst Index 0.4136 0.4648 0.4668 0.4719 0.3943
VaR −0.68% 0.00% 0.00% 0.00% −0.64%
CVaR −0.68% −0.66% −0.66% −0.66% −0.64%
Sortino Ratio 1.4008 1.6077 1.4663 1.5720 1.0945
USD → EUR 1985-2020
Return 7.12% 7.20% 6.74% 7.09% 10.18%
Standard Deviation 15.22% 14.19% 14.28% 14.25% 17.15%
Sharpe Ratio 0.4677 0.5076 0.4720 0.4975 0.5936
Cumulative Return 1,085.41% 1,120.46% 943.82% 1,073.87% 3,168.48%
Worst Drawdown 46.38% 48.67% 46.90% 49.49% 41.30%
Average Drawdown 2.85% 2.85% 2.86% 2.96% 3.00%
Average Length 43.0293 42.6893 44.8223 44.0800 30.1419
Average Recovery 18.6146 25.8010 25.5990 26.0000 17.5294
Hurst Index 0.3254 0.2773 0.3052 0.2760 0.3541
VaR −1.50% −1.40% −1.41% −1.40% −1.64%
CVaR −2.59% −2.11% −2.22% −2.11% −3.43%
Sortino Ratio 0.7538 0.8078 0.7589 0.7953 0.9212
USD → EUR 2000-2020
Return 4.14% 2.89% 3.00% 2.68% 3.35%
Standard Deviation 13.36% 12.07% 11.91% 12.09% 14.48%
Sharpe Ratio 0.3099 0.2396 0.2521 0.2217 0.2315
Cumulative Return 129.82% 79.51% 83.47% 72.03% 96.70%
Worst Drawdown 44.67% 49.70% 47.02% 51.00% 55.46%
Average Drawdown 1.95% 2.21% 1.94% 2.40% 2.63%
Average Length 47.3738 60.6786 58.5172 67.1579 59.3256
Average Recovery 20.3364 38.6667 39.8851 44.3289 28.0465
Hurst Index 0.3282 0.3040 0.3117 0.3047 0.3491
VaR −1.31% −1.21% −1.19% −1.21% −1.32%
CVaR −2.15% −1.87% −1.82% −1.86% −1.80%
Sortino Ratio 0.5236 0.4195 0.4369 0.3953 0.4220
USD → EUR 2010-2020
Return 9.48% 6.37% 7.06% 6.09% 9.79%
Standard Deviation 11.02% 8.41% 8.66% 8.44% 11.49%
Sharpe Ratio 0.8604 0.7566 0.8154 0.7217 0.8519
Cumulative Return 153.50% 88.44% 101.52% 83.43% 160.87%
Worst Drawdown 20.32% 14.94% 11.86% 15.51% 19.11%
Average Drawdown 1.48% 1.35% 1.30% 1.43% 1.87%
Average Length 20.1639 25.8854 24.0485 27.9551 22.2072
Average Recovery 10.4754 13.4583 12.2136 14.5618 10.5315
Hurst Index 0.3826 0.3763 0.3775 0.3778 0.3371
VaR −1.01% −0.77% −0.80% −0.76% −1.13%
CVaR −1.76% −1.18% −1.32% −1.14% −2.02%
Sortino Ratio 1.2438 1.1312 1.2056 1.0831 1.2422
EUR 1985-2020
Return 6.11% 6.29% 6.03% 5.75% 6.44%
Standard Deviation 7.29% 5.14% 4.84% 4.72% 7.87%
Sharpe Ratio 0.8381 1.2242 1.2474 1.2184 0.8185
Cumulative Return 743.31% 798.04% 722.17% 647.65% 842.89%
Worst Drawdown 28.97% 24.18% 19.79% 20.98% 31.20%
Average Drawdown 1.44% 1.16% 1.07% 1.03% 1.99%
Average Length 30.0356 30.4928 29.6725 30.6232 43.5590
Average Recovery 15.4377 16.6304 14.9789 15.5036 24.8564
Hurst Index 0.3340 0.2987 0.2868 0.2881 0.2943
VaR −0.74% −0.52% −0.48% −0.46% −0.79%
CVaR −1.55% −0.94% −0.78% −0.76% −1.59%
Sortino Ratio 1.1922 1.7462 1.8061 1.7683 1.1651
EUR 2000-2020
Return 3.22% 3.41% 3.14% 3.00% 3.38%
Standard Deviation 8.61% 4.70% 4.81% 4.60% 9.00%
Sharpe Ratio 0.3735 0.7254 0.6521 0.6516 0.3752
Cumulative Return 91.47% 98.77% 88.47% 83.28% 97.63%
Worst Drawdown 28.95% 10.64% 9.79% 11.50% 47.26%
Average Drawdown 1.69% 0.98% 1.15% 1.10% 1.66%
Average Length 38.0152 37.2932 42.6154 45.0090 45.6455
Average Recovery 21.4015 21.1353 21.4444 22.4595 22.9273
Hurst Index 0.3379 0.3041 0.3062 0.3047 0.3699
VaR −0.88% −0.46% −0.47% −0.45% −0.80%
CVaR −1.74% −0.72% −0.73% −0.70% −0.94%
Sortino Ratio 0.5720 1.0661 0.9684 0.9640 0.5738
EUR 2010-2020
Return 5.04% 3.40% 3.38% 3.50% 2.07%
Standard Deviation 9.61% 4.89% 4.95% 4.75% 8.71%
Sharpe Ratio 0.5245 0.6952 0.6830 0.7363 0.2379
Cumulative Return 65.63% 40.90% 40.72% 42.36% 23.43%
Worst Drawdown 23.28% 9.94% 9.85% 10.10% 21.60%
Average Drawdown 1.59% 1.34% 1.15% 1.20% 2.45%
Average Length 26.5106 46.1296 47.0943 38.9062 82.0323
Average Recovery 13.7766 28.6111 31.5849 24.1875 34.3226
Hurst Index 0.3461 0.3241 0.3263 0.3279 0.3168
VaR −1.00% −0.49% −0.49% −0.47% −0.90%
CVaR −2.19% −0.83% −0.84% −0.83% −1.65%
Sortino Ratio 0.7751 1.0099 0.9961 1.0681 0.3854

Two funds 20/80

Two funds 20/80: Modelli dinamici vincolati e modello statico standard
Performance delle 12 misure statistiche calcolate sulla base di ciascun modello di ottimizzazione
Misura statisticaModello StaticoModelli dinamici
vincolati
StandardBoudt SD ROIBoudt SD RandomBoudt CVaR ROITCOV ROBNaif
USD 1985-2020
Return 6.33% 6.32% 6.27% 6.48% 6.37% 6.32%
Standard Deviation 7.90% 7.70% 7.65% 7.73% 7.73% 7.69%
Sharpe Ratio 0.8018 0.8207 0.8191 0.8386 0.8247 0.8221
Cumulative Return 809.63% 805.34% 790.64% 857.74% 822.44% 806.65%
Worst Drawdown 18.44% 19.04% 18.97% 17.91% 19.02% 18.99%
Average Drawdown 1.01% 0.94% 0.95% 0.97% 0.96% 0.94%
Average Length 19.9671 19.5958 19.7030 18.8731 19.4966 19.5241
Average Recovery 10.4272 10.4711 10.7355 9.4009 10.7402 10.5080
Hurst Index 0.3457 0.3458 0.3436 0.3445 0.3482 0.3456
VaR −0.70% −0.68% −0.68% −0.69% −0.69% −0.68%
CVaR −0.95% −0.93% −0.95% −0.99% −0.96% −0.93%
Sortino Ratio 1.1884 1.2138 1.2128 1.2387 1.2172 1.2159
USD 2000-2020
Return 3.82% 3.69% 3.65% 3.71% 3.68% 3.70%
Standard Deviation 6.24% 6.00% 5.96% 6.13% 6.06% 5.99%
Sharpe Ratio 0.6114 0.6158 0.6117 0.6058 0.6073 0.6169
Cumulative Return 115.56% 110.36% 108.44% 111.18% 109.81% 110.51%
Worst Drawdown 17.93% 18.43% 18.39% 18.08% 18.58% 18.42%
Average Drawdown 0.59% 0.52% 0.53% 0.57% 0.54% 0.52%
Average Length 18.8249 17.8339 18.1386 17.8235 17.9444 17.8339
Average Recovery 11.0039 11.2546 10.3783 11.2353 10.2704 10.3173
Hurst Index 0.3953 0.3964 0.3949 0.3987 0.3977 0.3963
VaR −0.44% −0.42% −0.43% −0.41% −0.42% −0.42%
CVaR −0.44% −0.42% −0.43% −0.41% −0.42% −0.42%
Sortino Ratio 0.8906 0.8952 0.8891 0.8837 0.8852 0.8966
USD 2010-2020
Return 5.77% 5.42% 5.34% 5.52% 5.53% 5.42%
Standard Deviation 4.57% 4.27% 4.23% 4.39% 4.32% 4.27%
Sharpe Ratio 1.2637 1.2680 1.2629 1.2561 1.2790 1.2681
Cumulative Return 77.90% 71.92% 70.64% 73.58% 73.69% 71.92%
Worst Drawdown 10.92% 9.94% 9.89% 9.94% 9.94% 9.94%
Average Drawdown 0.40% 0.39% 0.39% 0.40% 0.39% 0.39%
Average Length 10.1982 10.2711 10.2889 10.0696 10.0917 10.2711
Average Recovery 5.7401 5.8222 6.0089 5.7478 5.7511 5.8222
Hurst Index 0.4675 0.4711 0.4714 0.4676 0.4697 0.4711
VaR 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
CVaR −0.66% −0.66% −0.66% −0.66% −0.66% −0.66%
Sortino Ratio 1.7216 1.7185 1.7116 1.7127 1.7359 1.7186
USD → EUR 1985-2020
Return 5.32% 5.42% 5.41% 5.54% 5.39% 5.35%
Standard Deviation 15.04% 14.76% 14.75% 14.84% 14.76% 14.75%
Sharpe Ratio 0.3535 0.3669 0.3664 0.3730 0.3653 0.3624
Cumulative Return 544.55% 566.37% 564.15% 594.38% 561.27% 550.65%
Worst Drawdown 49.83% 49.34% 49.31% 48.15% 49.82% 49.74%
Average Drawdown 3.63% 3.51% 3.59% 3.46% 3.57% 3.57%
Average Length 60.5850 59.3267 60.9658 57.7727 60.5306 60.5442
Average Recovery 29.8639 29.2467 30.1233 28.4481 29.8844 29.8844
Hurst Index 0.2835 0.2751 0.2758 0.2916 0.2750 0.2751
VaR −1.45% −1.42% −1.42% −1.43% −1.42% −1.42%
CVaR −2.11% −2.07% −2.07% −2.13% −2.08% −2.07%
Sortino Ratio 0.6072 0.6241 0.6232 0.6320 0.6214 0.6177
USD → EUR 2000-2020
Return 2.37% 2.29% 2.32% 2.51% 2.27% 2.24%
Standard Deviation 12.01% 11.84% 11.83% 11.93% 11.81% 11.80%
Sharpe Ratio 0.1976 0.1934 0.1964 0.2100 0.1923 0.1897
Cumulative Return 61.78% 59.11% 60.14% 66.14% 58.48% 57.47%
Worst Drawdown 49.44% 49.73% 49.49% 49.08% 49.79% 49.76%
Average Drawdown 2.54% 2.71% 2.68% 2.50% 2.69% 2.61%
Average Length 78.7385 83.8852 82.5323 77.4545 85.2167 82.5323
Average Recovery 40.6615 43.5082 42.5484 40.2273 44.4667 42.8871
Hurst Index 0.3162 0.3125 0.3129 0.3126 0.3128 0.3129
VaR −1.19% −1.18% −1.18% −1.19% −1.18% −1.17%
CVaR −1.83% −1.80% −1.80% −1.82% −1.79% −1.79%
Sortino Ratio 0.3629 0.3558 0.3598 0.3793 0.3539 0.3502
USD → EUR 2010-2020
Return 6.51% 6.40% 6.41% 6.56% 6.45% 6.38%
Standard Deviation 8.89% 8.59% 8.60% 8.77% 8.63% 8.60%
Sharpe Ratio 0.7315 0.7446 0.7447 0.7474 0.7477 0.7424
Cumulative Return 91.00% 89.00% 89.15% 91.90% 90.03% 88.74%
Worst Drawdown 13.90% 12.88% 12.82% 12.78% 12.69% 12.78%
Average Drawdown 1.45% 1.34% 1.36% 1.39% 1.33% 1.36%
Average Length 28.3409 26.7419 27.0326 28.3750 26.5213 27.0761
Average Recovery 17.4091 16.3871 16.4891 17.6250 16.2447 16.5326
Hurst Index 0.3831 0.3814 0.3816 0.3800 0.3808 0.3813
VaR −0.80% −0.78% −0.78% −0.80% −0.78% −0.78%
CVaR −1.20% −1.17% −1.17% −1.24% −1.20% −1.17%
Sortino Ratio 1.0926 1.1122 1.1122 1.1156 1.1158 1.1091
EUR 1985-2020
Return 5.33% 5.41% 5.39% 5.35% 5.42% 5.46%
Standard Deviation 5.02% 4.88% 4.85% 5.00% 4.95% 4.88%
Sharpe Ratio 1.0627 1.1079 1.1109 1.0687 1.0936 1.1185
Cumulative Return 547.93% 564.79% 559.82% 550.83% 567.01% 577.36%
Worst Drawdown 18.17% 17.86% 17.86% 18.00% 17.90% 17.90%
Average Drawdown 1.00% 0.98% 0.96% 1.02% 0.97% 0.97%
Average Length 28.9524 27.6266 27.7068 27.9279 27.3280 27.3183
Average Recovery 13.4150 13.3961 12.9088 13.3213 13.1222 13.3473
Hurst Index 0.3105 0.2999 0.3011 0.3010 0.3054 0.2998
VaR −0.49% −0.47% −0.47% −0.49% −0.48% −0.47%
CVaR −0.82% −0.77% −0.77% −0.80% −0.80% −0.77%
Sortino Ratio 1.5462 1.6166 1.6216 1.5563 1.5903 1.6303
EUR 2000-2020
Return 3.19% 3.25% 3.15% 3.28% 3.30% 3.27%
Standard Deviation 5.01% 4.82% 4.78% 4.95% 4.83% 4.82%
Sharpe Ratio 0.6364 0.6741 0.6603 0.6629 0.6833 0.6796
Cumulative Return 90.44% 92.66% 89.09% 93.90% 94.77% 93.64%
Worst Drawdown 14.34% 12.93% 12.90% 12.93% 12.93% 12.93%
Average Drawdown 1.15% 1.10% 1.08% 1.14% 1.10% 1.09%
Average Length 42.9914 39.1260 40.4878 39.4921 38.8359 38.5039
Average Recovery 20.2241 21.1339 21.0325 20.3810 20.7891 20.8062
Hurst Index 0.3232 0.3148 0.3156 0.3117 0.3145 0.3149
VaR −0.50% −0.48% −0.47% −0.49% −0.48% −0.48%
CVaR −0.90% −0.82% −0.81% −0.83% −0.82% −0.82%
Sortino Ratio 0.9306 0.9873 0.9697 0.9698 0.9992 0.9950
EUR 2010-2020
Return 4.06% 3.87% 3.89% 3.92% 3.82% 3.86%
Standard Deviation 5.44% 5.16% 5.09% 5.33% 5.18% 5.16%
Sharpe Ratio 0.7456 0.7491 0.7634 0.7358 0.7384 0.7485
Cumulative Return 50.43% 47.62% 47.94% 48.44% 46.98% 47.56%
Worst Drawdown 14.51% 13.07% 13.04% 13.07% 13.07% 13.07%
Average Drawdown 1.23% 1.18% 1.11% 1.11% 1.19% 1.17%
Average Length 38.1846 39.3333 36.4118 38.7500 39.4127 38.7031
Average Recovery 18.8923 20.0476 17.6765 27.3125 19.9683 19.7031
Hurst Index 0.3429 0.3353 0.3367 0.3312 0.3349 0.3353
VaR −0.55% −0.52% −0.51% −0.54% −0.52% −0.52%
CVaR −1.14% −1.00% −1.00% −1.01% −1.00% −1.00%
Sortino Ratio 1.0706 1.0800 1.0993 1.0629 1.0647 1.0792
Two funds 20/80: Modelli dinamici non vincolati e modello statico 1/N
Performance delle 12 misure statistiche calcolate sulla base di ciascun modello di ottimizzazione
Misura statisticaModello StaticoModelli dinamici non vincolati
1/NBoudt SD No-boxHRPBoudt Random MVPBoudt Random HS
USD 1985-2020
Return 8.15% 7.01% 6.73% 6.82% 8.51%
Standard Deviation 9.71% 7.54% 7.43% 7.50% 9.94%
Sharpe Ratio 0.8389 0.9297 0.9064 0.9082 0.8561
Cumulative Return 1,572.92% 1,042.09% 940.62% 971.19% 1,786.00%
Worst Drawdown 26.04% 19.80% 20.05% 20.26% 23.62%
Average Drawdown 1.18% 0.96% 1.04% 0.99% 1.38%
Average Length 17.8962 18.5793 20.7115 19.6340 19.2255
Average Recovery 9.2839 9.7621 11.5623 10.8695 9.5786
Hurst Index 0.3720 0.3481 0.3391 0.3461 0.3166
VaR −0.85% −0.68% −0.68% −0.67% −0.96%
CVaR −1.06% −1.03% −1.11% −0.99% −1.80%
Sortino Ratio 1.2038 1.3536 1.3230 1.3278 1.2441
USD 2000-2020
Return 5.61% 3.67% 3.32% 3.42% 3.95%
Standard Deviation 9.73% 5.92% 5.91% 5.89% 10.55%
Sharpe Ratio 0.5763 0.6205 0.5615 0.5813 0.3741
Cumulative Return 206.22% 109.50% 95.41% 99.49% 121.19%
Worst Drawdown 27.89% 18.92% 19.70% 19.32% 41.82%
Average Drawdown 1.07% 0.60% 0.70% 0.65% 1.53%
Average Length 18.5211 18.3409 22.0404 20.5485 31.5190
Average Recovery 9.5862 10.8750 13.2466 12.4810 20.9937
Hurst Index 0.3735 0.3941 0.3886 0.3929 0.3947
VaR −0.82% −0.43% −0.46% −0.43% −0.47%
CVaR −0.82% −0.43% −0.46% −0.43% −0.47%
Sortino Ratio 0.8579 0.9024 0.8204 0.8479 0.5834
USD 2010-2020
Return 8.73% 5.12% 4.33% 4.69% 5.91%
Standard Deviation 8.61% 4.29% 4.03% 4.03% 7.57%
Sharpe Ratio 1.0142 1.1929 1.0750 1.1621 0.7804
Cumulative Return 136.12% 66.96% 54.52% 60.07% 80.29%
Worst Drawdown 19.33% 9.43% 8.96% 9.38% 17.94%
Average Drawdown 0.80% 0.43% 0.47% 0.43% 0.83%
Average Length 10.8774 12.2158 15.0633 13.2443 13.9000
Average Recovery 5.4151 6.9263 8.6329 8.0568 8.0706
Hurst Index 0.4136 0.4648 0.4668 0.4719 0.3943
VaR −0.68% 0.00% 0.00% 0.00% −0.64%
CVaR −0.68% −0.66% −0.66% −0.66% −0.64%
Sortino Ratio 1.4008 1.6077 1.4663 1.5719 1.0944
USD → EUR 1985-2020
Return 7.12% 7.20% 6.74% 7.09% 10.18%
Standard Deviation 15.22% 14.19% 14.28% 14.25% 17.15%
Sharpe Ratio 0.4677 0.5076 0.4720 0.4975 0.5936
Cumulative Return 1,085.41% 1,120.46% 943.82% 1,073.96% 3,167.81%
Worst Drawdown 46.38% 48.67% 46.90% 49.49% 41.30%
Average Drawdown 2.85% 2.85% 2.86% 2.96% 3.00%
Average Length 43.0293 42.6893 44.8223 44.0800 30.1419
Average Recovery 18.6146 25.8010 25.5990 26.0000 17.5294
Hurst Index 0.3254 0.2773 0.3052 0.2760 0.3541
VaR −1.50% −1.40% −1.41% −1.40% −1.64%
CVaR −2.59% −2.11% −2.22% −2.11% −3.43%
Sortino Ratio 0.7538 0.8078 0.7589 0.7953 0.9212
USD → EUR 2000-2020
Return 4.14% 2.89% 3.00% 2.68% 3.35%
Standard Deviation 13.36% 12.07% 11.91% 12.09% 14.48%
Sharpe Ratio 0.3099 0.2396 0.2521 0.2218 0.2316
Cumulative Return 129.82% 79.51% 83.47% 72.06% 96.72%
Worst Drawdown 44.67% 49.70% 47.02% 51.00% 55.46%
Average Drawdown 1.95% 2.21% 1.94% 2.40% 2.63%
Average Length 47.3738 60.6786 58.5172 67.1579 59.3256
Average Recovery 20.3364 38.6667 39.8851 44.3289 28.0465
Hurst Index 0.3282 0.3040 0.3117 0.3047 0.3491
VaR −1.31% −1.21% −1.19% −1.21% −1.32%
CVaR −2.15% −1.87% −1.82% −1.86% −1.80%
Sortino Ratio 0.5236 0.4195 0.4369 0.3954 0.4221
USD → EUR 2010-2020
Return 9.48% 6.37% 7.06% 6.09% 9.79%
Standard Deviation 11.02% 8.41% 8.66% 8.44% 11.49%
Sharpe Ratio 0.8604 0.7566 0.8154 0.7218 0.8519
Cumulative Return 153.50% 88.44% 101.52% 83.44% 160.87%
Worst Drawdown 20.32% 14.94% 11.86% 15.51% 19.11%
Average Drawdown 1.48% 1.35% 1.30% 1.43% 1.87%
Average Length 20.1639 25.8854 24.0485 27.9551 22.2072
Average Recovery 10.4754 13.4583 12.2136 14.5618 10.5315
Hurst Index 0.3826 0.3763 0.3775 0.3778 0.3371
VaR −1.01% −0.77% −0.80% −0.76% −1.13%
CVaR −1.76% −1.18% −1.32% −1.14% −2.02%
Sortino Ratio 1.2438 1.1312 1.2056 1.0833 1.2423
EUR 1985-2020
Return 6.11% 6.29% 6.03% 5.75% 6.44%
Standard Deviation 7.29% 5.14% 4.84% 4.72% 7.87%
Sharpe Ratio 0.8381 1.2242 1.2474 1.2184 0.8185
Cumulative Return 743.31% 798.04% 722.17% 647.65% 842.86%
Worst Drawdown 28.97% 24.18% 19.79% 20.98% 31.20%
Average Drawdown 1.44% 1.16% 1.07% 1.04% 1.99%
Average Length 30.0356 30.4928 29.6725 30.6232 43.5590
Average Recovery 15.4377 16.6304 14.9789 15.5036 24.8564
Hurst Index 0.3340 0.2987 0.2868 0.2881 0.2943
VaR −0.74% −0.52% −0.48% −0.46% −0.79%
CVaR −1.55% −0.94% −0.78% −0.76% −1.59%
Sortino Ratio 1.1922 1.7462 1.8061 1.7683 1.1652
EUR 2000-2020
Return 3.22% 3.41% 3.14% 3.00% 3.38%
Standard Deviation 8.61% 4.70% 4.81% 4.60% 9.00%
Sharpe Ratio 0.3735 0.7254 0.6521 0.6515 0.3753
Cumulative Return 91.47% 98.77% 88.47% 83.27% 97.65%
Worst Drawdown 28.95% 10.64% 9.79% 11.50% 47.26%
Average Drawdown 1.69% 0.98% 1.15% 1.10% 1.66%
Average Length 38.0152 37.2932 42.6154 45.0090 45.6455
Average Recovery 21.4015 21.1353 21.4444 22.4595 22.9273
Hurst Index 0.3379 0.3041 0.3062 0.3048 0.3699
VaR −0.88% −0.46% −0.47% −0.45% −0.80%
CVaR −1.74% −0.72% −0.73% −0.70% −0.95%
Sortino Ratio 0.5720 1.0661 0.9684 0.9638 0.5739
EUR 2010-2020
Return 5.04% 3.40% 3.38% 3.50% 2.07%
Standard Deviation 9.61% 4.89% 4.95% 4.75% 8.71%
Sharpe Ratio 0.5245 0.6952 0.6830 0.7362 0.2379
Cumulative Return 65.63% 40.90% 40.72% 42.35% 23.43%
Worst Drawdown 23.28% 9.94% 9.85% 10.10% 21.60%
Average Drawdown 1.59% 1.34% 1.15% 1.20% 2.45%
Average Length 26.5106 46.1296 47.0943 38.9062 82.0323
Average Recovery 13.7766 28.6111 31.5849 24.1875 34.3226
Hurst Index 0.3461 0.3241 0.3263 0.3279 0.3168
VaR −1.00% −0.49% −0.49% −0.47% −0.90%
CVaR −2.19% −0.83% −0.84% −0.83% −1.65%
Sortino Ratio 0.7751 1.0099 0.9961 1.0680 0.3855

Two funds 30/70

Two funds 30/70: Modelli dinamici vincolati e modello statico standard
Performance delle 12 misure statistiche calcolate sulla base di ciascun modello di ottimizzazione
Misura statisticaModello StaticoModelli dinamici
vincolati
StandardBoudt SD ROIBoudt SD RandomBoudt CVaR ROITCOV ROBNaif
USD 1985-2020
Return 6.96% 6.84% 6.85% 7.09% 6.94% 6.86%
Standard Deviation 8.10% 7.76% 7.74% 7.87% 7.81% 7.75%
Sharpe Ratio 0.8595 0.8814 0.8854 0.9000 0.8890 0.8855
Cumulative Return 1,024.91% 979.02% 983.70% 1,073.19% 1,017.26% 988.75%
Worst Drawdown 18.85% 18.15% 18.05% 18.04% 17.95% 18.15%
Average Drawdown 1.02% 0.99% 0.98% 1.01% 0.99% 0.99%
Average Length 18.3391 18.1111 17.9915 17.5821 17.9979 18.0340
Average Recovery 10.1166 9.5192 9.4713 9.0499 9.4735 9.4553
Hurst Index 0.3577 0.3522 0.3520 0.3510 0.3523 0.3523
VaR −0.71% −0.68% −0.68% −0.70% −0.69% −0.68%
CVaR −0.95% −0.93% −0.94% −1.04% −1.01% −0.95%
Sortino Ratio 1.2545 1.2884 1.2942 1.3120 1.2950 1.2931
USD 2000-2020
Return 4.44% 4.28% 4.24% 4.33% 4.37% 4.28%
Standard Deviation 7.00% 6.51% 6.50% 6.75% 6.53% 6.51%
Sharpe Ratio 0.6343 0.6576 0.6523 0.6415 0.6693 0.6578
Cumulative Return 143.75% 136.39% 134.48% 138.46% 140.45% 136.41%
Worst Drawdown 16.91% 15.62% 15.62% 17.59% 15.62% 15.62%
Average Drawdown 0.69% 0.68% 0.69% 0.75% 0.69% 0.68%
Average Length 17.3262 17.0389 17.1099 17.2250 16.9018 17.0424
Average Recovery 10.6165 10.7244 10.7482 10.5393 10.5754 10.7279
Hurst Index 0.3921 0.3950 0.3946 0.3978 0.3947 0.3950
VaR −0.51% −0.46% −0.46% −0.45% −0.47% −0.46%
CVaR −0.51% −0.46% −0.46% −0.45% −0.47% −0.46%
Sortino Ratio 0.9258 0.9551 0.9480 0.9352 0.9707 0.9553
USD 2010-2020
Return 6.77% 6.36% 6.25% 6.44% 6.43% 6.36%
Standard Deviation 5.67% 5.15% 5.05% 5.32% 5.19% 5.15%
Sharpe Ratio 1.1950 1.2344 1.2363 1.2099 1.2391 1.2344
Cumulative Return 95.93% 88.27% 86.28% 89.81% 89.62% 88.27%
Worst Drawdown 13.60% 12.27% 12.23% 12.27% 12.27% 12.27%
Average Drawdown 0.50% 0.44% 0.43% 0.47% 0.45% 0.44%
Average Length 9.9657 9.8178 9.7764 9.9657 9.8974 9.8178
Average Recovery 5.6309 5.6271 5.6034 5.7082 5.6923 5.6271
Hurst Index 0.4494 0.4570 0.4585 0.4527 0.4560 0.4570
VaR −0.17% −0.05% −0.02% −0.12% −0.07% −0.05%
CVaR −0.17% −0.05% −0.02% −0.12% −0.07% −0.05%
Sortino Ratio 1.6342 1.6809 1.6877 1.6532 1.6881 1.6809
USD → EUR 1985-2020
Return 5.94% 5.95% 5.96% 6.22% 6.01% 6.02%
Standard Deviation 14.86% 14.54% 14.54% 14.70% 14.54% 14.54%
Sharpe Ratio 0.4000 0.4095 0.4100 0.4232 0.4136 0.4142
Cumulative Return 697.10% 700.51% 702.64% 775.88% 716.36% 719.02%
Worst Drawdown 47.98% 47.23% 47.23% 45.95% 47.47% 47.26%
Average Drawdown 3.19% 3.18% 3.18% 3.16% 3.19% 3.19%
Average Length 53.5361 51.3237 51.3179 50.4261 51.6163 51.6163
Average Recovery 24.6446 24.7746 24.7688 23.5909 24.9186 24.9186
Hurst Index 0.3000 0.2929 0.2929 0.3059 0.2929 0.2929
VaR −1.44% −1.41% −1.41% −1.43% −1.42% −1.41%
CVaR −2.19% −2.12% −2.12% −2.23% −2.14% −2.13%
Sortino Ratio 0.6673 0.6790 0.6796 0.6972 0.6837 0.6850
USD → EUR 2000-2020
Return 2.99% 3.03% 2.99% 3.10% 2.98% 3.01%
Standard Deviation 12.13% 11.84% 11.84% 12.06% 11.86% 11.85%
Sharpe Ratio 0.2465 0.2554 0.2523 0.2569 0.2515 0.2540
Cumulative Return 82.94% 84.28% 82.89% 86.95% 82.74% 83.75%
Worst Drawdown 47.25% 47.12% 47.12% 46.68% 46.99% 47.12%
Average Drawdown 2.35% 2.18% 2.21% 2.21% 2.24% 2.21%
Average Length 67.9867 65.2821 66.1429 62.9383 67.0132 66.1429
Average Recovery 33.4533 45.0128 45.6364 30.5926 46.2500 45.6364
Hurst Index 0.3235 0.3211 0.3212 0.3200 0.3209 0.3210
VaR −1.20% −1.18% −1.18% −1.19% −1.18% −1.18%
CVaR −1.89% −1.84% −1.83% −1.86% −1.84% −1.84%
Sortino Ratio 0.4303 0.4408 0.4365 0.4446 0.4355 0.4389
USD → EUR 2010-2020
Return 7.51% 7.34% 7.29% 7.55% 7.44% 7.37%
Standard Deviation 9.31% 8.94% 8.93% 9.17% 8.98% 8.96%
Sharpe Ratio 0.8066 0.8207 0.8172 0.8239 0.8289 0.8232
Cumulative Return 110.35% 106.89% 106.02% 111.18% 108.97% 107.59%
Worst Drawdown 16.09% 14.92% 14.92% 15.00% 14.92% 14.92%
Average Drawdown 1.32% 1.25% 1.25% 1.33% 1.29% 1.26%
Average Length 23.5714 23.5714 23.7981 23.8269 23.3302 23.5619
Average Recovery 12.9429 13.4476 13.5962 12.6250 12.1698 13.4381
Hurst Index 0.3866 0.3860 0.3863 0.3840 0.3855 0.3858
VaR −0.84% −0.80% −0.80% −0.83% −0.81% −0.81%
CVaR −1.29% −1.24% −1.23% −1.36% −1.28% −1.25%
Sortino Ratio 1.1848 1.2056 1.2009 1.2094 1.2161 1.2090
EUR 1985-2020
Return 5.62% 5.68% 5.59% 5.61% 5.71% 5.69%
Standard Deviation 5.48% 5.17% 5.15% 5.38% 5.23% 5.18%
Sharpe Ratio 1.0258 1.0970 1.0851 1.0418 1.0930 1.0985
Cumulative Return 615.37% 628.05% 606.33% 610.91% 637.11% 630.95%
Worst Drawdown 17.83% 17.53% 17.53% 17.40% 17.57% 17.57%
Average Drawdown 1.06% 1.01% 1.03% 1.08% 1.01% 1.01%
Average Length 26.1692 25.6636 26.5737 26.8703 26.0708 25.6636
Average Recovery 12.5292 12.8364 13.3824 13.8418 13.1631 12.8333
Hurst Index 0.3137 0.3082 0.3087 0.3046 0.3078 0.3081
VaR −0.55% −0.52% −0.51% −0.54% −0.52% −0.52%
CVaR −1.02% −0.92% −0.92% −0.95% −0.93% −0.92%
Sortino Ratio 1.4715 1.5773 1.5611 1.4967 1.5690 1.5793
EUR 2000-2020
Return 3.23% 3.24% 3.18% 3.31% 3.35% 3.26%
Standard Deviation 5.86% 5.36% 5.34% 5.60% 5.41% 5.36%
Sharpe Ratio 0.5512 0.6050 0.5962 0.5916 0.6194 0.6080
Cumulative Return 91.93% 92.38% 90.20% 95.20% 96.53% 93.08%
Worst Drawdown 17.18% 15.75% 15.67% 15.99% 15.75% 15.75%
Average Drawdown 1.28% 1.21% 1.22% 1.30% 1.18% 1.21%
Average Length 35.7286 38.6047 39.9520 37.9618 37.3910 38.6124
Average Recovery 17.7500 20.2403 20.5600 18.1985 19.4962 20.2403
Hurst Index 0.3279 0.3274 0.3271 0.3221 0.3263 0.3273
VaR −0.59% −0.54% −0.54% −0.57% −0.55% −0.54%
CVaR −1.15% −1.02% −1.02% −1.05% −1.03% −1.02%
Sortino Ratio 0.8069 0.8820 0.8700 0.8617 0.9019 0.8862
EUR 2010-2020
Return 4.41% 4.18% 4.20% 4.12% 4.15% 4.18%
Standard Deviation 6.52% 5.93% 5.89% 6.08% 5.97% 5.93%
Sharpe Ratio 0.6762 0.7049 0.7135 0.6780 0.6940 0.7044
Cumulative Return 55.73% 52.22% 52.62% 51.42% 51.75% 52.20%
Worst Drawdown 17.41% 15.96% 15.88% 15.96% 15.96% 15.96%
Average Drawdown 1.29% 1.19% 1.19% 1.26% 1.24% 1.19%
Average Length 29.2824 30.6914 30.6543 31.4810 31.8974 30.7037
Average Recovery 14.3176 15.6173 15.5802 15.8354 16.1154 15.6296
Hurst Index 0.3450 0.3451 0.3452 0.3419 0.3441 0.3451
VaR −0.67% −0.61% −0.60% −0.63% −0.61% −0.61%
CVaR −1.47% −1.30% −1.29% −1.29% −1.30% −1.30%
Sortino Ratio 0.9715 1.0107 1.0229 0.9751 0.9959 1.0101
Two funds 30/70: Modelli dinamici non vincolati e modello statico 1/N
Performance delle 12 misure statistiche calcolate sulla base di ciascun modello di ottimizzazione
Misura statisticaModello StaticoModelli dinamici non vincolati
1/NBoudt SD No-boxHRPBoudt Random MVPBoudt Random HS
USD 1985-2020
Return 8.15% 7.01% 6.73% 6.82% 8.51%
Standard Deviation 9.71% 7.54% 7.43% 7.50% 9.94%
Sharpe Ratio 0.8389 0.9297 0.9064 0.9082 0.8561
Cumulative Return 1,572.92% 1,042.09% 940.62% 971.19% 1,786.14%
Worst Drawdown 26.04% 19.80% 20.05% 20.26% 23.62%
Average Drawdown 1.18% 0.96% 1.04% 0.99% 1.38%
Average Length 17.8962 18.5793 20.7115 19.6799 19.2255
Average Recovery 9.2839 9.7621 11.5623 10.8972 9.5786
Hurst Index 0.3720 0.3481 0.3391 0.3461 0.3166
VaR −0.85% −0.68% −0.68% −0.67% −0.96%
CVaR −1.06% −1.03% −1.11% −0.99% −1.80%
Sortino Ratio 1.2038 1.3536 1.3230 1.3278 1.2442
USD 2000-2020
Return 5.61% 3.67% 3.32% 3.42% 3.95%
Standard Deviation 9.73% 5.92% 5.91% 5.89% 10.55%
Sharpe Ratio 0.5763 0.6205 0.5615 0.5813 0.3741
Cumulative Return 206.22% 109.50% 95.41% 99.48% 121.19%
Worst Drawdown 27.89% 18.92% 19.70% 19.32% 41.82%
Average Drawdown 1.07% 0.60% 0.70% 0.65% 1.54%
Average Length 18.5211 18.3409 22.0404 20.5527 31.7197
Average Recovery 9.5862 10.8750 13.2466 12.4852 21.1210
Hurst Index 0.3735 0.3941 0.3886 0.3929 0.3947
VaR −0.82% −0.43% −0.46% −0.43% −0.47%
CVaR −0.82% −0.43% −0.46% −0.43% −0.47%
Sortino Ratio 0.8579 0.9024 0.8204 0.8479 0.5834
USD 2010-2020
Return 8.73% 5.12% 4.33% 4.69% 5.91%
Standard Deviation 8.61% 4.29% 4.03% 4.03% 7.57%
Sharpe Ratio 1.0142 1.1929 1.0750 1.1620 0.7804
Cumulative Return 136.12% 66.96% 54.52% 60.06% 80.29%
Worst Drawdown 19.33% 9.43% 8.96% 9.38% 17.94%
Average Drawdown 0.80% 0.43% 0.47% 0.43% 0.83%
Average Length 10.8774 12.2158 15.0633 13.2443 13.9763
Average Recovery 5.4151 6.9263 8.6329 8.0568 8.0414
Hurst Index 0.4136 0.4648 0.4668 0.4719 0.3943
VaR −0.68% 0.00% 0.00% 0.00% −0.64%
CVaR −0.68% −0.22% −0.22% −0.22% −0.64%
Sortino Ratio 1.4008 1.6077 1.4663 1.5718 1.0945
USD → EUR 1985-2020
Return 7.12% 7.20% 6.74% 7.09% 10.18%
Standard Deviation 15.22% 14.19% 14.28% 14.25% 17.15%
Sharpe Ratio 0.4677 0.5076 0.4720 0.4975 0.5936
Cumulative Return 1,085.41% 1,120.46% 943.82% 1,073.72% 3,168.75%
Worst Drawdown 46.38% 48.67% 46.90% 49.49% 41.30%
Average Drawdown 2.85% 2.85% 2.86% 2.96% 3.00%
Average Length 43.0293 42.6893 44.8223 44.0800 30.1419
Average Recovery 18.6146 25.8010 25.5990 26.0000 17.5294
Hurst Index 0.3254 0.2773 0.3052 0.2760 0.3541
VaR −1.50% −1.40% −1.41% −1.40% −1.64%
CVaR −2.59% −2.11% −2.22% −2.11% −3.43%
Sortino Ratio 0.7538 0.8078 0.7589 0.7952 0.9212
USD → EUR 2000-2020
Return 4.14% 2.89% 3.00% 2.68% 3.35%
Standard Deviation 13.36% 12.07% 11.91% 12.09% 14.48%
Sharpe Ratio 0.3099 0.2396 0.2521 0.2217 0.2315
Cumulative Return 129.82% 79.51% 83.47% 72.03% 96.70%
Worst Drawdown 44.67% 49.70% 47.02% 51.00% 55.46%
Average Drawdown 1.95% 2.21% 1.94% 2.40% 2.63%
Average Length 47.3738 60.6786 58.5172 67.1579 59.3256
Average Recovery 20.3364 38.6667 39.8851 44.3289 28.0465
Hurst Index 0.3282 0.3040 0.3117 0.3047 0.3491
VaR −1.31% −1.21% −1.19% −1.21% −1.32%
CVaR −2.15% −1.87% −1.82% −1.86% −1.80%
Sortino Ratio 0.5236 0.4195 0.4369 0.3953 0.4220
USD → EUR 2010-2020
Return 9.48% 6.37% 7.06% 6.09% 9.79%
Standard Deviation 11.02% 8.41% 8.66% 8.44% 11.49%
Sharpe Ratio 0.8604 0.7566 0.8154 0.7217 0.8519
Cumulative Return 153.50% 88.44% 101.52% 83.43% 160.88%
Worst Drawdown 20.32% 14.94% 11.86% 15.51% 19.11%
Average Drawdown 1.48% 1.35% 1.30% 1.43% 1.87%
Average Length 20.1639 25.8854 24.0485 27.9551 22.2072
Average Recovery 10.4754 13.4583 12.2136 14.5618 10.5315
Hurst Index 0.3826 0.3763 0.3775 0.3778 0.3371
VaR −1.01% −0.77% −0.80% −0.76% −1.13%
CVaR −1.76% −1.18% −1.32% −1.14% −2.02%
Sortino Ratio 1.2438 1.1312 1.2056 1.0831 1.2422
EUR 1985-2020
Return 6.11% 6.29% 6.03% 5.75% 6.44%
Standard Deviation 7.29% 5.14% 4.84% 4.72% 7.87%
Sharpe Ratio 0.8381 1.2242 1.2474 1.2184 0.8185
Cumulative Return 743.31% 798.04% 722.17% 647.67% 842.85%
Worst Drawdown 28.97% 24.18% 19.79% 20.98% 31.20%
Average Drawdown 1.44% 1.16% 1.07% 1.04% 1.99%
Average Length 30.0356 30.4928 29.6725 30.6232 43.5590
Average Recovery 15.4377 16.6304 14.9789 15.5036 24.8564
Hurst Index 0.3340 0.2987 0.2868 0.2881 0.2943
VaR −0.74% −0.52% −0.48% −0.46% −0.79%
CVaR −1.55% −0.94% −0.78% −0.76% −1.59%
Sortino Ratio 1.1922 1.7462 1.8061 1.7683 1.1652
EUR 2000-2020
Return 3.22% 3.41% 3.14% 3.00% 3.38%
Standard Deviation 8.61% 4.70% 4.81% 4.60% 9.00%
Sharpe Ratio 0.3735 0.7254 0.6521 0.6515 0.3753
Cumulative Return 91.47% 98.77% 88.47% 83.27% 97.64%
Worst Drawdown 28.95% 10.64% 9.79% 11.50% 47.26%
Average Drawdown 1.69% 0.98% 1.15% 1.10% 1.66%
Average Length 38.0152 37.2932 42.6154 45.0090 45.6455
Average Recovery 21.4015 21.1353 21.4444 22.4595 22.9273
Hurst Index 0.3379 0.3041 0.3062 0.3048 0.3699
VaR −0.88% −0.46% −0.47% −0.45% −0.80%
CVaR −1.74% −0.72% −0.73% −0.70% −0.95%
Sortino Ratio 0.5720 1.0661 0.9684 0.9638 0.5739
EUR 2010-2020
Return 5.04% 3.40% 3.38% 3.50% 2.07%
Standard Deviation 9.61% 4.89% 4.95% 4.75% 8.71%
Sharpe Ratio 0.5245 0.6952 0.6830 0.7362 0.2379
Cumulative Return 65.63% 40.90% 40.72% 42.35% 23.43%
Worst Drawdown 23.28% 9.94% 9.85% 10.10% 21.60%
Average Drawdown 1.59% 1.34% 1.15% 1.20% 2.45%
Average Length 26.5106 46.1296 47.0943 38.9062 82.0323
Average Recovery 13.7766 28.6111 31.5849 24.1875 34.3226
Hurst Index 0.3461 0.3241 0.3263 0.3279 0.3168
VaR −1.00% −0.49% −0.49% −0.47% −0.90%
CVaR −2.19% −0.83% −0.84% −0.83% −1.65%
Sortino Ratio 0.7751 1.0099 0.9961 1.0679 0.3854

Two funds 40/60

Two funds 40/60: Modelli dinamici vincolati e modello statico standard
Performance delle 12 misure statistiche calcolate sulla base di ciascun modello di ottimizzazione
Misura statisticaModello StaticoModelli dinamici
vincolati
StandardBoudt SD ROIBoudt SD RandomBoudt CVaR ROITCOV ROBNaif
USD 1985-2020
Return 7.57% 7.47% 7.48% 7.68% 7.46% 7.47%
Standard Deviation 8.73% 8.27% 8.27% 8.45% 8.29% 8.27%
Sharpe Ratio 0.8670 0.9038 0.9036 0.9089 0.8998 0.9033
Cumulative Return 1,278.27% 1,234.18% 1,236.79% 1,330.59% 1,228.38% 1,232.96%
Worst Drawdown 20.88% 19.73% 19.67% 20.41% 19.73% 19.73%
Average Drawdown 1.10% 1.04% 1.04% 1.08% 1.04% 1.04%
Average Length 18.1156 17.4773 17.4876 17.4421 17.5373 17.3992
Average Recovery 9.3640 9.3512 9.3905 9.2686 9.2739 9.3066
Hurst Index 0.3681 0.3652 0.3654 0.3628 0.3649 0.3652
VaR −0.76% −0.72% −0.72% −0.75% −0.73% −0.72%
CVaR −0.97% −0.93% −0.92% −1.14% −0.95% −0.93%
Sortino Ratio 1.2505 1.3040 1.3035 1.3093 1.2986 1.3034
USD 2000-2020
Return 5.04% 4.82% 4.81% 4.86% 4.87% 4.82%
Standard Deviation 8.21% 7.56% 7.57% 7.82% 7.58% 7.56%
Sharpe Ratio 0.6133 0.6378 0.6360 0.6217 0.6419 0.6380
Cumulative Return 174.01% 162.68% 162.36% 164.80% 165.01% 162.76%
Worst Drawdown 21.50% 18.72% 18.83% 21.62% 18.72% 18.72%
Average Drawdown 0.86% 0.81% 0.81% 0.85% 0.81% 0.81%
Average Length 17.4928 17.7316 17.6667 18.5287 17.6593 17.7279
Average Recovery 9.3152 9.6581 9.6813 10.0766 9.6374 9.6397
Hurst Index 0.3835 0.3877 0.3878 0.3907 0.3874 0.3877
VaR −0.65% −0.58% −0.58% −0.58% −0.58% −0.58%
CVaR −0.65% −0.58% −0.58% −0.58% −0.58% −0.58%
Sortino Ratio 0.9018 0.9323 0.9302 0.9114 0.9377 0.9326
USD 2010-2020
Return 7.76% 7.31% 7.27% 7.43% 7.35% 7.31%
Standard Deviation 7.06% 6.39% 6.36% 6.64% 6.43% 6.39%
Sharpe Ratio 1.0990 1.1441 1.1418 1.1202 1.1431 1.1441
Cumulative Return 115.31% 106.29% 105.49% 108.77% 107.13% 106.23%
Worst Drawdown 16.34% 14.91% 14.97% 14.91% 14.91% 14.91%
Average Drawdown 0.64% 0.57% 0.57% 0.63% 0.58% 0.57%
Average Length 10.1674 10.0870 10.1310 10.4661 10.0913 10.0870
Average Recovery 5.4317 5.3826 5.4192 5.6380 5.3783 5.3826
Hurst Index 0.4304 0.4387 0.4395 0.4338 0.4378 0.4387
VaR −0.44% −0.33% −0.31% −0.40% −0.34% −0.33%
CVaR −0.44% −0.33% −0.31% −0.40% −0.34% −0.33%
Sortino Ratio 1.5089 1.5656 1.5643 1.5355 1.5631 1.5657
USD → EUR 1985-2020
Return 6.54% 6.50% 6.50% 6.81% 6.61% 6.51%
Standard Deviation 14.91% 14.56% 14.57% 14.77% 14.57% 14.55%
Sharpe Ratio 0.4387 0.4464 0.4462 0.4614 0.4539 0.4472
Cumulative Return 876.63% 862.88% 863.10% 970.80% 900.58% 865.87%
Worst Drawdown 46.89% 45.86% 45.86% 44.63% 45.86% 45.86%
Average Drawdown 2.88% 2.87% 2.88% 2.78% 2.81% 2.86%
Average Length 45.4103 46.3455 46.5947 43.3627 45.3641 46.1094
Average Recovery 20.3795 20.9424 21.0632 19.5392 20.4205 20.8229
Hurst Index 0.3147 0.3094 0.3099 0.3196 0.3093 0.3094
VaR −1.46% −1.43% −1.43% −1.45% −1.43% −1.43%
CVaR −2.35% −2.25% −2.26% −2.41% −2.28% −2.25%
Sortino Ratio 0.7169 0.7263 0.7260 0.7458 0.7354 0.7272
USD → EUR 2000-2020
Return 3.58% 3.51% 3.52% 3.61% 3.59% 3.50%
Standard Deviation 12.58% 12.19% 12.21% 12.43% 12.20% 12.19%
Sharpe Ratio 0.2843 0.2882 0.2882 0.2904 0.2945 0.2874
Cumulative Return 105.65% 103.01% 103.23% 106.92% 106.23% 102.62%
Worst Drawdown 45.30% 44.89% 44.82% 45.37% 44.89% 44.89%
Average Drawdown 1.91% 1.87% 1.88% 1.91% 1.86% 1.89%
Average Length 50.8600 51.8673 51.8776 50.8400 51.3232 52.4124
Average Recovery 24.3800 34.2755 34.2551 24.2900 33.8990 34.6701
Hurst Index 0.3273 0.3261 0.3262 0.3247 0.3260 0.3261
VaR −1.24% −1.21% −1.21% −1.23% −1.21% −1.21%
CVaR −2.00% −1.92% −1.93% −1.95% −1.92% −1.92%
Sortino Ratio 0.4844 0.4874 0.4875 0.4920 0.4961 0.4863
USD → EUR 2010-2020
Return 8.50% 8.23% 8.22% 8.57% 8.27% 8.20%
Standard Deviation 10.04% 9.60% 9.62% 9.88% 9.62% 9.59%
Sharpe Ratio 0.8469 0.8580 0.8543 0.8675 0.8598 0.8545
Cumulative Return 131.16% 125.31% 124.91% 132.63% 126.12% 124.53%
Worst Drawdown 18.24% 17.09% 17.15% 17.17% 17.09% 17.09%
Average Drawdown 1.32% 1.29% 1.28% 1.35% 1.32% 1.29%
Average Length 20.9153 21.4435 21.2586 20.5833 21.1197 21.4435
Average Recovery 10.8644 11.2348 11.1552 10.4917 10.9658 11.0609
Hurst Index 0.3860 0.3863 0.3864 0.3836 0.3859 0.3863
VaR −0.91% −0.87% −0.87% −0.91% −0.87% −0.87%
CVaR −1.49% −1.40% −1.40% −1.57% −1.43% −1.40%
Sortino Ratio 1.2307 1.2493 1.2441 1.2601 1.2500 1.2440
EUR 1985-2020
Return 5.88% 5.89% 5.78% 5.94% 5.98% 5.91%
Standard Deviation 6.27% 5.83% 5.82% 6.02% 5.85% 5.83%
Sharpe Ratio 0.9387 1.0105 0.9942 0.9867 1.0217 1.0129
Cumulative Return 681.10% 682.29% 655.74% 697.11% 707.40% 687.46%
Worst Drawdown 23.02% 20.24% 20.35% 20.72% 20.24% 20.24%
Average Drawdown 1.23% 1.15% 1.15% 1.20% 1.15% 1.16%
Average Length 26.8952 26.6038 26.6877 26.9809 26.5110 26.9331
Average Recovery 13.1841 13.1635 13.1735 13.2994 13.1191 13.3471
Hurst Index 0.3252 0.3184 0.3191 0.3148 0.3179 0.3183
VaR −0.63% −0.59% −0.59% −0.61% −0.59% −0.59%
CVaR −1.27% −1.15% −1.15% −1.17% −1.16% −1.15%
Sortino Ratio 1.3363 1.4379 1.4158 1.4030 1.4530 1.4412
EUR 2000-2020
Return 3.24% 3.21% 3.21% 3.25% 3.31% 3.21%
Standard Deviation 7.11% 6.43% 6.45% 6.73% 6.46% 6.43%
Sharpe Ratio 0.4553 0.4987 0.4966 0.4837 0.5129 0.4987
Cumulative Return 92.28% 91.05% 91.00% 92.83% 95.18% 91.05%
Worst Drawdown 22.06% 19.34% 19.44% 22.64% 19.34% 19.34%
Average Drawdown 1.54% 1.42% 1.44% 1.46% 1.41% 1.42%
Average Length 35.9784 35.1831 35.4397 35.7000 34.4207 35.1831
Average Recovery 18.0935 17.6268 17.7447 18.1929 17.2000 17.6268
Hurst Index 0.3335 0.3298 0.3298 0.3244 0.3292 0.3298
VaR −0.73% −0.66% −0.66% −0.69% −0.66% −0.66%
CVaR −1.44% −1.29% −1.29% −1.32% −1.29% −1.29%
Sortino Ratio 0.6774 0.7348 0.7321 0.7143 0.7542 0.7348
EUR 2010-2020
Return 4.74% 4.55% 4.56% 4.46% 4.51% 4.55%
Standard Deviation 7.96% 7.19% 7.22% 7.38% 7.24% 7.19%
Sharpe Ratio 0.5951 0.6328 0.6316 0.6045 0.6230 0.6328
Cumulative Return 60.81% 57.90% 58.01% 56.55% 57.29% 57.90%
Worst Drawdown 20.26% 18.84% 18.82% 18.84% 18.84% 18.84%
Average Drawdown 1.42% 1.38% 1.38% 1.45% 1.38% 1.38%
Average Length 26.1895 28.8953 28.8953 29.3412 28.9186 28.8953
Average Recovery 12.8105 14.5116 14.5116 14.7294 14.5349 14.5116
Hurst Index 0.3413 0.3438 0.3431 0.3404 0.3429 0.3438
VaR −0.83% −0.75% −0.75% −0.77% −0.75% −0.75%
CVaR −1.82% −1.64% −1.65% −1.64% −1.64% −1.64%
Sortino Ratio 0.8640 0.9130 0.9114 0.8756 0.8994 0.9130
Two funds 40/60: Modelli dinamici non vincolati e modello statico 1/N
Performance delle 12 misure statistiche calcolate sulla base di ciascun modello di ottimizzazione
Misura statisticaModello StaticoModelli dinamici non vincolati
1/NBoudt SD No-boxHRPBoudt Random MVPBoudt Random HS
USD 1985-2020
Return 8.15% 7.01% 6.73% 6.82% 8.51%
Standard Deviation 9.71% 7.54% 7.43% 7.50% 9.94%
Sharpe Ratio 0.8389 0.9297 0.9064 0.9082 0.8561
Cumulative Return 1,572.92% 1,042.09% 940.62% 971.19% 1,786.00%
Worst Drawdown 26.04% 19.80% 20.05% 20.26% 23.62%
Average Drawdown 1.18% 0.96% 1.04% 0.99% 1.38%
Average Length 17.8962 18.5793 20.7115 19.6340 19.2255
Average Recovery 9.2839 9.7621 11.5623 10.8695 9.5786
Hurst Index 0.3720 0.3481 0.3391 0.3461 0.3166
VaR −0.85% −0.68% −0.68% −0.67% −0.96%
CVaR −1.06% −1.03% −1.11% −0.99% −1.80%
Sortino Ratio 1.2038 1.3536 1.3230 1.3278 1.2441
USD 2000-2020
Return 5.61% 3.67% 3.32% 3.42% 3.95%
Standard Deviation 9.73% 5.92% 5.91% 5.89% 10.55%
Sharpe Ratio 0.5763 0.6205 0.5615 0.5813 0.3741
Cumulative Return 206.22% 109.50% 95.41% 99.49% 121.19%
Worst Drawdown 27.89% 18.92% 19.70% 19.32% 41.82%
Average Drawdown 1.07% 0.60% 0.70% 0.65% 1.53%
Average Length 18.5211 18.3409 22.0404 20.5485 31.5190
Average Recovery 9.5862 10.8750 13.2466 12.4810 20.9937
Hurst Index 0.3735 0.3941 0.3886 0.3929 0.3947
VaR −0.82% −0.43% −0.46% −0.43% −0.47%
CVaR −0.82% −0.43% −0.46% −0.43% −0.47%
Sortino Ratio 0.8579 0.9024 0.8204 0.8479 0.5834
USD 2010-2020
Return 8.73% 5.12% 4.33% 4.69% 5.91%
Standard Deviation 8.61% 4.29% 4.03% 4.03% 7.57%
Sharpe Ratio 1.0142 1.1929 1.0750 1.1621 0.7804
Cumulative Return 136.12% 66.96% 54.52% 60.07% 80.29%
Worst Drawdown 19.33% 9.43% 8.96% 9.38% 17.94%
Average Drawdown 0.80% 0.43% 0.47% 0.43% 0.83%
Average Length 10.8774 12.2158 15.0633 13.2443 13.9000
Average Recovery 5.4151 6.9263 8.6329 8.0568 8.0706
Hurst Index 0.4136 0.4648 0.4668 0.4719 0.3943
VaR −0.68% 0.00% 0.00% 0.00% −0.64%
CVaR −0.68% −0.43% −0.43% −0.43% −0.64%
Sortino Ratio 1.4008 1.6077 1.4663 1.5719 1.0944
USD → EUR 1985-2020
Return 7.12% 7.20% 6.74% 7.09% 10.18%
Standard Deviation 15.22% 14.19% 14.28% 14.25% 17.15%
Sharpe Ratio 0.4677 0.5076 0.4720 0.4975 0.5936
Cumulative Return 1,085.41% 1,120.46% 943.82% 1,073.96% 3,167.81%
Worst Drawdown 46.38% 48.67% 46.90% 49.49% 41.30%
Average Drawdown 2.85% 2.85% 2.86% 2.96% 3.00%
Average Length 43.0293 42.6893 44.8223 44.0800 30.1419
Average Recovery 18.6146 25.8010 25.5990 26.0000 17.5294
Hurst Index 0.3254 0.2773 0.3052 0.2760 0.3541
VaR −1.50% −1.40% −1.41% −1.40% −1.64%
CVaR −2.59% −2.11% −2.22% −2.11% −3.43%
Sortino Ratio 0.7538 0.8078 0.7589 0.7953 0.9212
USD → EUR 2000-2020
Return 4.14% 2.89% 3.00% 2.68% 3.35%
Standard Deviation 13.36% 12.07% 11.91% 12.09% 14.48%
Sharpe Ratio 0.3099 0.2396 0.2521 0.2218 0.2316
Cumulative Return 129.82% 79.51% 83.47% 72.06% 96.72%
Worst Drawdown 44.67% 49.70% 47.02% 51.00% 55.46%
Average Drawdown 1.95% 2.21% 1.94% 2.40% 2.63%
Average Length 47.3738 60.6786 58.5172 67.1579 59.3256
Average Recovery 20.3364 38.6667 39.8851 44.3289 28.0465
Hurst Index 0.3282 0.3040 0.3117 0.3047 0.3491
VaR −1.31% −1.21% −1.19% −1.21% −1.32%
CVaR −2.15% −1.87% −1.82% −1.86% −1.80%
Sortino Ratio 0.5236 0.4195 0.4369 0.3954 0.4221
USD → EUR 2010-2020
Return 9.48% 6.37% 7.06% 6.09% 9.79%
Standard Deviation 11.02% 8.41% 8.66% 8.44% 11.49%
Sharpe Ratio 0.8604 0.7566 0.8154 0.7218 0.8519
Cumulative Return 153.50% 88.44% 101.52% 83.44% 160.87%
Worst Drawdown 20.32% 14.94% 11.86% 15.51% 19.11%
Average Drawdown 1.48% 1.35% 1.30% 1.43% 1.87%
Average Length 20.1639 25.8854 24.0485 27.9551 22.2072
Average Recovery 10.4754 13.4583 12.2136 14.5618 10.5315
Hurst Index 0.3826 0.3763 0.3775 0.3778 0.3371
VaR −1.01% −0.77% −0.80% −0.76% −1.13%
CVaR −1.76% −1.18% −1.32% −1.14% −2.02%
Sortino Ratio 1.2438 1.1312 1.2056 1.0833 1.2423
EUR 1985-2020
Return 6.11% 6.29% 6.03% 5.75% 6.44%
Standard Deviation 7.29% 5.14% 4.84% 4.72% 7.87%
Sharpe Ratio 0.8381 1.2242 1.2474 1.2184 0.8185
Cumulative Return 743.31% 798.04% 722.17% 647.65% 842.86%
Worst Drawdown 28.97% 24.18% 19.79% 20.98% 31.20%
Average Drawdown 1.44% 1.16% 1.07% 1.04% 1.99%
Average Length 30.0356 30.4928 29.6725 30.6232 43.5590
Average Recovery 15.4377 16.6304 14.9789 15.5036 24.8564
Hurst Index 0.3340 0.2987 0.2868 0.2881 0.2943
VaR −0.74% −0.52% −0.48% −0.46% −0.79%
CVaR −1.55% −0.94% −0.78% −0.76% −1.59%
Sortino Ratio 1.1922 1.7462 1.8061 1.7683 1.1652
EUR 2000-2020
Return 3.22% 3.41% 3.14% 3.00% 3.38%
Standard Deviation 8.61% 4.70% 4.81% 4.60% 9.00%
Sharpe Ratio 0.3735 0.7254 0.6521 0.6515 0.3753
Cumulative Return 91.47% 98.77% 88.47% 83.27% 97.65%
Worst Drawdown 28.95% 10.64% 9.79% 11.50% 47.26%
Average Drawdown 1.69% 0.98% 1.15% 1.10% 1.66%
Average Length 38.0152 37.2932 42.6154 45.0090 45.6455
Average Recovery 21.4015 21.1353 21.4444 22.4595 22.9273
Hurst Index 0.3379 0.3041 0.3062 0.3048 0.3699
VaR −0.88% −0.46% −0.47% −0.45% −0.80%
CVaR −1.74% −0.72% −0.73% −0.70% −0.95%
Sortino Ratio 0.5720 1.0661 0.9684 0.9638 0.5739
EUR 2010-2020
Return 5.04% 3.40% 3.38% 3.50% 2.07%
Standard Deviation 9.61% 4.89% 4.95% 4.75% 8.71%
Sharpe Ratio 0.5245 0.6952 0.6830 0.7362 0.2379
Cumulative Return 65.63% 40.90% 40.72% 42.35% 23.43%
Worst Drawdown 23.28% 9.94% 9.85% 10.10% 21.60%
Average Drawdown 1.59% 1.34% 1.15% 1.20% 2.45%
Average Length 26.5106 46.1296 47.0943 38.9062 82.0323
Average Recovery 13.7766 28.6111 31.5849 24.1875 34.3226
Hurst Index 0.3461 0.3241 0.3263 0.3279 0.3168
VaR −1.00% −0.49% −0.49% −0.47% −0.90%
CVaR −2.19% −0.83% −0.84% −0.83% −1.65%
Sortino Ratio 0.7751 1.0099 0.9961 1.0680 0.3855

Two funds 50/50

Two funds 50/50: Modelli dinamici vincolati e modello statico standard
Performance delle 12 misure statistiche calcolate sulla base di ciascun modello di ottimizzazione
Misura statisticaModello StaticoModelli dinamici
vincolati
StandardBoudt SD ROIBoudt SD RandomBoudt CVaR ROITCOV ROBNaif
USD 1985-2020
Return 8.15% 7.98% 7.97% 8.21% 8.01% 7.98%
Standard Deviation 9.71% 9.13% 9.12% 9.35% 9.14% 9.13%
Sharpe Ratio 0.8389 0.8740 0.8737 0.8784 0.8757 0.8743
Cumulative Return 1,572.92% 1,482.38% 1,477.44% 1,606.99% 1,495.13% 1,483.82%
Worst Drawdown 26.04% 22.98% 22.98% 24.04% 22.98% 22.98%
Average Drawdown 1.18% 1.12% 1.12% 1.13% 1.12% 1.12%
Average Length 17.8962 17.5708 17.5750 17.3814 17.5625 17.6075
Average Recovery 9.2839 8.9938 9.1583 8.7010 8.9750 9.0230
Hurst Index 0.3720 0.3713 0.3712 0.3687 0.3711 0.3713
VaR −0.85% −0.80% −0.80% −0.83% −0.80% −0.80%
CVaR −1.06% −0.98% −0.98% −1.25% −1.00% −0.98%
Sortino Ratio 1.2038 1.2518 1.2514 1.2583 1.2542 1.2522
USD 2000-2020
Return 5.61% 5.31% 5.31% 5.41% 5.33% 5.31%
Standard Deviation 9.73% 8.92% 8.92% 9.24% 8.93% 8.92%
Sharpe Ratio 0.5763 0.5950 0.5954 0.5853 0.5964 0.5951
Cumulative Return 206.22% 188.96% 189.15% 194.56% 190.01% 189.01%
Worst Drawdown 27.89% 24.78% 24.78% 28.02% 24.83% 24.78%
Average Drawdown 1.07% 0.96% 0.96% 0.99% 0.96% 0.96%
Average Length 18.5211 17.8118 17.7463 18.0373 17.8007 17.8118
Average Recovery 9.5862 9.4428 9.4007 9.7351 9.4317 9.4428
Hurst Index 0.3735 0.3783 0.3783 0.3812 0.3781 0.3783
VaR −0.82% −0.73% −0.73% −0.74% −0.73% −0.73%
CVaR −0.82% −0.73% −0.73% −0.74% −0.73% −0.73%
Sortino Ratio 0.8579 0.8797 0.8802 0.8674 0.8815 0.8799
USD 2010-2020
Return 8.73% 8.23% 8.23% 8.39% 8.33% 8.23%
Standard Deviation 8.61% 7.82% 7.82% 8.11% 7.92% 7.82%
Sharpe Ratio 1.0142 1.0527 1.0527 1.0336 1.0529 1.0527
Cumulative Return 136.12% 125.23% 125.23% 128.56% 127.47% 125.23%
Worst Drawdown 19.33% 17.83% 17.83% 17.83% 17.83% 17.83%
Average Drawdown 0.80% 0.71% 0.71% 0.76% 0.73% 0.71%
Average Length 10.8774 10.4344 10.4344 10.5616 10.4864 10.4344
Average Recovery 5.4151 5.4163 5.4163 5.5114 5.4909 5.4163
Hurst Index 0.4136 0.4217 0.4217 0.4170 0.4201 0.4217
VaR −0.68% −0.56% −0.56% −0.63% −0.59% −0.56%
CVaR −0.68% −0.56% −0.56% −0.63% −0.59% −0.56%
Sortino Ratio 1.4008 1.4493 1.4493 1.4243 1.4475 1.4493
USD → EUR 1985-2020
Return 7.12% 7.03% 7.04% 7.40% 7.04% 7.04%
Standard Deviation 15.22% 14.80% 14.80% 15.10% 14.81% 14.80%
Sharpe Ratio 0.4677 0.4752 0.4754 0.4899 0.4755 0.4756
Cumulative Return 1,085.41% 1,052.27% 1,053.53% 1,202.59% 1,056.22% 1,053.78%
Worst Drawdown 46.38% 44.83% 44.82% 43.65% 44.83% 44.71%
Average Drawdown 2.85% 2.71% 2.71% 2.73% 2.71% 2.71%
Average Length 43.0293 42.0524 42.0476 40.4679 42.0524 41.8483
Average Recovery 18.6146 18.7381 18.7333 18.4128 18.7381 18.6303
Hurst Index 0.3254 0.3216 0.3215 0.3293 0.3215 0.3216
VaR −1.50% −1.46% −1.46% −1.49% −1.46% −1.46%
CVaR −2.59% −2.46% −2.46% −2.67% −2.46% −2.46%
Sortino Ratio 0.7538 0.7624 0.7627 0.7817 0.7630 0.7630
USD → EUR 2000-2020
Return 4.14% 3.97% 3.97% 3.98% 3.97% 3.97%
Standard Deviation 13.36% 12.83% 12.83% 13.12% 12.83% 12.83%
Sharpe Ratio 0.3099 0.3092 0.3092 0.3034 0.3092 0.3092
Cumulative Return 129.82% 122.17% 122.17% 122.65% 122.17% 122.17%
Worst Drawdown 44.67% 42.78% 42.78% 45.11% 42.78% 42.78%
Average Drawdown 1.95% 1.80% 1.80% 1.83% 1.80% 1.80%
Average Length 47.3738 45.7207 45.7207 47.4673 45.7207 45.7207
Average Recovery 20.3364 20.1802 20.1802 22.7009 20.1802 20.1802
Hurst Index 0.3282 0.3281 0.3281 0.3264 0.3281 0.3281
VaR −1.31% −1.26% −1.26% −1.29% −1.26% −1.26%
CVaR −2.15% −2.06% −2.06% −2.09% −2.06% −2.06%
Sortino Ratio 0.5236 0.5194 0.5194 0.5131 0.5194 0.5194
USD → EUR 2010-2020
Return 9.48% 8.95% 8.95% 9.62% 9.01% 8.95%
Standard Deviation 11.02% 10.45% 10.45% 10.81% 10.45% 10.45%
Sharpe Ratio 0.8604 0.8570 0.8570 0.8901 0.8619 0.8570
Cumulative Return 153.50% 141.12% 141.12% 156.71% 142.45% 141.12%
Worst Drawdown 20.32% 19.21% 19.21% 19.29% 19.21% 19.21%
Average Drawdown 1.48% 1.40% 1.40% 1.47% 1.40% 1.40%
Average Length 20.1639 19.8710 19.8710 19.5317 19.7120 19.8710
Average Recovery 10.4754 10.2661 10.2661 10.1270 10.1760 10.2661
Hurst Index 0.3826 0.3843 0.3843 0.3809 0.3842 0.3843
VaR −1.01% −0.95% −0.95% −1.00% −0.95% −0.95%
CVaR −1.76% −1.62% −1.62% −1.82% −1.63% −1.62%
Sortino Ratio 1.2438 1.2407 1.2407 1.2853 1.2475 1.2407
EUR 1985-2020
Return 6.11% 6.10% 6.05% 6.18% 6.19% 6.12%
Standard Deviation 7.29% 6.75% 6.73% 6.96% 6.77% 6.76%
Sharpe Ratio 0.8381 0.9038 0.8979 0.8869 0.9139 0.9056
Cumulative Return 743.31% 742.04% 726.09% 762.78% 767.49% 746.52%
Worst Drawdown 28.97% 26.06% 26.06% 26.04% 26.06% 26.06%
Average Drawdown 1.44% 1.40% 1.39% 1.46% 1.42% 1.41%
Average Length 30.0356 29.3299 29.1241 29.7430 29.7148 29.5280
Average Recovery 15.4377 15.4097 15.2621 15.8662 15.5775 15.5175
Hurst Index 0.3340 0.3303 0.3304 0.3269 0.3299 0.3302
VaR −0.74% −0.68% −0.68% −0.71% −0.69% −0.69%
CVaR −1.55% −1.42% −1.42% −1.45% −1.43% −1.42%
Sortino Ratio 1.1922 1.2817 1.2740 1.2576 1.2953 1.2842
EUR 2000-2020
Return 3.22% 3.22% 3.22% 3.20% 3.21% 3.22%
Standard Deviation 8.61% 7.83% 7.83% 8.15% 7.83% 7.83%
Sharpe Ratio 0.3735 0.4109 0.4110 0.3927 0.4103 0.4109
Cumulative Return 91.47% 91.43% 91.44% 90.77% 91.27% 91.43%
Worst Drawdown 28.95% 25.58% 25.56% 29.50% 25.63% 25.58%
Average Drawdown 1.69% 1.65% 1.65% 1.70% 1.65% 1.65%
Average Length 38.0152 37.4776 37.4776 39.1250 37.4776 37.4776
Average Recovery 21.4015 19.4627 19.4179 22.1016 19.4627 19.4627
Hurst Index 0.3379 0.3363 0.3362 0.3316 0.3363 0.3363
VaR −0.88% −0.80% −0.80% −0.84% −0.80% −0.80%
CVaR −1.74% −1.59% −1.58% −1.62% −1.59% −1.59%
Sortino Ratio 0.5720 0.6192 0.6194 0.5953 0.6185 0.6192
EUR 2010-2020
Return 5.04% 4.86% 4.86% 4.77% 4.86% 4.86%
Standard Deviation 9.61% 8.75% 8.75% 8.95% 8.75% 8.75%
Sharpe Ratio 0.5245 0.5559 0.5559 0.5337 0.5559 0.5559
Cumulative Return 65.63% 62.83% 62.83% 61.41% 62.83% 62.83%
Worst Drawdown 23.28% 21.74% 21.74% 21.74% 21.74% 21.74%
Average Drawdown 1.59% 1.61% 1.61% 1.66% 1.61% 1.61%
Average Length 26.5106 27.3956 27.3956 27.5055 27.3956 27.3956
Average Recovery 13.7766 13.6044 13.6044 13.7033 13.6044 13.6044
Hurst Index 0.3461 0.3434 0.3434 0.3406 0.3434 0.3434
VaR −1.00% −0.91% −0.91% −0.94% −0.91% −0.91%
CVaR −2.19% −2.01% −2.01% −2.00% −2.01% −2.01%
Sortino Ratio 0.7751 0.8136 0.8136 0.7849 0.8136 0.8136
Two funds 50/50: Modelli dinamici non vincolati e modello statico 1/N
Performance delle 12 misure statistiche calcolate sulla base di ciascun modello di ottimizzazione
Misura statisticaModello StaticoModelli dinamici non vincolati
1/NBoudt SD No-boxHRPBoudt Random MVPBoudt Random HS
USD 1985-2020
Return 8.15% 7.01% 6.73% 6.82% 8.51%
Standard Deviation 9.71% 7.54% 7.43% 7.50% 9.94%
Sharpe Ratio 0.8389 0.9297 0.9064 0.9082 0.8561
Cumulative Return 1,572.92% 1,042.09% 940.62% 971.19% 1,786.14%
Worst Drawdown 26.04% 19.80% 20.05% 20.26% 23.62%
Average Drawdown 1.18% 0.96% 1.04% 0.99% 1.38%
Average Length 17.8962 18.5793 20.7115 19.6799 19.2255
Average Recovery 9.2839 9.7621 11.5623 10.8972 9.5786
Hurst Index 0.3720 0.3481 0.3391 0.3461 0.3166
VaR −0.85% −0.68% −0.68% −0.67% −0.96%
CVaR −1.06% −1.03% −1.11% −0.99% −1.80%
Sortino Ratio 1.2038 1.3536 1.3230 1.3278 1.2442
USD 2000-2020
Return 5.61% 3.67% 3.32% 3.42% 3.95%
Standard Deviation 9.73% 5.92% 5.91% 5.89% 10.55%
Sharpe Ratio 0.5763 0.6205 0.5615 0.5813 0.3741
Cumulative Return 206.22% 109.50% 95.41% 99.48% 121.19%
Worst Drawdown 27.89% 18.92% 19.70% 19.32% 41.82%
Average Drawdown 1.07% 0.60% 0.70% 0.65% 1.54%
Average Length 18.5211 18.3409 22.0404 20.5527 31.7197
Average Recovery 9.5862 10.8750 13.2466 12.4852 21.1210
Hurst Index 0.3735 0.3941 0.3886 0.3929 0.3947
VaR −0.82% −0.43% −0.46% −0.43% −0.47%
CVaR −0.82% −0.43% −0.46% −0.43% −0.47%
Sortino Ratio 0.8579 0.9024 0.8204 0.8479 0.5834
USD 2010-2020
Return 8.73% 5.12% 4.33% 4.69% 5.91%
Standard Deviation 8.61% 4.29% 4.03% 4.03% 7.57%
Sharpe Ratio 1.0142 1.1929 1.0750 1.1620 0.7804
Cumulative Return 136.12% 66.96% 54.52% 60.06% 80.29%
Worst Drawdown 19.33% 9.43% 8.96% 9.38% 17.94%
Average Drawdown 0.80% 0.43% 0.47% 0.43% 0.83%
Average Length 10.8774 12.2158 15.0633 13.2443 13.9763
Average Recovery 5.4151 6.9263 8.6329 8.0568 8.0414
Hurst Index 0.4136 0.4648 0.4668 0.4719 0.3943
VaR −0.68% 0.00% 0.00% 0.00% −0.64%
CVaR −0.68% −0.61% −0.61% −0.61% −0.64%
Sortino Ratio 1.4008 1.6077 1.4663 1.5718 1.0945
USD → EUR 1985-2020
Return 7.12% 7.20% 6.74% 7.09% 10.18%
Standard Deviation 15.22% 14.19% 14.28% 14.25% 17.15%
Sharpe Ratio 0.4677 0.5076 0.4720 0.4975 0.5936
Cumulative Return 1,085.41% 1,120.46% 943.82% 1,073.72% 3,168.75%
Worst Drawdown 46.38% 48.67% 46.90% 49.49% 41.30%
Average Drawdown 2.85% 2.85% 2.86% 2.96% 3.00%
Average Length 43.0293 42.6893 44.8223 44.0800 30.1419
Average Recovery 18.6146 25.8010 25.5990 26.0000 17.5294
Hurst Index 0.3254 0.2773 0.3052 0.2760 0.3541
VaR −1.50% −1.40% −1.41% −1.40% −1.64%
CVaR −2.59% −2.11% −2.22% −2.11% −3.43%
Sortino Ratio 0.7538 0.8078 0.7589 0.7952 0.9212
USD → EUR 2000-2020
Return 4.14% 2.89% 3.00% 2.68% 3.35%
Standard Deviation 13.36% 12.07% 11.91% 12.09% 14.48%
Sharpe Ratio 0.3099 0.2396 0.2521 0.2217 0.2315
Cumulative Return 129.82% 79.51% 83.47% 72.03% 96.70%
Worst Drawdown 44.67% 49.70% 47.02% 51.00% 55.46%
Average Drawdown 1.95% 2.21% 1.94% 2.40% 2.63%
Average Length 47.3738 60.6786 58.5172 67.1579 59.3256
Average Recovery 20.3364 38.6667 39.8851 44.3289 28.0465
Hurst Index 0.3282 0.3040 0.3117 0.3047 0.3491
VaR −1.31% −1.21% −1.19% −1.21% −1.32%
CVaR −2.15% −1.87% −1.82% −1.86% −1.80%
Sortino Ratio 0.5236 0.4195 0.4369 0.3953 0.4220
USD → EUR 2010-2020
Return 9.48% 6.37% 7.06% 6.09% 9.79%
Standard Deviation 11.02% 8.41% 8.66% 8.44% 11.49%
Sharpe Ratio 0.8604 0.7566 0.8154 0.7217 0.8519
Cumulative Return 153.50% 88.44% 101.52% 83.43% 160.88%
Worst Drawdown 20.32% 14.94% 11.86% 15.51% 19.11%
Average Drawdown 1.48% 1.35% 1.30% 1.43% 1.87%
Average Length 20.1639 25.8854 24.0485 27.9551 22.2072
Average Recovery 10.4754 13.4583 12.2136 14.5618 10.5315
Hurst Index 0.3826 0.3763 0.3775 0.3778 0.3371
VaR −1.01% −0.77% −0.80% −0.76% −1.13%
CVaR −1.76% −1.18% −1.32% −1.14% −2.02%
Sortino Ratio 1.2438 1.1312 1.2056 1.0831 1.2422
EUR 1985-2020
Return 6.11% 6.29% 6.03% 5.75% 6.44%
Standard Deviation 7.29% 5.14% 4.84% 4.72% 7.87%
Sharpe Ratio 0.8381 1.2242 1.2474 1.2184 0.8185
Cumulative Return 743.31% 798.04% 722.17% 647.67% 842.85%
Worst Drawdown 28.97% 24.18% 19.79% 20.98% 31.20%
Average Drawdown 1.44% 1.16% 1.07% 1.04% 1.99%
Average Length 30.0356 30.4928 29.6725 30.6232 43.5590
Average Recovery 15.4377 16.6304 14.9789 15.5036 24.8564
Hurst Index 0.3340 0.2987 0.2868 0.2881 0.2943
VaR −0.74% −0.52% −0.48% −0.46% −0.79%
CVaR −1.55% −0.94% −0.78% −0.76% −1.59%
Sortino Ratio 1.1922 1.7462 1.8061 1.7683 1.1652
EUR 2000-2020
Return 3.22% 3.41% 3.14% 3.00% 3.38%
Standard Deviation 8.61% 4.70% 4.81% 4.60% 9.00%
Sharpe Ratio 0.3735 0.7254 0.6521 0.6515 0.3753
Cumulative Return 91.47% 98.77% 88.47% 83.27% 97.64%
Worst Drawdown 28.95% 10.64% 9.79% 11.50% 47.26%
Average Drawdown 1.69% 0.98% 1.15% 1.10% 1.66%
Average Length 38.0152 37.2932 42.6154 45.0090 45.6455
Average Recovery 21.4015 21.1353 21.4444 22.4595 22.9273
Hurst Index 0.3379 0.3041 0.3062 0.3048 0.3699
VaR −0.88% −0.46% −0.47% −0.45% −0.80%
CVaR −1.74% −0.72% −0.73% −0.70% −0.95%
Sortino Ratio 0.5720 1.0661 0.9684 0.9638 0.5739
EUR 2010-2020
Return 5.04% 3.40% 3.38% 3.50% 2.07%
Standard Deviation 9.61% 4.89% 4.95% 4.75% 8.71%
Sharpe Ratio 0.5245 0.6952 0.6830 0.7362 0.2379
Cumulative Return 65.63% 40.90% 40.72% 42.35% 23.43%
Worst Drawdown 23.28% 9.94% 9.85% 10.10% 21.60%
Average Drawdown 1.59% 1.34% 1.15% 1.20% 2.45%
Average Length 26.5106 46.1296 47.0943 38.9062 82.0323
Average Recovery 13.7766 28.6111 31.5849 24.1875 34.3226
Hurst Index 0.3461 0.3241 0.3263 0.3279 0.3168
VaR −1.00% −0.49% −0.49% −0.47% −0.90%
CVaR −2.19% −0.83% −0.84% −0.83% −1.65%
Sortino Ratio 0.7751 1.0099 0.9961 1.0679 0.3854

Two funds 60/40

Two funds 60/40: Modelli dinamici vincolati e modello statico standard
Performance delle 12 misure statistiche calcolate sulla base di ciascun modello di ottimizzazione
Misura statisticaModello StaticoModelli dinamici
vincolati
StandardBoudt SD ROIBoudt SD RandomBoudt CVaR ROITCOV ROBNaif
USD 1985-2020
Return 8.70% 8.48% 8.49% 8.67% 8.49% 8.48%
Standard Deviation 10.97% 10.29% 10.29% 10.52% 10.30% 10.28%
Sharpe Ratio 0.7933 0.8242 0.8249 0.8238 0.8244 0.8243
Cumulative Return 1,911.31% 1,770.46% 1,772.17% 1,887.66% 1,772.93% 1,765.78%
Worst Drawdown 32.24% 29.20% 29.20% 30.19% 29.20% 29.20%
Average Drawdown 1.32% 1.24% 1.24% 1.25% 1.24% 1.24%
Average Length 18.1677 18.0600 18.0214 17.3265 18.0214 18.0642
Average Recovery 9.4258 9.2527 9.2308 8.8378 9.2308 9.2570
Hurst Index 0.3722 0.3726 0.3725 0.3702 0.3726 0.3727
VaR −0.97% −0.90% −0.90% −0.94% −0.90% −0.90%
CVaR −1.26% −1.14% −1.15% −1.43% −1.15% −1.12%
Sortino Ratio 1.1407 1.1806 1.1816 1.1821 1.1807 1.1810
USD 2000-2020
Return 6.15% 5.88% 5.88% 5.99% 5.88% 5.88%
Standard Deviation 11.45% 10.56% 10.56% 10.87% 10.56% 10.56%
Sharpe Ratio 0.5373 0.5565 0.5565 0.5513 0.5572 0.5565
Cumulative Return 240.24% 222.53% 222.53% 229.87% 222.92% 222.53%
Worst Drawdown 34.00% 31.04% 31.04% 33.57% 31.00% 31.04%
Average Drawdown 1.26% 1.16% 1.16% 1.17% 1.16% 1.16%
Average Length 19.0945 18.3409 18.3409 18.7791 18.3409 18.3409
Average Recovery 10.1220 9.3750 9.3750 9.7597 9.3750 9.3750
Hurst Index 0.3642 0.3684 0.3684 0.3706 0.3684 0.3684
VaR −1.00% −0.91% −0.91% −0.92% −0.91% −0.91%
CVaR −1.07% −0.91% −0.91% −0.92% −0.91% −0.91%
Sortino Ratio 0.8134 0.8349 0.8349 0.8286 0.8357 0.8349
USD 2010-2020
Return 9.69% 9.19% 9.20% 9.27% 9.23% 9.20%
Standard Deviation 10.25% 9.42% 9.42% 9.65% 9.46% 9.42%
Sharpe Ratio 0.9453 0.9760 0.9762 0.9604 0.9765 0.9762
Cumulative Return 158.41% 146.70% 146.74% 148.50% 147.63% 146.74%
Worst Drawdown 22.63% 20.99% 20.99% 20.99% 20.99% 20.99%
Average Drawdown 0.99% 0.88% 0.88% 0.93% 0.88% 0.88%
Average Length 11.7222 11.0909 11.0909 11.3317 11.0957 11.0909
Average Recovery 5.8232 5.4833 5.4833 5.6341 5.4833 5.4833
Hurst Index 0.3995 0.4063 0.4063 0.4031 0.4058 0.4063
VaR −0.88% −0.78% −0.78% −0.82% −0.79% −0.78%
CVaR −0.88% −0.78% −0.78% −0.82% −0.79% −0.78%
Sortino Ratio 1.3157 1.3531 1.3534 1.3339 1.3532 1.3534
USD → EUR 1985-2020
Return 7.67% 7.61% 7.61% 7.94% 7.59% 7.61%
Standard Deviation 15.77% 15.27% 15.28% 15.65% 15.30% 15.27%
Sharpe Ratio 0.4862 0.4983 0.4979 0.5076 0.4959 0.4980
Cumulative Return 1,325.19% 1,298.10% 1,297.15% 1,463.51% 1,286.86% 1,296.73%
Worst Drawdown 47.75% 44.82% 44.88% 44.28% 45.23% 44.82%
Average Drawdown 2.85% 2.76% 2.75% 2.87% 2.76% 2.76%
Average Length 39.1156 39.9773 39.6171 37.6910 39.9864 39.9864
Average Recovery 17.2044 17.1864 17.0315 16.5536 17.1955 17.1955
Hurst Index 0.3326 0.3301 0.3303 0.3359 0.3299 0.3301
VaR −1.56% −1.51% −1.51% −1.55% −1.51% −1.51%
CVaR −2.87% −2.73% −2.73% −2.96% −2.73% −2.73%
Sortino Ratio 0.7778 0.7923 0.7917 0.8041 0.7892 0.7920
USD → EUR 2000-2020
Return 4.68% 4.51% 4.52% 4.49% 4.52% 4.52%
Standard Deviation 14.41% 13.79% 13.80% 14.10% 13.78% 13.78%
Sharpe Ratio 0.3245 0.3273 0.3274 0.3184 0.3276 0.3276
Cumulative Return 155.35% 147.22% 147.49% 146.22% 147.42% 147.42%
Worst Drawdown 45.94% 43.76% 43.82% 46.10% 43.76% 43.76%
Average Drawdown 2.01% 1.94% 1.93% 2.02% 1.93% 1.93%
Average Length 43.5086 44.3421 43.9565 43.9130 43.9565 43.9565
Average Recovery 19.5862 20.0263 19.8435 19.9130 19.8435 19.8435
Hurst Index 0.3269 0.3275 0.3275 0.3256 0.3275 0.3275
VaR −1.40% −1.35% −1.35% −1.37% −1.35% −1.35%
CVaR −2.34% −2.24% −2.24% −2.26% −2.24% −2.24%
Sortino Ratio 0.5495 0.5492 0.5496 0.5391 0.5497 0.5497
USD → EUR 2010-2020
Return 10.45% 9.92% 9.94% 10.58% 9.92% 9.92%
Standard Deviation 12.20% 11.54% 11.55% 11.93% 11.54% 11.54%
Sharpe Ratio 0.8566 0.8599 0.8602 0.8870 0.8599 0.8599
Cumulative Return 177.43% 164.14% 164.50% 180.77% 164.14% 164.14%
Worst Drawdown 22.36% 21.27% 21.28% 21.35% 21.27% 21.27%
Average Drawdown 1.62% 1.55% 1.55% 1.60% 1.55% 1.55%
Average Length 19.2756 19.4921 19.4921 19.1016 19.4921 19.4921
Average Recovery 10.9921 11.2063 11.2063 11.0625 11.2063 11.2063
Hurst Index 0.3779 0.3800 0.3800 0.3767 0.3800 0.3800
VaR −1.12% −1.06% −1.06% −1.11% −1.06% −1.06%
CVaR −2.05% −1.91% −1.91% −2.12% −1.91% −1.91%
Sortino Ratio 1.2367 1.2412 1.2416 1.2774 1.2412 1.2412
EUR 1985-2020
Return 6.30% 6.30% 6.25% 6.34% 6.35% 6.31%
Standard Deviation 8.48% 7.88% 7.86% 8.09% 7.89% 7.88%
Sharpe Ratio 0.7427 0.7999 0.7953 0.7835 0.8051 0.8007
Cumulative Return 800.08% 800.77% 785.67% 812.32% 816.70% 802.90%
Worst Drawdown 34.64% 31.87% 31.87% 31.84% 31.87% 31.87%
Average Drawdown 1.71% 1.58% 1.53% 1.68% 1.60% 1.58%
Average Length 34.0605 32.7171 31.8566 34.0040 32.9531 32.7248
Average Recovery 19.2661 18.5620 18.0491 19.6210 18.7031 18.5698
Hurst Index 0.3388 0.3366 0.3368 0.3336 0.3364 0.3366
VaR −0.85% −0.79% −0.79% −0.82% −0.80% −0.79%
CVaR −1.83% −1.70% −1.70% −1.73% −1.71% −1.70%
Sortino Ratio 1.0629 1.1380 1.1319 1.1158 1.1451 1.1391
EUR 2000-2020
Return 3.16% 3.18% 3.18% 3.15% 3.18% 3.18%
Standard Deviation 10.27% 9.42% 9.42% 9.76% 9.42% 9.42%
Sharpe Ratio 0.3080 0.3376 0.3376 0.3225 0.3375 0.3376
Cumulative Return 89.47% 90.07% 90.04% 88.83% 90.02% 90.07%
Worst Drawdown 35.48% 32.26% 32.26% 35.99% 32.28% 32.26%
Average Drawdown 2.07% 1.90% 1.89% 2.01% 1.90% 1.90%
Average Length 44.0614 41.8167 41.8167 41.5372 41.8250 41.8167
Average Recovery 25.5789 23.7833 23.7833 24.5455 23.7917 23.7833
Hurst Index 0.3398 0.3391 0.3391 0.3350 0.3391 0.3391
VaR −1.05% −0.96% −0.96% −1.00% −0.96% −0.96%
CVaR −2.06% −1.90% −1.90% −1.94% −1.90% −1.90%
Sortino Ratio 0.4922 0.5274 0.5274 0.5085 0.5272 0.5274
EUR 2010-2020
Return 5.32% 5.15% 5.15% 5.06% 5.15% 5.15%
Standard Deviation 11.38% 10.47% 10.47% 10.67% 10.47% 10.47%
Sharpe Ratio 0.4670 0.4921 0.4921 0.4748 0.4921 0.4921
Cumulative Return 70.18% 67.51% 67.51% 66.06% 67.51% 67.51%
Worst Drawdown 26.30% 24.80% 24.80% 24.80% 24.80% 24.80%
Average Drawdown 1.84% 1.67% 1.67% 1.84% 1.67% 1.67%
Average Length 27.0870 26.2105 26.2105 26.8280 26.2105 26.2105
Average Recovery 14.2609 13.4421 13.4421 14.3118 13.4421 13.4421
Hurst Index 0.3500 0.3484 0.3484 0.3460 0.3484 0.3484
VaR −1.19% −1.10% −1.10% −1.12% −1.10% −1.10%
CVaR −2.58% −2.39% −2.39% −2.38% −2.39% −2.39%
Sortino Ratio 0.7072 0.7359 0.7359 0.7140 0.7359 0.7359
Two funds 60/40: Modelli dinamici non vincolati e modello statico 1/N
Performance delle 12 misure statistiche calcolate sulla base di ciascun modello di ottimizzazione
Misura statisticaModello StaticoModelli dinamici non vincolati
1/NBoudt SD No-boxHRPBoudt Random MVPBoudt Random HS
USD 1985-2020
Return 8.15% 7.01% 6.73% 6.82% 8.51%
Standard Deviation 9.71% 7.54% 7.43% 7.50% 9.94%
Sharpe Ratio 0.8389 0.9297 0.9064 0.9082 0.8561
Cumulative Return 1,572.92% 1,042.09% 940.62% 971.17% 1,785.97%
Worst Drawdown 26.04% 19.80% 20.05% 20.26% 23.62%
Average Drawdown 1.18% 0.96% 1.04% 0.99% 1.38%
Average Length 17.8962 18.5793 20.7115 19.6799 19.2255
Average Recovery 9.2839 9.7621 11.5623 10.8972 9.5786
Hurst Index 0.3720 0.3481 0.3391 0.3461 0.3166
VaR −0.85% −0.68% −0.68% −0.67% −0.96%
CVaR −1.06% −1.03% −1.11% −0.99% −1.80%
Sortino Ratio 1.2038 1.3536 1.3230 1.3278 1.2441
USD 2000-2020
Return 5.61% 3.67% 3.32% 3.42% 3.95%
Standard Deviation 9.73% 5.92% 5.91% 5.89% 10.55%
Sharpe Ratio 0.5763 0.6205 0.5615 0.5813 0.3741
Cumulative Return 206.22% 109.50% 95.41% 99.49% 121.19%
Worst Drawdown 27.89% 18.92% 19.70% 19.33% 41.82%
Average Drawdown 1.07% 0.60% 0.70% 0.65% 1.53%
Average Length 18.5211 18.3409 22.0404 20.5485 31.5190
Average Recovery 9.5862 10.8750 13.2466 12.4810 20.9937
Hurst Index 0.3735 0.3941 0.3886 0.3929 0.3947
VaR −0.82% −0.43% −0.46% −0.43% −0.47%
CVaR −0.82% −0.43% −0.46% −0.43% −0.47%
Sortino Ratio 0.8579 0.9024 0.8204 0.8480 0.5834
USD 2010-2020
Return 8.73% 5.12% 4.33% 4.69% 5.91%
Standard Deviation 8.61% 4.29% 4.03% 4.03% 7.57%
Sharpe Ratio 1.0142 1.1929 1.0750 1.1621 0.7804
Cumulative Return 136.12% 66.96% 54.52% 60.06% 80.29%
Worst Drawdown 19.33% 9.43% 8.96% 9.38% 17.94%
Average Drawdown 0.80% 0.43% 0.47% 0.43% 0.83%
Average Length 10.8774 12.2158 15.0633 13.2443 13.9763
Average Recovery 5.4151 6.9263 8.6329 8.0568 8.0414
Hurst Index 0.4136 0.4648 0.4668 0.4719 0.3943
VaR −0.68% 0.00% 0.00% 0.00% −0.64%
CVaR −0.68% −0.77% −0.77% −0.77% −0.64%
Sortino Ratio 1.4008 1.6077 1.4663 1.5719 1.0945
USD → EUR 1985-2020
Return 7.12% 7.20% 6.74% 7.09% 10.18%
Standard Deviation 15.22% 14.19% 14.28% 14.25% 17.15%
Sharpe Ratio 0.4677 0.5076 0.4720 0.4975 0.5936
Cumulative Return 1,085.41% 1,120.46% 943.82% 1,073.82% 3,168.75%
Worst Drawdown 46.38% 48.67% 46.90% 49.49% 41.30%
Average Drawdown 2.85% 2.85% 2.86% 2.96% 3.00%
Average Length 43.0293 42.6893 44.8223 44.0800 30.1419
Average Recovery 18.6146 25.8010 25.5990 26.0000 17.5294
Hurst Index 0.3254 0.2773 0.3052 0.2760 0.3541
VaR −1.50% −1.40% −1.41% −1.40% −1.64%
CVaR −2.59% −2.11% −2.22% −2.11% −3.43%
Sortino Ratio 0.7538 0.8078 0.7589 0.7952 0.9212
USD → EUR 2000-2020
Return 4.14% 2.89% 3.00% 2.68% 3.35%
Standard Deviation 13.36% 12.07% 11.91% 12.09% 14.48%
Sharpe Ratio 0.3099 0.2396 0.2521 0.2217 0.2315
Cumulative Return 129.82% 79.51% 83.47% 72.02% 96.70%
Worst Drawdown 44.67% 49.70% 47.02% 51.00% 55.46%
Average Drawdown 1.95% 2.21% 1.94% 2.40% 2.63%
Average Length 47.3738 60.6786 58.5172 67.1579 59.3256
Average Recovery 20.3364 38.6667 39.8851 44.3289 28.0465
Hurst Index 0.3282 0.3040 0.3117 0.3047 0.3491
VaR −1.31% −1.21% −1.19% −1.21% −1.32%
CVaR −2.15% −1.87% −1.82% −1.86% −1.80%
Sortino Ratio 0.5236 0.4195 0.4369 0.3953 0.4220
USD → EUR 2010-2020
Return 9.48% 6.37% 7.06% 6.09% 9.79%
Standard Deviation 11.02% 8.41% 8.66% 8.44% 11.49%
Sharpe Ratio 0.8604 0.7566 0.8154 0.7216 0.8519
Cumulative Return 153.50% 88.44% 101.52% 83.43% 160.87%
Worst Drawdown 20.32% 14.94% 11.86% 15.52% 19.11%
Average Drawdown 1.48% 1.35% 1.30% 1.43% 1.87%
Average Length 20.1639 25.8854 24.0485 27.9551 22.2072
Average Recovery 10.4754 13.4583 12.2136 14.5618 10.5315
Hurst Index 0.3826 0.3763 0.3775 0.3778 0.3371
VaR −1.01% −0.77% −0.80% −0.76% −1.13%
CVaR −1.76% −1.18% −1.32% −1.14% −2.02%
Sortino Ratio 1.2438 1.1312 1.2056 1.0831 1.2422
EUR 1985-2020
Return 6.11% 6.29% 6.03% 5.75% 6.44%
Standard Deviation 7.29% 5.14% 4.84% 4.72% 7.86%
Sharpe Ratio 0.8381 1.2242 1.2474 1.2184 0.8186
Cumulative Return 743.31% 798.04% 722.17% 647.65% 842.85%
Worst Drawdown 28.97% 24.18% 19.79% 20.98% 31.19%
Average Drawdown 1.44% 1.16% 1.07% 1.03% 1.99%
Average Length 30.0356 30.4928 29.6725 30.6232 43.5590
Average Recovery 15.4377 16.6304 14.9789 15.5036 24.8564
Hurst Index 0.3340 0.2987 0.2868 0.2881 0.2943
VaR −0.74% −0.52% −0.48% −0.46% −0.79%
CVaR −1.55% −0.94% −0.78% −0.76% −1.59%
Sortino Ratio 1.1922 1.7462 1.8061 1.7683 1.1653
EUR 2000-2020
Return 3.22% 3.41% 3.14% 3.00% 3.38%
Standard Deviation 8.61% 4.70% 4.81% 4.60% 9.00%
Sharpe Ratio 0.3735 0.7254 0.6521 0.6516 0.3753
Cumulative Return 91.47% 98.77% 88.47% 83.29% 97.65%
Worst Drawdown 28.95% 10.64% 9.79% 11.50% 47.25%
Average Drawdown 1.69% 0.98% 1.15% 1.10% 1.68%
Average Length 38.0152 37.2932 42.6154 45.0090 46.0459
Average Recovery 21.4015 21.1353 21.4444 22.4595 23.1284
Hurst Index 0.3379 0.3041 0.3062 0.3047 0.3699
VaR −0.88% −0.46% −0.47% −0.45% −0.80%
CVaR −1.74% −0.72% −0.73% −0.70% −0.95%
Sortino Ratio 0.5720 1.0661 0.9684 0.9640 0.5740
EUR 2010-2020
Return 5.04% 3.40% 3.38% 3.50% 2.07%
Standard Deviation 9.61% 4.89% 4.95% 4.75% 8.71%
Sharpe Ratio 0.5245 0.6952 0.6830 0.7363 0.2381
Cumulative Return 65.63% 40.90% 40.72% 42.36% 23.44%
Worst Drawdown 23.28% 9.94% 9.85% 10.10% 21.59%
Average Drawdown 1.59% 1.34% 1.15% 1.20% 2.45%
Average Length 26.5106 46.1296 47.0943 38.9062 82.0323
Average Recovery 13.7766 28.6111 31.5849 24.1875 34.3226
Hurst Index 0.3461 0.3241 0.3263 0.3279 0.3168
VaR −1.00% −0.49% −0.49% −0.47% −0.90%
CVaR −2.19% −0.83% −0.84% −0.83% −1.65%
Sortino Ratio 0.7751 1.0099 0.9961 1.0681 0.3857

Two funds 70/30

Two funds 70/30: Modelli dinamici vincolati e modello statico standard
Performance delle 12 misure statistiche calcolate sulla base di ciascun modello di ottimizzazione
Misura statisticaModello StaticoModelli dinamici
vincolati
StandardBoudt SD ROIBoudt SD RandomBoudt CVaR ROITCOV ROBNaif
USD 1985-2020
Return 9.23% 9.01% 9.02% 9.18% 9.00% 8.98%
Standard Deviation 12.44% 11.67% 11.67% 11.88% 11.67% 11.67%
Sharpe Ratio 0.7421 0.7721 0.7725 0.7729 0.7712 0.7695
Cumulative Return 2,294.75% 2,127.04% 2,130.94% 2,256.23% 2,117.49% 2,104.68%
Worst Drawdown 38.29% 35.32% 35.32% 35.29% 35.32% 35.32%
Average Drawdown 1.46% 1.37% 1.36% 1.40% 1.37% 1.37%
Average Length 18.5702 18.1438 18.1049 18.1006 18.1352 18.2241
Average Recovery 10.0373 9.5944 9.5717 9.3448 9.5944 9.6422
Hurst Index 0.3704 0.3716 0.3716 0.3696 0.3716 0.3716
VaR −1.11% −1.03% −1.03% −1.06% −1.03% −1.03%
CVaR −1.55% −1.39% −1.39% −1.65% −1.39% −1.39%
Sortino Ratio 1.0762 1.1130 1.1136 1.1159 1.1118 1.1097
USD 2000-2020
Return 6.67% 6.40% 6.40% 6.69% 6.41% 6.40%
Standard Deviation 13.31% 12.35% 12.35% 12.52% 12.35% 12.35%
Sharpe Ratio 0.5011 0.5184 0.5184 0.5341 0.5190 0.5184
Cumulative Return 275.84% 257.29% 257.29% 277.30% 257.73% 257.29%
Worst Drawdown 39.81% 37.00% 37.00% 37.27% 36.96% 37.00%
Average Drawdown 1.40% 1.29% 1.29% 1.34% 1.29% 1.29%
Average Length 19.7967 19.5020 19.5020 19.4200 19.4940 19.5020
Average Recovery 10.3740 10.0683 10.0683 9.8840 10.0602 10.0683
Hurst Index 0.3562 0.3597 0.3597 0.3585 0.3597 0.3597
VaR −1.18% −1.09% −1.09% −1.12% −1.09% −1.09%
CVaR −1.53% −1.34% −1.34% −1.50% −1.34% −1.34%
Sortino Ratio 0.7746 0.7925 0.7925 0.8138 0.7933 0.7925
USD 2010-2020
Return 10.64% 10.16% 10.16% 10.22% 10.15% 10.15%
Standard Deviation 11.95% 11.10% 11.10% 11.34% 11.10% 11.10%
Sharpe Ratio 0.8898 0.9153 0.9156 0.9020 0.9146 0.9145
Cumulative Return 182.26% 169.94% 170.02% 171.67% 169.74% 169.73%
Worst Drawdown 25.84% 24.24% 24.24% 24.24% 24.24% 24.24%
Average Drawdown 1.16% 1.07% 1.07% 1.11% 1.07% 1.07%
Average Length 12.0359 11.8827 11.8827 12.1399 11.8878 11.8878
Average Recovery 6.0769 5.9286 5.9286 6.1347 5.9286 5.9286
Hurst Index 0.3878 0.3934 0.3934 0.3907 0.3934 0.3934
VaR −1.07% −0.98% −0.98% −1.02% −0.98% −0.98%
CVaR −1.72% −1.32% −1.32% −1.64% −1.32% −1.32%
Sortino Ratio 1.2498 1.2796 1.2801 1.2634 1.2787 1.2786
USD --> EUR 1985-2020
Return 8.19% 8.14% 8.14% 8.38% 8.11% 8.11%
Standard Deviation 16.55% 15.99% 15.99% 16.38% 15.98% 15.98%
Sharpe Ratio 0.4949 0.5094 0.5094 0.5117 0.5076 0.5071
Cumulative Return 1,596.89% 1,570.40% 1,570.40% 1,708.91% 1,553.78% 1,549.58%
Worst Drawdown 50.24% 46.94% 46.94% 46.46% 47.31% 47.44%
Average Drawdown 2.95% 2.84% 2.84% 2.88% 2.84% 2.86%
Average Length 37.7931 36.9578 36.9578 36.4708 37.1398 37.4573
Average Recovery 16.0776 16.2658 16.2658 16.4750 16.3814 16.5299
Hurst Index 0.3372 0.3356 0.3356 0.3403 0.3356 0.3356
VaR −1.63% −1.58% −1.58% −1.61% −1.58% −1.58%
CVaR −3.17% −3.03% −3.03% −3.23% −3.03% −3.03%
Sortino Ratio 0.7899 0.8069 0.8069 0.8100 0.8046 0.8039
USD --> EUR 2000-2020
Return 5.19% 5.03% 5.03% 4.99% 5.04% 5.03%
Standard Deviation 15.70% 14.99% 14.99% 15.33% 14.99% 14.99%
Sharpe Ratio 0.3303 0.3357 0.3357 0.3256 0.3360 0.3354
Cumulative Return 182.07% 173.73% 173.73% 171.60% 173.95% 173.44%
Worst Drawdown 48.10% 45.59% 45.59% 48.04% 45.59% 45.69%
Average Drawdown 2.24% 2.06% 2.06% 2.15% 2.06% 2.06%
Average Length 43.7652 41.9167 41.9167 44.1579 41.9167 41.9167
Average Recovery 17.8696 17.9167 17.9167 19.8947 17.9167 17.9167
Hurst Index 0.3263 0.3252 0.3252 0.3267 0.3252 0.3252
VaR −1.52% −1.46% −1.46% −1.48% −1.46% −1.46%
CVaR −2.55% −2.45% −2.45% −2.46% −2.45% −2.45%
Sortino Ratio 0.5651 0.5677 0.5677 0.5560 0.5681 0.5673
USD --> EUR 2010-2020
Return 11.40% 10.89% 10.89% 11.27% 10.88% 10.88%
Standard Deviation 13.53% 12.81% 12.81% 13.17% 12.81% 12.81%
Sharpe Ratio 0.8430 0.8500 0.8500 0.8558 0.8498 0.8498
Cumulative Return 203.04% 188.92% 188.92% 199.24% 188.79% 188.79%
Worst Drawdown 25.30% 23.71% 23.71% 23.71% 23.71% 23.71%
Average Drawdown 1.77% 1.67% 1.67% 1.75% 1.67% 1.67%
Average Length 19.3492 19.0703 19.0703 19.3571 19.0703 19.0703
Average Recovery 10.0952 10.8906 10.8906 11.0794 10.8906 10.8906
Hurst Index 0.3756 0.3749 0.3749 0.3721 0.3749 0.3749
VaR −1.25% −1.18% −1.18% −1.23% −1.18% −1.18%
CVaR −2.34% −2.21% −2.21% −2.40% −2.21% −2.21%
Sortino Ratio 1.2192 1.2275 1.2275 1.2350 1.2271 1.2271
EUR 1985-2020
Return 6.46% 6.47% 6.39% 6.54% 6.49% 6.43%
Standard Deviation 9.81% 9.15% 9.13% 9.33% 9.16% 9.14%
Sharpe Ratio 0.6582 0.7070 0.6995 0.7008 0.7077 0.7031
Cumulative Return 849.46% 853.84% 827.55% 874.83% 858.27% 839.35%
Worst Drawdown 40.09% 37.44% 37.44% 37.40% 37.44% 37.44%
Average Drawdown 2.01% 1.94% 1.91% 2.00% 1.95% 1.92%
Average Length 38.0495 37.1982 36.8515 38.4000 37.2026 36.8734
Average Recovery 22.5000 21.9207 21.6987 22.6455 21.9251 21.7205
Hurst Index 0.3415 0.3400 0.3403 0.3380 0.3399 0.3402
VaR −0.97% −0.92% −0.91% −0.94% −0.92% −0.91%
CVaR −2.10% −1.98% −1.97% −2.01% −1.98% −1.98%
Sortino Ratio 0.9536 1.0156 1.0056 1.0076 1.0165 1.0104
EUR 2000-2020
Return 3.08% 3.11% 3.11% 3.06% 3.12% 3.11%
Standard Deviation 12.05% 11.14% 11.14% 11.50% 11.14% 11.14%
Sharpe Ratio 0.2556 0.2795 0.2795 0.2663 0.2796 0.2792
Cumulative Return 86.27% 87.56% 87.56% 85.64% 87.64% 87.47%
Worst Drawdown 41.63% 38.60% 38.60% 42.12% 38.60% 38.60%
Average Drawdown 2.51% 2.25% 2.25% 2.52% 2.25% 2.25%
Average Length 48.4712 46.6111 46.6111 51.4286 46.6111 46.6111
Average Recovery 29.0577 27.6111 27.6111 31.0918 27.6111 27.6111
Hurst Index 0.3408 0.3405 0.3405 0.3368 0.3405 0.3405
VaR −1.22% −1.13% −1.13% −1.17% −1.13% −1.13%
CVaR −2.39% −2.22% −2.22% −2.27% −2.22% −2.22%
Sortino Ratio 0.4322 0.4587 0.4587 0.4429 0.4590 0.4584
EUR 2010-2020
Return 5.57% 5.42% 5.42% 5.33% 5.42% 5.42%
Standard Deviation 13.25% 12.30% 12.30% 12.49% 12.30% 12.30%
Sharpe Ratio 0.4202 0.4405 0.4405 0.4266 0.4405 0.4405
Cumulative Return 74.42% 71.89% 71.89% 70.40% 71.89% 71.89%
Worst Drawdown 29.25% 27.78% 27.78% 27.78% 27.78% 27.78%
Average Drawdown 2.14% 2.06% 2.06% 2.17% 2.06% 2.06%
Average Length 28.3409 28.2727 28.2727 30.0602 28.2727 28.2727
Average Recovery 15.5227 15.7045 15.7045 16.9518 15.7045 15.7045
Hurst Index 0.3527 0.3515 0.3515 0.3496 0.3515 0.3515
VaR −1.38% −1.29% −1.29% −1.31% −1.29% −1.29%
CVaR −2.98% −2.78% −2.78% −2.77% −2.78% −2.78%
Sortino Ratio 0.6557 0.6771 0.6771 0.6597 0.6771 0.6771
Two funds 70/30: Modelli dinamici non vincolati e modello statico 1/N
Performance delle 12 misure statistiche calcolate sulla base di ciascun modello di ottimizzazione
Misura statisticaModello StaticoModelli dinamici non vincolati
1/NBoudt SD No-boxHRPBoudt Random MVPBoudt Random HS
USD 1985-2020
Return 8.15% 7.01% 6.73% 6.82% 8.51%
Standard Deviation 9.71% 7.54% 7.43% 7.50% 9.94%
Sharpe Ratio 0.8389 0.9297 0.9064 0.9082 0.8561
Cumulative Return 1,572.92% 1,042.09% 940.62% 971.17% 1,785.97%
Worst Drawdown 26.04% 19.80% 20.05% 20.26% 23.62%
Average Drawdown 1.18% 0.96% 1.04% 0.99% 1.38%
Average Length 17.8962 18.5793 20.7115 19.6799 19.2255
Average Recovery 9.2839 9.7621 11.5623 10.8972 9.5786
Hurst Index 0.3720 0.3481 0.3391 0.3461 0.3166
VaR −0.85% −0.68% −0.68% −0.67% −0.96%
CVaR −1.06% −1.03% −1.11% −0.99% −1.80%
Sortino Ratio 1.2038 1.3536 1.3230 1.3278 1.2441
USD 2000-2020
Return 5.61% 3.67% 3.32% 3.42% 3.95%
Standard Deviation 9.73% 5.92% 5.91% 5.89% 10.55%
Sharpe Ratio 0.5763 0.6205 0.5615 0.5813 0.3741
Cumulative Return 206.22% 109.50% 95.41% 99.49% 121.19%
Worst Drawdown 27.89% 18.92% 19.70% 19.33% 41.82%
Average Drawdown 1.07% 0.60% 0.70% 0.65% 1.53%
Average Length 18.5211 18.3409 22.0404 20.5485 31.5190
Average Recovery 9.5862 10.8750 13.2466 12.4810 20.9937
Hurst Index 0.3735 0.3941 0.3886 0.3929 0.3947
VaR −0.82% −0.43% −0.46% −0.43% −0.47%
CVaR −0.82% −0.43% −0.46% −0.43% −0.47%
Sortino Ratio 0.8579 0.9024 0.8204 0.8480 0.5834
USD 2010-2020
Return 8.73% 5.12% 4.33% 4.69% 5.91%
Standard Deviation 8.61% 4.29% 4.03% 4.03% 7.57%
Sharpe Ratio 1.0142 1.1929 1.0750 1.1621 0.7804
Cumulative Return 136.12% 66.96% 54.52% 60.06% 80.29%
Worst Drawdown 19.33% 9.43% 8.96% 9.38% 17.94%
Average Drawdown 0.80% 0.43% 0.47% 0.43% 0.83%
Average Length 10.8774 12.2158 15.0633 13.2443 13.9763
Average Recovery 5.4151 6.9263 8.6329 8.0568 8.0414
Hurst Index 0.4136 0.4648 0.4668 0.4719 0.3943
VaR −0.68% 0.00% 0.00% 0.00% −0.64%
CVaR −0.68% −0.77% −0.77% −0.77% −0.64%
Sortino Ratio 1.4008 1.6077 1.4663 1.5719 1.0945
USD → EUR 1985-2020
Return 7.12% 7.20% 6.74% 7.09% 10.18%
Standard Deviation 15.22% 14.19% 14.28% 14.25% 17.15%
Sharpe Ratio 0.4677 0.5076 0.4720 0.4975 0.5936
Cumulative Return 1,085.41% 1,120.46% 943.82% 1,073.82% 3,168.75%
Worst Drawdown 46.38% 48.67% 46.90% 49.49% 41.30%
Average Drawdown 2.85% 2.85% 2.86% 2.96% 3.00%
Average Length 43.0293 42.6893 44.8223 44.0800 30.1419
Average Recovery 18.6146 25.8010 25.5990 26.0000 17.5294
Hurst Index 0.3254 0.2773 0.3052 0.2760 0.3541
VaR −1.50% −1.40% −1.41% −1.40% −1.64%
CVaR −2.59% −2.11% −2.22% −2.11% −3.43%
Sortino Ratio 0.7538 0.8078 0.7589 0.7952 0.9212
USD → EUR 2000-2020
Return 4.14% 2.89% 3.00% 2.68% 3.35%
Standard Deviation 13.36% 12.07% 11.91% 12.09% 14.48%
Sharpe Ratio 0.3099 0.2396 0.2521 0.2217 0.2315
Cumulative Return 129.82% 79.51% 83.47% 72.02% 96.70%
Worst Drawdown 44.67% 49.70% 47.02% 51.00% 55.46%
Average Drawdown 1.95% 2.21% 1.94% 2.40% 2.63%
Average Length 47.3738 60.6786 58.5172 67.1579 59.3256
Average Recovery 20.3364 38.6667 39.8851 44.3289 28.0465
Hurst Index 0.3282 0.3040 0.3117 0.3047 0.3491
VaR −1.31% −1.21% −1.19% −1.21% −1.32%
CVaR −2.15% −1.87% −1.82% −1.86% −1.80%
Sortino Ratio 0.5236 0.4195 0.4369 0.3953 0.4220
USD → EUR 2010-2020
Return 9.48% 6.37% 7.06% 6.09% 9.79%
Standard Deviation 11.02% 8.41% 8.66% 8.44% 11.49%
Sharpe Ratio 0.8604 0.7566 0.8154 0.7216 0.8519
Cumulative Return 153.50% 88.44% 101.52% 83.43% 160.87%
Worst Drawdown 20.32% 14.94% 11.86% 15.52% 19.11%
Average Drawdown 1.48% 1.35% 1.30% 1.43% 1.87%
Average Length 20.1639 25.8854 24.0485 27.9551 22.2072
Average Recovery 10.4754 13.4583 12.2136 14.5618 10.5315
Hurst Index 0.3826 0.3763 0.3775 0.3778 0.3371
VaR −1.01% −0.77% −0.80% −0.76% −1.13%
CVaR −1.76% −1.18% −1.32% −1.14% −2.02%
Sortino Ratio 1.2438 1.1312 1.2056 1.0831 1.2422
EUR 1985-2020
Return 6.11% 6.29% 6.03% 5.75% 6.44%
Standard Deviation 7.29% 5.14% 4.84% 4.72% 7.86%
Sharpe Ratio 0.8381 1.2242 1.2474 1.2184 0.8186
Cumulative Return 743.31% 798.04% 722.17% 647.65% 842.85%
Worst Drawdown 28.97% 24.18% 19.79% 20.98% 31.19%
Average Drawdown 1.44% 1.16% 1.07% 1.03% 1.99%
Average Length 30.0356 30.4928 29.6725 30.6232 43.5590
Average Recovery 15.4377 16.6304 14.9789 15.5036 24.8564
Hurst Index 0.3340 0.2987 0.2868 0.2881 0.2943
VaR −0.74% −0.52% −0.48% −0.46% −0.79%
CVaR −1.55% −0.94% −0.78% −0.76% −1.59%
Sortino Ratio 1.1922 1.7462 1.8061 1.7683 1.1653
EUR 2000-2020
Return 3.22% 3.41% 3.14% 3.00% 3.38%
Standard Deviation 8.61% 4.70% 4.81% 4.60% 9.00%
Sharpe Ratio 0.3735 0.7254 0.6521 0.6516 0.3753
Cumulative Return 91.47% 98.77% 88.47% 83.29% 97.65%
Worst Drawdown 28.95% 10.64% 9.79% 11.50% 47.25%
Average Drawdown 1.69% 0.98% 1.15% 1.10% 1.68%
Average Length 38.0152 37.2932 42.6154 45.0090 46.0459
Average Recovery 21.4015 21.1353 21.4444 22.4595 23.1284
Hurst Index 0.3379 0.3041 0.3062 0.3047 0.3699
VaR −0.88% −0.46% −0.47% −0.45% −0.80%
CVaR −1.74% −0.72% −0.73% −0.70% −0.95%
Sortino Ratio 0.5720 1.0661 0.9684 0.9640 0.5740
EUR 2010-2020
Return 5.04% 3.40% 3.38% 3.50% 2.07%
Standard Deviation 9.61% 4.89% 4.95% 4.75% 8.71%
Sharpe Ratio 0.5245 0.6952 0.6830 0.7363 0.2381
Cumulative Return 65.63% 40.90% 40.72% 42.36% 23.44%
Worst Drawdown 23.28% 9.94% 9.85% 10.10% 21.59%
Average Drawdown 1.59% 1.34% 1.15% 1.20% 2.45%
Average Length 26.5106 46.1296 47.0943 38.9062 82.0323
Average Recovery 13.7766 28.6111 31.5849 24.1875 34.3226
Hurst Index 0.3461 0.3241 0.3263 0.3279 0.3168
VaR −1.00% −0.49% −0.49% −0.47% −0.90%
CVaR −2.19% −0.83% −0.84% −0.83% −1.65%
Sortino Ratio 0.7751 1.0099 0.9961 1.0681 0.3857

Two funds 80/20

Two funds 80/20: Modelli dinamici vincolati e modello statico standard
Performance delle 12 misure statistiche calcolate sulla base di ciascun modello di ottimizzazione
Misura statisticaModello StaticoModelli dinamici
vincolati
StandardBoudt SD ROIBoudt SD RandomBoudt CVaR ROITCOV ROBNaif
USD 1985-2020
Return 9.73% 9.49% 9.48% 9.70% 9.47% 9.47%
Standard Deviation 14.07% 13.24% 13.24% 13.42% 13.24% 13.24%
Sharpe Ratio 0.6915 0.7172 0.7158 0.7230 0.7156 0.7158
Cumulative Return 2,722.93% 2,509.77% 2,494.47% 2,692.37% 2,492.71% 2,493.66%
Worst Drawdown 44.17% 41.28% 41.28% 41.25% 41.28% 41.28%
Average Drawdown 1.65% 1.56% 1.56% 1.56% 1.56% 1.56%
Average Length 18.5546 18.5131 18.5624 18.4130 18.5624 18.5218
Average Recovery 10.5546 10.5109 10.5427 10.1500 10.5427 10.5175
Hurst Index 0.3676 0.3691 0.3691 0.3676 0.3691 0.3691
VaR −1.26% −1.18% −1.18% −1.21% −1.18% −1.18%
CVaR −1.85% −1.71% −1.71% −1.92% −1.71% −1.70%
Sortino Ratio 1.0166 1.0462 1.0444 1.0552 1.0442 1.0444
USD 2000-2020
Return 7.16% 6.91% 6.91% 7.19% 6.91% 6.91%
Standard Deviation 15.27% 14.27% 14.27% 14.44% 14.27% 14.27%
Sharpe Ratio 0.4686 0.4839 0.4842 0.4981 0.4844 0.4839
Cumulative Return 312.74% 293.57% 293.84% 315.67% 294.05% 293.57%
Worst Drawdown 45.31% 42.64% 42.64% 42.86% 42.60% 42.64%
Average Drawdown 1.64% 1.52% 1.52% 1.58% 1.51% 1.52%
Average Length 20.5462 20.1860 20.1860 19.9143 20.1029 20.1860
Average Recovery 11.3067 10.6281 10.6281 10.2204 10.5802 10.6281
Hurst Index 0.3497 0.3528 0.3528 0.3514 0.3528 0.3528
VaR −1.37% −1.27% −1.27% −1.30% −1.27% −1.27%
CVaR −1.87% −1.71% −1.71% −1.87% −1.71% −1.71%
Sortino Ratio 0.7426 0.7571 0.7574 0.7764 0.7578 0.7571
USD 2010-2020
Return 11.57% 11.10% 11.10% 11.17% 11.09% 11.10%
Standard Deviation 13.70% 12.82% 12.82% 13.07% 12.82% 12.82%
Sharpe Ratio 0.8445 0.8656 0.8656 0.8545 0.8647 0.8656
Cumulative Return 207.74% 194.66% 194.66% 196.44% 194.36% 194.66%
Worst Drawdown 28.97% 27.41% 27.41% 27.41% 27.41% 27.41%
Average Drawdown 1.31% 1.22% 1.22% 1.26% 1.22% 1.22%
Average Length 12.2062 12.1753 12.1753 12.1907 12.1753 12.1753
Average Recovery 6.2062 6.1907 6.1907 6.1959 6.1907 6.1907
Hurst Index 0.3779 0.3827 0.3827 0.3803 0.3826 0.3827
VaR −1.25% −1.16% −1.16% −1.20% −1.16% −1.16%
CVaR −2.28% −2.03% −2.03% −2.26% −2.03% −2.03%
Sortino Ratio 1.1985 1.2220 1.2220 1.2086 1.2208 1.2220
USD → EUR 1985-2020
Return 8.69% 8.63% 8.63% 8.88% 8.60% 8.59%
Standard Deviation 17.55% 16.92% 16.93% 17.36% 16.91% 16.91%
Sharpe Ratio 0.4949 0.5104 0.5100 0.5113 0.5084 0.5079
Cumulative Return 1,900.30% 1,865.32% 1,865.31% 2,030.75% 1,842.60% 1,835.75%
Worst Drawdown 53.97% 50.60% 50.63% 50.00% 51.17% 51.34%
Average Drawdown 3.06% 2.81% 2.81% 3.02% 2.83% 2.83%
Average Length 37.0424 35.1124 35.2460 36.0537 35.4008 35.4049
Average Recovery 16.6229 15.9839 16.0121 16.3678 16.1255 16.1296
Hurst Index 0.3415 0.3398 0.3399 0.3431 0.3398 0.3399
VaR −1.72% −1.66% −1.66% −1.70% −1.66% −1.66%
CVaR −3.44% −3.32% −3.32% −3.51% −3.32% −3.32%
Sortino Ratio 0.7927 0.8100 0.8096 0.8120 0.8074 0.8066
USD → EUR 2000-2020
Return 5.67% 5.53% 5.53% 5.48% 5.43% 5.42%
Standard Deviation 17.19% 16.41% 16.42% 16.75% 16.37% 16.37%
Sharpe Ratio 0.3297 0.3372 0.3371 0.3271 0.3318 0.3311
Cumulative Return 209.77% 201.75% 201.89% 198.70% 196.04% 195.16%
Worst Drawdown 50.49% 47.97% 48.01% 50.35% 48.95% 49.10%
Average Drawdown 2.50% 2.32% 2.32% 2.48% 2.36% 2.36%
Average Length 42.9316 42.5424 42.5508 44.5221 43.2931 43.3017
Average Recovery 17.1538 17.2119 17.2203 18.4248 17.5517 17.5603
Hurst Index 0.3296 0.3273 0.3273 0.3319 0.3275 0.3276
VaR −1.65% −1.58% −1.58% −1.60% −1.58% −1.58%
CVaR −2.77% −2.67% −2.67% −2.67% −2.66% −2.66%
Sortino Ratio 0.5736 0.5785 0.5785 0.5668 0.5712 0.5702
USD → EUR 2010-2020
Return 12.35% 11.83% 11.85% 12.18% 11.83% 11.83%
Standard Deviation 14.97% 14.21% 14.21% 14.57% 14.21% 14.21%
Sharpe Ratio 0.8245 0.8330 0.8334 0.8362 0.8328 0.8330
Cumulative Return 230.39% 215.28% 215.58% 225.48% 215.15% 215.28%
Worst Drawdown 28.42% 26.86% 26.86% 26.86% 26.86% 26.86%
Average Drawdown 1.98% 1.81% 1.81% 1.94% 1.81% 1.81%
Average Length 19.2857 19.1575 19.1654 18.8605 19.1575 19.1575
Average Recovery 9.7302 9.9528 9.9606 9.1705 9.9528 9.9528
Hurst Index 0.3761 0.3758 0.3758 0.3730 0.3758 0.3758
VaR −1.38% −1.31% −1.31% −1.36% −1.31% −1.31%
CVaR −2.60% −2.49% −2.48% −2.69% −2.49% −2.49%
Sortino Ratio 1.1975 1.2068 1.2073 1.2110 1.2065 1.2068
EUR 1985-2020
Return 6.58% 6.56% 6.53% 6.61% 6.62% 6.50%
Standard Deviation 11.25% 10.53% 10.52% 10.72% 10.56% 10.53%
Sharpe Ratio 0.5847 0.6226 0.6206 0.6170 0.6270 0.6174
Cumulative Return 889.47% 881.92% 871.94% 899.73% 902.70% 862.96%
Worst Drawdown 46.12% 43.02% 43.02% 43.12% 43.01% 43.02%
Average Drawdown 2.27% 2.18% 2.14% 2.21% 2.19% 2.15%
Average Length 41.9703 41.0631 40.4785 40.6683 41.0631 40.4928
Average Recovery 26.0644 25.4078 24.6459 25.1971 25.4612 25.0383
Hurst Index 0.3430 0.3422 0.3424 0.3403 0.3420 0.3423
VaR −1.11% −1.04% −1.04% −1.07% −1.04% −1.04%
CVaR −2.34% −2.23% −2.23% −2.28% −2.24% −2.23%
Sortino Ratio 0.8625 0.9087 0.9062 0.9017 0.9146 0.9018
EUR 2000-2020
Return 2.96% 3.01% 3.01% 2.94% 3.01% 3.01%
Standard Deviation 13.91% 12.96% 12.96% 13.33% 12.96% 12.96%
Sharpe Ratio 0.2128 0.2322 0.2322 0.2207 0.2326 0.2322
Cumulative Return 81.89% 83.73% 83.73% 81.29% 83.89% 83.73%
Worst Drawdown 47.44% 44.58% 44.58% 47.90% 44.58% 44.58%
Average Drawdown 2.96% 2.84% 2.84% 2.77% 2.84% 2.84%
Average Length 56.1333 55.4725 55.4725 54.8913 55.4725 55.4725
Average Recovery 34.8556 34.0000 34.0000 33.8152 34.0000 34.0000
Hurst Index 0.3415 0.3412 0.3412 0.3379 0.3412 0.3412
VaR −1.40% −1.31% −1.31% −1.35% −1.31% −1.31%
CVaR −2.72% −2.56% −2.56% −2.61% −2.56% −2.56%
Sortino Ratio 0.3866 0.4065 0.4065 0.3932 0.4070 0.4065
EUR 2010-2020
Return 5.80% 5.66% 5.66% 5.57% 5.66% 5.66%
Standard Deviation 15.19% 14.20% 14.20% 14.39% 14.20% 14.20%
Sharpe Ratio 0.3817 0.3984 0.3984 0.3869 0.3985 0.3984
Cumulative Return 78.34% 75.96% 75.96% 74.43% 75.97% 75.96%
Worst Drawdown 32.14% 30.70% 30.70% 30.70% 30.70% 30.70%
Average Drawdown 2.41% 2.33% 2.33% 2.43% 2.33% 2.33%
Average Length 28.1124 28.7471 28.7471 30.5244 28.7471 28.7471
Average Recovery 15.7416 16.0575 16.0575 17.1707 16.0575 16.0575
Hurst Index 0.3549 0.3539 0.3539 0.3522 0.3539 0.3539
VaR −1.58% −1.48% −1.48% −1.50% −1.48% −1.48%
CVaR −3.38% −3.18% −3.18% −3.17% −3.18% −3.18%
Sortino Ratio 0.6166 0.6325 0.6325 0.6185 0.6326 0.6325
Two funds 80/20: Modelli dinamici non vincolati e modello statico 1/N
Performance delle 12 misure statistiche calcolate sulla base di ciascun modello di ottimizzazione
Misura statisticaModello StaticoModelli dinamici non vincolati
1/NBoudt SD No-boxHRPBoudt Random MVPBoudt Random HS
USD 1985-2020
Return 8.15% 7.01% 6.73% 6.82% 8.51%
Standard Deviation 9.71% 7.54% 7.43% 7.50% 9.94%
Sharpe Ratio 0.8389 0.9297 0.9064 0.9082 0.8561
Cumulative Return 1,572.92% 1,042.09% 940.62% 971.17% 1,785.97%
Worst Drawdown 26.04% 19.80% 20.05% 20.26% 23.62%
Average Drawdown 1.18% 0.96% 1.04% 0.99% 1.38%
Average Length 17.8962 18.5793 20.7115 19.6799 19.2255
Average Recovery 9.2839 9.7621 11.5623 10.8972 9.5786
Hurst Index 0.3720 0.3481 0.3391 0.3461 0.3166
VaR −0.85% −0.68% −0.68% −0.67% −0.96%
CVaR −1.06% −1.03% −1.11% −0.99% −1.80%
Sortino Ratio 1.2038 1.3536 1.3230 1.3278 1.2441
USD 2000-2020
Return 5.61% 3.67% 3.32% 3.42% 3.95%
Standard Deviation 9.73% 5.92% 5.91% 5.89% 10.55%
Sharpe Ratio 0.5763 0.6205 0.5615 0.5813 0.3741
Cumulative Return 206.22% 109.50% 95.41% 99.49% 121.19%
Worst Drawdown 27.89% 18.92% 19.70% 19.33% 41.82%
Average Drawdown 1.07% 0.60% 0.70% 0.65% 1.53%
Average Length 18.5211 18.3409 22.0404 20.5485 31.5190
Average Recovery 9.5862 10.8750 13.2466 12.4810 20.9937
Hurst Index 0.3735 0.3941 0.3886 0.3929 0.3947
VaR −0.82% −0.43% −0.46% −0.43% −0.47%
CVaR −0.82% −0.43% −0.46% −0.43% −0.47%
Sortino Ratio 0.8579 0.9024 0.8204 0.8480 0.5834
USD 2010-2020
Return 8.73% 5.12% 4.33% 4.69% 5.91%
Standard Deviation 8.61% 4.29% 4.03% 4.03% 7.57%
Sharpe Ratio 1.0142 1.1929 1.0750 1.1621 0.7804
Cumulative Return 136.12% 66.96% 54.52% 60.06% 80.29%
Worst Drawdown 19.33% 9.43% 8.96% 9.38% 17.94%
Average Drawdown 0.80% 0.43% 0.47% 0.43% 0.83%
Average Length 10.8774 12.2158 15.0633 13.2443 13.9763
Average Recovery 5.4151 6.9263 8.6329 8.0568 8.0414
Hurst Index 0.4136 0.4648 0.4668 0.4719 0.3943
VaR −0.68% 0.00% 0.00% 0.00% −0.64%
CVaR −0.68% −1.75% −1.75% −1.75% −0.64%
Sortino Ratio 1.4008 1.6077 1.4663 1.5719 1.0945
USD → EUR 1985-2020
Return 7.12% 7.20% 6.74% 7.09% 10.18%
Standard Deviation 15.22% 14.19% 14.28% 14.25% 17.15%
Sharpe Ratio 0.4677 0.5076 0.4720 0.4975 0.5936
Cumulative Return 1,085.41% 1,120.46% 943.82% 1,073.82% 3,168.75%
Worst Drawdown 46.38% 48.67% 46.90% 49.49% 41.30%
Average Drawdown 2.85% 2.85% 2.86% 2.96% 3.00%
Average Length 43.0293 42.6893 44.8223 44.0800 30.1419
Average Recovery 18.6146 25.8010 25.5990 26.0000 17.5294
Hurst Index 0.3254 0.2773 0.3052 0.2760 0.3541
VaR −1.50% −1.40% −1.41% −1.40% −1.64%
CVaR −2.59% −2.11% −2.22% −2.11% −3.43%
Sortino Ratio 0.7538 0.8078 0.7589 0.7952 0.9212
USD → EUR 2000-2020
Return 4.14% 2.89% 3.00% 2.68% 3.35%
Standard Deviation 13.36% 12.07% 11.91% 12.09% 14.48%
Sharpe Ratio 0.3099 0.2396 0.2521 0.2217 0.2315
Cumulative Return 129.82% 79.51% 83.47% 72.02% 96.70%
Worst Drawdown 44.67% 49.70% 47.02% 51.00% 55.46%
Average Drawdown 1.95% 2.21% 1.94% 2.40% 2.63%
Average Length 47.3738 60.6786 58.5172 67.1579 59.3256
Average Recovery 20.3364 38.6667 39.8851 44.3289 28.0465
Hurst Index 0.3282 0.3040 0.3117 0.3047 0.3491
VaR −1.31% −1.21% −1.19% −1.21% −1.32%
CVaR −2.15% −1.87% −1.82% −1.86% −1.80%
Sortino Ratio 0.5236 0.4195 0.4369 0.3953 0.4220
USD → EUR 2010-2020
Return 9.48% 6.37% 7.06% 6.09% 9.79%
Standard Deviation 11.02% 8.41% 8.66% 8.44% 11.49%
Sharpe Ratio 0.8604 0.7566 0.8154 0.7216 0.8519
Cumulative Return 153.50% 88.44% 101.52% 83.43% 160.87%
Worst Drawdown 20.32% 14.94% 11.86% 15.52% 19.11%
Average Drawdown 1.48% 1.35% 1.30% 1.43% 1.87%
Average Length 20.1639 25.8854 24.0485 27.9551 22.2072
Average Recovery 10.4754 13.4583 12.2136 14.5618 10.5315
Hurst Index 0.3826 0.3763 0.3775 0.3778 0.3371
VaR −1.01% −0.77% −0.80% −0.76% −1.13%
CVaR −1.76% −1.18% −1.32% −1.14% −2.02%
Sortino Ratio 1.2438 1.1312 1.2056 1.0831 1.2422
EUR 1985-2020
Return 6.11% 6.29% 6.03% 5.75% 6.44%
Standard Deviation 7.29% 5.14% 4.84% 4.72% 7.86%
Sharpe Ratio 0.8381 1.2242 1.2474 1.2184 0.8186
Cumulative Return 743.31% 798.04% 722.17% 647.65% 842.85%
Worst Drawdown 28.97% 24.18% 19.79% 20.98% 31.19%
Average Drawdown 1.44% 1.16% 1.07% 1.03% 1.99%
Average Length 30.0356 30.4928 29.6725 30.6232 43.5590
Average Recovery 15.4377 16.6304 14.9789 15.5036 24.8564
Hurst Index 0.3340 0.2987 0.2868 0.2881 0.2943
VaR −0.74% −0.52% −0.48% −0.46% −0.79%
CVaR −1.55% −0.94% −0.78% −0.76% −1.59%
Sortino Ratio 1.1922 1.7462 1.8061 1.7683 1.1653
EUR 2000-2020
Return 3.22% 3.41% 3.14% 3.00% 3.38%
Standard Deviation 8.61% 4.70% 4.81% 4.60% 9.00%
Sharpe Ratio 0.3735 0.7254 0.6521 0.6516 0.3753
Cumulative Return 91.47% 98.77% 88.47% 83.29% 97.65%
Worst Drawdown 28.95% 10.64% 9.79% 11.50% 47.25%
Average Drawdown 1.69% 0.98% 1.15% 1.10% 1.68%
Average Length 38.0152 37.2932 42.6154 45.0090 46.0459
Average Recovery 21.4015 21.1353 21.4444 22.4595 23.1284
Hurst Index 0.3379 0.3041 0.3062 0.3047 0.3699
VaR −0.88% −0.46% −0.47% −0.45% −0.80%
CVaR −1.74% −0.72% −0.73% −0.70% −0.95%
Sortino Ratio 0.5720 1.0661 0.9684 0.9640 0.5740
EUR 2010-2020
Return 5.04% 3.40% 3.38% 3.50% 2.07%
Standard Deviation 9.61% 4.89% 4.95% 4.75% 8.71%
Sharpe Ratio 0.5245 0.6952 0.6830 0.7363 0.2381
Cumulative Return 65.63% 40.90% 40.72% 42.36% 23.44%
Worst Drawdown 23.28% 9.94% 9.85% 10.10% 21.59%
Average Drawdown 1.59% 1.34% 1.15% 1.20% 2.45%
Average Length 26.5106 46.1296 47.0943 38.9062 82.0323
Average Recovery 13.7766 28.6111 31.5849 24.1875 34.3226
Hurst Index 0.3461 0.3241 0.3263 0.3279 0.3168
VaR −1.00% −0.49% −0.49% −0.47% −0.90%
CVaR −2.19% −0.83% −0.84% −0.83% −1.65%
Sortino Ratio 0.7751 1.0099 0.9961 1.0681 0.3857

Two funds 90/10

Two funds 90/10: Modelli dinamici vincolati e modello statico standard
Performance delle 12 misure statistiche calcolate sulla base di ciascun modello di ottimizzazione
Misura statisticaModello StaticoModelli dinamici
vincolati
StandardBoudt SD ROIBoudt SD RandomBoudt CVaR ROITCOV ROBNaif
USD 1985-2020
Return 10.20% 9.95% 9.94% 10.18% 9.94% 9.93%
Standard Deviation 15.85% 14.95% 14.95% 15.11% 14.95% 14.94%
Sharpe Ratio 0.6438 0.6656 0.6653 0.6738 0.6654 0.6644
Cumulative Return 3,193.41% 2,932.38% 2,925.40% 3,166.15% 2,925.72% 2,908.15%
Worst Drawdown 49.89% 47.08% 47.08% 47.05% 47.08% 47.08%
Average Drawdown 1.78% 1.72% 1.71% 1.74% 1.71% 1.71%
Average Length 19.1959 19.1599 19.1599 18.7792 19.1191 19.2077
Average Recovery 10.6914 10.7365 10.7365 10.4084 10.7124 10.7630
Hurst Index 0.3645 0.3661 0.3661 0.3649 0.3661 0.3661
VaR −1.42% −1.34% −1.34% −1.36% −1.34% −1.34%
CVaR −2.10% −1.99% −1.99% −2.18% −1.98% −1.97%
Sortino Ratio 0.9639 0.9872 0.9868 0.9990 0.9869 0.9857
USD 2000-2020
Return 7.62% 7.39% 7.39% 7.66% 7.39% 7.38%
Standard Deviation 17.32% 16.29% 16.29% 16.46% 16.28% 16.29%
Sharpe Ratio 0.4396 0.4534 0.4534 0.4657 0.4540 0.4534
Cumulative Return 350.60% 331.24% 331.24% 354.76% 331.94% 331.23%
Worst Drawdown 50.53% 48.00% 48.00% 48.19% 47.96% 48.00%
Average Drawdown 1.88% 1.76% 1.76% 1.82% 1.76% 1.76%
Average Length 21.4737 20.6456 20.6456 20.7500 20.6456 20.6456
Average Recovery 11.7588 11.1772 11.1772 11.1441 11.1772 11.1772
Hurst Index 0.3486 0.3486 0.3486 0.3474 0.3486 0.3486
VaR −1.55% −1.46% −1.46% −1.49% −1.46% −1.46%
CVaR −2.13% −2.01% −2.01% −2.17% −2.01% −2.01%
Sortino Ratio 0.7166 0.7285 0.7285 0.7454 0.7293 0.7285
USD 2010-2020
Return 12.50% 12.03% 12.03% 12.09% 12.03% 12.03%
Standard Deviation 15.49% 14.59% 14.59% 14.84% 14.59% 14.59%
Sharpe Ratio 0.8067 0.8244 0.8244 0.8151 0.8245 0.8244
Cumulative Return 234.92% 220.97% 220.97% 222.87% 220.99% 220.97%
Worst Drawdown 32.02% 30.51% 30.51% 30.51% 30.51% 30.51%
Average Drawdown 1.46% 1.37% 1.37% 1.41% 1.37% 1.37%
Average Length 12.2953 12.2474 12.2474 12.1795 12.2474 12.2474
Average Recovery 6.2383 6.2216 6.2216 6.1744 6.2216 6.2216
Hurst Index 0.3750 0.3761 0.3761 0.3740 0.3761 0.3761
VaR −1.42% −1.34% −1.34% −1.37% −1.34% −1.34%
CVaR −2.66% −2.49% −2.49% −2.68% −2.49% −2.49%
Sortino Ratio 1.1581 1.1766 1.1766 1.1656 1.1767 1.1766
USD → EUR 1985-2020
Return 9.15% 9.08% 9.08% 9.35% 9.02% 9.02%
Standard Deviation 18.76% 18.06% 18.06% 18.54% 18.04% 18.03%
Sharpe Ratio 0.4880 0.5032 0.5032 0.5041 0.4999 0.5002
Cumulative Return 2,233.68% 2,181.06% 2,181.06% 2,385.79% 2,131.76% 2,131.01%
Worst Drawdown 57.90% 54.99% 54.99% 54.07% 55.81% 55.81%
Average Drawdown 3.09% 3.00% 3.00% 3.04% 3.03% 3.04%
Average Length 35.6408 35.7541 35.7541 34.4506 36.0661 36.2158
Average Recovery 16.3592 16.2582 16.2582 15.9842 16.4215 16.4979
Hurst Index 0.3441 0.3431 0.3431 0.3455 0.3431 0.3432
VaR −1.82% −1.76% −1.76% −1.80% −1.76% −1.76%
CVaR −3.67% −3.58% −3.58% −3.74% −3.57% −3.56%
Sortino Ratio 0.7886 0.8045 0.8045 0.8072 0.8002 0.8006
USD → EUR 2000-2020
Return 6.12% 5.97% 5.97% 5.93% 5.89% 5.89%
Standard Deviation 18.85% 18.00% 18.00% 18.34% 17.95% 17.95%
Sharpe Ratio 0.3247 0.3318 0.3316 0.3234 0.3280 0.3280
Cumulative Return 238.18% 228.56% 228.41% 225.99% 223.42% 223.42%
Worst Drawdown 53.09% 50.80% 50.82% 52.84% 51.57% 51.57%
Average Drawdown 2.64% 2.52% 2.52% 2.61% 2.55% 2.55%
Average Length 41.8500 41.1393 41.1475 41.8500 41.5041 41.5041
Average Recovery 16.4750 16.2459 16.2541 16.9083 16.4380 16.4380
Hurst Index 0.3340 0.3318 0.3318 0.3369 0.3320 0.3320
VaR −1.79% −1.72% −1.72% −1.74% −1.71% −1.71%
CVaR −2.97% −2.89% −2.89% −2.86% −2.87% −2.87%
Sortino Ratio 0.5777 0.5814 0.5812 0.5721 0.5763 0.5763
USD → EUR 2010-2020
Return 13.28% 12.77% 12.77% 13.12% 12.77% 12.77%
Standard Deviation 16.51% 15.71% 15.71% 16.08% 15.71% 15.71%
Sharpe Ratio 0.8039 0.8130 0.8129 0.8160 0.8130 0.8130
Cumulative Return 259.57% 243.42% 243.42% 254.42% 243.42% 243.42%
Worst Drawdown 31.50% 29.97% 29.97% 29.97% 29.97% 29.97%
Average Drawdown 2.12% 2.02% 2.02% 2.10% 2.02% 2.02%
Average Length 18.5267 18.8217 18.8217 18.7442 18.8217 18.8217
Average Recovery 9.2748 9.4419 9.4419 9.5349 9.4419 9.4419
Hurst Index 0.3760 0.3759 0.3759 0.3733 0.3759 0.3759
VaR −1.52% −1.45% −1.45% −1.50% −1.45% −1.45%
CVaR −2.82% −2.73% −2.72% −2.94% −2.73% −2.73%
Sortino Ratio 1.1753 1.1843 1.1842 1.1885 1.1843 1.1843
EUR 1985-2020
Return 6.67% 6.65% 6.67% 6.63% 6.71% 6.60%
Standard Deviation 12.80% 12.03% 12.01% 12.21% 12.05% 12.02%
Sharpe Ratio 0.5207 0.5527 0.5550 0.5429 0.5566 0.5494
Cumulative Return 918.25% 912.69% 918.80% 905.72% 933.16% 897.06%
Worst Drawdown 52.17% 49.17% 49.17% 49.27% 49.17% 49.17%
Average Drawdown 2.54% 2.44% 2.35% 2.46% 2.48% 2.43%
Average Length 45.6398 44.0052 42.8485 44.2188 44.0052 44.2240
Average Recovery 28.8602 27.6995 27.0051 27.9375 27.8549 27.8542
Hurst Index 0.3439 0.3434 0.3436 0.3418 0.3432 0.3435
VaR −1.24% −1.18% −1.17% −1.20% −1.18% −1.17%
CVaR −2.55% −2.46% −2.45% −2.52% −2.47% −2.46%
Sortino Ratio 0.7863 0.8239 0.8270 0.8115 0.8291 0.8195
EUR 2000-2020
Return 2.80% 2.87% 2.87% 2.79% 2.88% 2.88%
Standard Deviation 15.85% 14.86% 14.86% 15.25% 14.86% 14.86%
Sharpe Ratio 0.1770 0.1934 0.1933 0.1829 0.1937 0.1936
Cumulative Return 76.36% 78.85% 78.78% 75.83% 79.01% 78.94%
Worst Drawdown 52.89% 50.21% 50.21% 53.33% 50.21% 50.21%
Average Drawdown 3.26% 3.07% 3.07% 2.90% 3.07% 3.07%
Average Length 58.3448 56.3000 56.3000 55.0870 56.3000 56.3000
Average Recovery 36.5057 35.0222 35.0222 35.2717 35.0222 35.0222
Hurst Index 0.3419 0.3417 0.3417 0.3387 0.3417 0.3417
VaR −1.59% −1.50% −1.50% −1.54% −1.50% −1.50%
CVaR −3.06% −2.89% −2.89% −2.95% −2.89% −2.89%
Sortino Ratio 0.3513 0.3668 0.3666 0.3550 0.3672 0.3670
EUR 2010-2020
Return 6.00% 5.88% 5.88% 5.79% 5.88% 5.88%
Standard Deviation 17.18% 16.17% 16.17% 16.36% 16.17% 16.17%
Sharpe Ratio 0.3494 0.3639 0.3639 0.3536 0.3635 0.3634
Cumulative Return 81.91% 79.85% 79.85% 78.13% 79.73% 79.70%
Worst Drawdown 34.97% 33.56% 33.56% 33.56% 33.56% 33.56%
Average Drawdown 2.72% 2.57% 2.57% 2.56% 2.57% 2.57%
Average Length 30.1687 28.4545 28.4545 28.4659 28.4545 28.4545
Average Recovery 17.0843 15.9432 15.9432 16.0000 15.9432 15.9432
Hurst Index 0.3569 0.3560 0.3560 0.3545 0.3560 0.3560
VaR −1.78% −1.68% −1.68% −1.70% −1.68% −1.68%
CVaR −3.80% −3.59% −3.59% −3.59% −3.59% −3.59%
Sortino Ratio 0.5866 0.5992 0.5992 0.5870 0.5987 0.5985
Two funds 90/10: Modelli dinamici non vincolati e modello statico 1/N
Performance delle 12 misure statistiche calcolate sulla base di ciascun modello di ottimizzazione
Misura statisticaModello StaticoModelli dinamici non vincolati
1/NBoudt SD No-boxHRPBoudt Random MVPBoudt Random HS
USD 1985-2020
Return 8.15% 7.01% 6.73% 6.82% 8.51%
Standard Deviation 9.71% 7.54% 7.43% 7.50% 9.94%
Sharpe Ratio 0.8389 0.9297 0.9064 0.9081 0.8562
Cumulative Return 1,572.92% 1,042.09% 940.62% 971.09% 1,785.95%
Worst Drawdown 26.04% 19.80% 20.05% 20.26% 23.62%
Average Drawdown 1.18% 0.96% 1.04% 0.99% 1.38%
Average Length 17.8962 18.5793 20.7115 19.6799 19.2255
Average Recovery 9.2839 9.7621 11.5623 10.8972 9.5786
Hurst Index 0.3720 0.3481 0.3391 0.3461 0.3166
VaR −0.85% −0.68% −0.68% −0.67% −0.96%
CVaR −1.06% −1.03% −1.11% −0.99% −1.80%
Sortino Ratio 1.2038 1.3536 1.3230 1.3278 1.2442
USD 2000-2020
Return 5.61% 3.67% 3.32% 3.42% 3.95%
Standard Deviation 9.73% 5.92% 5.91% 5.89% 10.55%
Sharpe Ratio 0.5763 0.6205 0.5615 0.5813 0.3742
Cumulative Return 206.22% 109.50% 95.41% 99.49% 121.19%
Worst Drawdown 27.89% 18.92% 19.70% 19.32% 41.81%
Average Drawdown 1.07% 0.60% 0.70% 0.65% 1.52%
Average Length 18.5211 18.3409 22.0404 20.5527 31.3333
Average Recovery 9.5862 10.8750 13.2466 12.4852 20.8679
Hurst Index 0.3735 0.3941 0.3886 0.3929 0.3947
VaR −0.82% −0.43% −0.46% −0.43% −0.47%
CVaR −0.82% −0.43% −0.46% −0.43% −0.47%
Sortino Ratio 0.8579 0.9024 0.8204 0.8479 0.5835
USD 2010-2020
Return 8.73% 5.12% 4.33% 4.69% 5.91%
Standard Deviation 8.61% 4.29% 4.03% 4.03% 7.57%
Sharpe Ratio 1.0142 1.1929 1.0750 1.1622 0.7806
Cumulative Return 136.12% 66.96% 54.52% 60.07% 80.31%
Worst Drawdown 19.33% 9.43% 8.96% 9.38% 17.93%
Average Drawdown 0.80% 0.43% 0.47% 0.43% 0.83%
Average Length 10.8774 12.2158 15.0633 13.2443 13.8941
Average Recovery 5.4151 6.9263 8.6329 8.0568 8.0706
Hurst Index 0.4136 0.4648 0.4668 0.4719 0.3943
VaR −0.68% 0.00% 0.00% 0.00% −0.64%
CVaR −0.68% −2.08% −2.08% −2.08% −0.64%
Sortino Ratio 1.4008 1.6077 1.4663 1.5720 1.0947
USD → EUR 1985-2020
Return 7.12% 7.20% 6.74% 7.09% 10.18%
Standard Deviation 15.22% 14.19% 14.28% 14.25% 17.15%
Sharpe Ratio 0.4677 0.5076 0.4720 0.4975 0.5936
Cumulative Return 1,085.41% 1,120.46% 943.82% 1,073.90% 3,168.42%
Worst Drawdown 46.38% 48.67% 46.90% 49.49% 41.30%
Average Drawdown 2.85% 2.85% 2.86% 2.96% 3.00%
Average Length 43.0293 42.6893 44.8223 44.0800 30.1419
Average Recovery 18.6146 25.8010 25.5990 26.0000 17.5294
Hurst Index 0.3254 0.2773 0.3052 0.2760 0.3541
VaR −1.50% −1.40% −1.41% −1.40% −1.64%
CVaR −2.59% −2.11% −2.22% −2.11% −3.43%
Sortino Ratio 0.7538 0.8078 0.7589 0.7953 0.9212
USD → EUR 2000-2020
Return 4.14% 2.89% 3.00% 2.68% 3.35%
Standard Deviation 13.36% 12.07% 11.91% 12.09% 14.48%
Sharpe Ratio 0.3099 0.2396 0.2521 0.2217 0.2315
Cumulative Return 129.82% 79.51% 83.47% 72.03% 96.70%
Worst Drawdown 44.67% 49.70% 47.02% 51.00% 55.46%
Average Drawdown 1.95% 2.21% 1.94% 2.40% 2.63%
Average Length 47.3738 60.6786 58.5172 67.1579 59.3256
Average Recovery 20.3364 38.6667 39.8851 44.3289 28.0465
Hurst Index 0.3282 0.3040 0.3117 0.3047 0.3491
VaR −1.31% −1.21% −1.19% −1.21% −1.32%
CVaR −2.15% −1.87% −1.82% −1.86% −1.80%
Sortino Ratio 0.5236 0.4195 0.4369 0.3953 0.4220
USD → EUR 2010-2020
Return 9.48% 6.37% 7.06% 6.09% 9.79%
Standard Deviation 11.02% 8.41% 8.66% 8.44% 11.49%
Sharpe Ratio 0.8604 0.7566 0.8154 0.7217 0.8519
Cumulative Return 153.50% 88.44% 101.52% 83.43% 160.87%
Worst Drawdown 20.32% 14.94% 11.86% 15.51% 19.11%
Average Drawdown 1.48% 1.35% 1.30% 1.43% 1.87%
Average Length 20.1639 25.8854 24.0485 27.9551 22.2072
Average Recovery 10.4754 13.4583 12.2136 14.5618 10.5315
Hurst Index 0.3826 0.3763 0.3775 0.3778 0.3371
VaR −1.01% −0.77% −0.80% −0.76% −1.13%
CVaR −1.76% −1.18% −1.32% −1.14% −2.02%
Sortino Ratio 1.2438 1.1312 1.2056 1.0831 1.2422
EUR 1985-2020
Return 6.11% 6.29% 6.03% 5.75% 6.44%
Standard Deviation 7.29% 5.14% 4.84% 4.72% 7.87%
Sharpe Ratio 0.8381 1.2242 1.2474 1.2184 0.8184
Cumulative Return 743.31% 798.04% 722.17% 647.61% 842.87%
Worst Drawdown 28.97% 24.18% 19.79% 20.98% 31.20%
Average Drawdown 1.44% 1.16% 1.07% 1.03% 1.99%
Average Length 30.0356 30.4928 29.6725 30.6232 43.5590
Average Recovery 15.4377 16.6304 14.9789 15.5036 24.8564
Hurst Index 0.3340 0.2987 0.2868 0.2881 0.2943
VaR −0.74% −0.52% −0.48% −0.46% −0.79%
CVaR −1.55% −0.94% −0.78% −0.76% −1.59%
Sortino Ratio 1.1922 1.7462 1.8061 1.7683 1.1651
EUR 2000-2020
Return 3.22% 3.41% 3.14% 3.00% 3.38%
Standard Deviation 8.61% 4.70% 4.81% 4.60% 9.00%
Sharpe Ratio 0.3735 0.7254 0.6521 0.6514 0.3752
Cumulative Return 91.47% 98.77% 88.47% 83.26% 97.64%
Worst Drawdown 28.95% 10.64% 9.79% 11.50% 47.26%
Average Drawdown 1.69% 0.98% 1.15% 1.10% 1.66%
Average Length 38.0152 37.2932 42.6154 45.0090 45.6455
Average Recovery 21.4015 21.1353 21.4444 22.4595 22.9273
Hurst Index 0.3379 0.3041 0.3062 0.3048 0.3699
VaR −0.88% −0.46% −0.47% −0.45% −0.80%
CVaR −1.74% −0.72% −0.73% −0.70% −0.95%
Sortino Ratio 0.5720 1.0661 0.9684 0.9638 0.5739
EUR 2010-2020
Return 5.04% 3.40% 3.38% 3.50% 2.07%
Standard Deviation 9.61% 4.89% 4.95% 4.75% 8.71%
Sharpe Ratio 0.5245 0.6952 0.6830 0.7360 0.2379
Cumulative Return 65.63% 40.90% 40.72% 42.34% 23.42%
Worst Drawdown 23.28% 9.94% 9.85% 10.10% 21.60%
Average Drawdown 1.59% 1.34% 1.15% 1.20% 2.45%
Average Length 26.5106 46.1296 47.0943 38.9062 82.0323
Average Recovery 13.7766 28.6111 31.5849 24.1875 34.3226
Hurst Index 0.3461 0.3241 0.3263 0.3279 0.3168
VaR −1.00% −0.49% −0.49% −0.47% −0.90%
CVaR −2.19% −0.83% −0.84% −0.83% −1.65%
Sortino Ratio 0.7751 1.0099 0.9961 1.0677 0.3854

Two funds dinamico

Two funds Dinamico: Modelli dinamici vincolati e modello statico standard
Performance delle 12 misure statistiche calcolate sulla base di ciascun modello di ottimizzazione
Misura statisticaModello StaticoModelli dinamici
vincolati
StandardBoudt SD ROIBoudt SD RandomBoudt CVaR ROITCOV ROBNaif
USD 1985-2020
Return 8.30% 7.98% 7.97% 8.21% 8.01% 7.98%
Standard Deviation 12.99% 9.13% 9.12% 9.35% 9.14% 9.13%
Sharpe Ratio 0.6392 0.8740 0.8737 0.8784 0.8757 0.8743
Cumulative Return 1,660.42% 1,482.38% 1,477.44% 1,606.99% 1,495.13% 1,483.82%
Worst Drawdown 49.89% 22.98% 22.98% 24.04% 22.98% 22.98%
Average Drawdown 1.56% 1.12% 1.12% 1.13% 1.12% 1.12%
Average Length 22.0876 17.5708 17.5750 17.3814 17.5625 17.6075
Average Recovery 12.2010 8.9938 9.1583 8.7010 8.9750 9.0230
Hurst Index 0.3616 0.3713 0.3712 0.3687 0.3711 0.3713
VaR −1.03% −0.80% −0.80% −0.83% −0.80% −0.80%
CVaR −1.03% −0.98% −0.98% −1.25% −1.00% −0.98%
Sortino Ratio 0.9479 1.2518 1.2514 1.2583 1.2542 1.2522
USD 2000-2020
Return 5.46% 5.31% 5.31% 5.41% 5.33% 5.31%
Standard Deviation 13.07% 8.92% 8.92% 9.24% 8.93% 8.92%
Sharpe Ratio 0.4180 0.5950 0.5954 0.5853 0.5964 0.5951
Cumulative Return 197.71% 188.96% 189.15% 194.56% 190.01% 189.01%
Worst Drawdown 40.53% 24.78% 24.78% 28.02% 24.83% 24.78%
Average Drawdown 1.83% 0.96% 0.96% 0.99% 0.96% 0.96%
Average Length 27.8101 17.8118 17.7463 18.0373 17.8007 17.8118
Average Recovery 15.3911 9.4428 9.4007 9.7351 9.4317 9.4428
Hurst Index 0.3816 0.3783 0.3783 0.3812 0.3781 0.3783
VaR −0.97% −0.73% −0.73% −0.74% −0.73% −0.73%
CVaR −0.97% −0.73% −0.73% −0.74% −0.73% −0.73%
Sortino Ratio 0.6566 0.8797 0.8802 0.8674 0.8815 0.8799
USD 2010-2020
Return 8.51% 8.23% 8.23% 8.39% 8.33% 8.23%
Standard Deviation 13.55% 7.82% 7.82% 8.11% 7.92% 7.82%
Sharpe Ratio 0.6276 1.0527 1.0527 1.0336 1.0529 1.0527
Cumulative Return 131.17% 125.23% 125.23% 128.56% 127.47% 125.23%
Worst Drawdown 32.02% 17.83% 17.83% 17.83% 17.83% 17.83%
Average Drawdown 1.39% 0.71% 0.71% 0.76% 0.73% 0.71%
Average Length 15.0377 10.4344 10.4344 10.5616 10.4864 10.4344
Average Recovery 8.7736 5.4163 5.4163 5.5114 5.4909 5.4163
Hurst Index 0.3920 0.4217 0.4217 0.4170 0.4201 0.4217
VaR −1.09% −0.56% −0.56% −0.63% −0.59% −0.56%
CVaR −1.09% −0.56% −0.56% −0.63% −0.59% −0.56%
Sortino Ratio 0.9248 1.4493 1.4493 1.4243 1.4475 1.4493
USD → EUR 1985-2020
Return 7.27% 7.03% 7.04% 7.40% 7.04% 7.04%
Standard Deviation 17.16% 14.80% 14.80% 15.10% 14.81% 14.80%
Sharpe Ratio 0.4237 0.4752 0.4754 0.4899 0.4755 0.4756
Cumulative Return 1,147.40% 1,052.27% 1,053.53% 1,202.59% 1,056.22% 1,053.78%
Worst Drawdown 57.88% 44.83% 44.82% 43.65% 44.83% 44.71%
Average Drawdown 3.31% 2.71% 2.71% 2.73% 2.71% 2.71%
Average Length 48.7403 42.0524 42.0476 40.4679 42.0524 41.8483
Average Recovery 22.0442 18.7381 18.7333 18.4128 18.7381 18.6303
Hurst Index 0.3290 0.3216 0.3215 0.3293 0.3215 0.3216
VaR −1.64% −1.46% −1.46% −1.49% −1.46% −1.46%
CVaR −2.89% −2.46% −2.46% −2.67% −2.46% −2.46%
Sortino Ratio 0.7018 0.7624 0.7627 0.7817 0.7630 0.7630
USD → EUR 2000-2020
Return 4.00% 3.97% 3.97% 3.98% 3.97% 3.97%
Standard Deviation 16.30% 12.83% 12.83% 13.12% 12.83% 12.83%
Sharpe Ratio 0.2453 0.3092 0.3092 0.3034 0.3092 0.3092
Cumulative Return 123.43% 122.17% 122.17% 122.65% 122.17% 122.17%
Worst Drawdown 55.56% 42.78% 42.78% 45.11% 42.78% 42.78%
Average Drawdown 3.22% 1.80% 1.80% 1.83% 1.80% 1.80%
Average Length 64.3924 45.7207 45.7207 47.4673 45.7207 45.7207
Average Recovery 30.7089 20.1802 20.1802 22.7009 20.1802 20.1802
Hurst Index 0.3510 0.3281 0.3281 0.3264 0.3281 0.3281
VaR −1.52% −1.26% −1.26% −1.29% −1.26% −1.26%
CVaR −2.43% −2.06% −2.06% −2.09% −2.06% −2.06%
Sortino Ratio 0.4518 0.5194 0.5194 0.5131 0.5194 0.5194
USD → EUR 2010-2020
Return 9.26% 8.95% 8.95% 9.62% 9.01% 8.95%
Standard Deviation 15.30% 10.45% 10.45% 10.81% 10.45% 10.45%
Sharpe Ratio 0.6051 0.8570 0.8570 0.8901 0.8619 0.8570
Cumulative Return 148.18% 141.12% 141.12% 156.71% 142.45% 141.12%
Worst Drawdown 31.50% 19.21% 19.21% 19.29% 19.21% 19.21%
Average Drawdown 2.21% 1.40% 1.40% 1.47% 1.40% 1.40%
Average Length 25.4227 19.8710 19.8710 19.5317 19.7120 19.8710
Average Recovery 10.0619 10.2661 10.2661 10.1270 10.1760 10.2661
Hurst Index 0.3857 0.3843 0.3843 0.3809 0.3842 0.3843
VaR −1.33% −0.95% −0.95% −1.00% −0.95% −0.95%
CVaR −1.33% −1.62% −1.62% −1.82% −1.63% −1.62%
Sortino Ratio 0.9178 1.2407 1.2407 1.2853 1.2475 1.2407
EUR 1985-2020
Return 5.54% 6.10% 6.05% 6.18% 6.19% 6.12%
Standard Deviation 10.61% 6.75% 6.73% 6.96% 6.77% 6.76%
Sharpe Ratio 0.5222 0.9038 0.8979 0.8869 0.9139 0.9056
Cumulative Return 595.88% 742.04% 726.09% 762.78% 767.49% 746.52%
Worst Drawdown 52.17% 26.06% 26.06% 26.04% 26.06% 26.06%
Average Drawdown 1.53% 1.40% 1.39% 1.46% 1.42% 1.41%
Average Length 34.7347 29.3299 29.1241 29.7430 29.7148 29.5280
Average Recovery 22.8000 15.4097 15.2621 15.8662 15.5775 15.5175
Hurst Index 0.3594 0.3303 0.3304 0.3269 0.3299 0.3302
VaR −0.96% −0.68% −0.68% −0.71% −0.69% −0.69%
CVaR −1.44% −1.42% −1.42% −1.45% −1.43% −1.42%
Sortino Ratio 0.7753 1.2817 1.2740 1.2576 1.2953 1.2842
EUR 2000-2020
Return 4.02% 3.22% 3.22% 3.20% 3.21% 3.22%
Standard Deviation 12.07% 7.83% 7.83% 8.15% 7.83% 7.83%
Sharpe Ratio 0.3331 0.4109 0.4110 0.3927 0.4103 0.4109
Cumulative Return 124.39% 91.43% 91.44% 90.77% 91.27% 91.43%
Worst Drawdown 43.94% 25.58% 25.56% 29.50% 25.63% 25.58%
Average Drawdown 2.15% 1.65% 1.65% 1.70% 1.65% 1.65%
Average Length 40.1520 37.4776 37.4776 39.1250 37.4776 37.4776
Average Recovery 23.0880 19.4627 19.4179 22.1016 19.4627 19.4627
Hurst Index 0.3688 0.3363 0.3362 0.3316 0.3363 0.3363
VaR −1.16% −0.80% −0.80% −0.84% −0.80% −0.80%
CVaR −2.50% −1.59% −1.58% −1.62% −1.59% −1.59%
Sortino Ratio 0.5303 0.6192 0.6194 0.5953 0.6185 0.6192
EUR 2010-2020
Return 3.61% 4.86% 4.86% 4.77% 4.86% 4.86%
Standard Deviation 14.91% 8.75% 8.75% 8.95% 8.75% 8.75%
Sharpe Ratio 0.2423 0.5559 0.5559 0.5337 0.5559 0.5559
Cumulative Return 43.94% 62.83% 62.83% 61.41% 62.83% 62.83%
Worst Drawdown 34.97% 21.74% 21.74% 21.74% 21.74% 21.74%
Average Drawdown 3.12% 1.61% 1.61% 1.66% 1.61% 1.61%
Average Length 46.0182 27.3956 27.3956 27.5055 27.3956 27.3956
Average Recovery 29.2182 13.6044 13.6044 13.7033 13.6044 13.6044
Hurst Index 0.3749 0.3434 0.3434 0.3406 0.3434 0.3434
VaR −1.52% −0.91% −0.91% −0.94% −0.91% −0.91%
CVaR −3.74% −2.01% −2.01% −2.00% −2.01% −2.01%
Sortino Ratio 0.4269 0.8136 0.8136 0.7849 0.8136 0.8136
Two funds Dinamico: Modelli dinamici non vincolati e modello statico 1/N
Performance delle 12 misure statistiche calcolate sulla base di ciascun modello di ottimizzazione
Misura statisticaModello StaticoModelli dinamici non vincolati
1/NBoudt SD No-boxHRPBoudt Random MVPBoudt Random HS
USD 1985-2020
Return 8.15% 7.01% 6.73% 6.82% 8.51%
Standard Deviation 9.71% 7.54% 7.43% 7.50% 9.94%
Sharpe Ratio 0.8389 0.9297 0.9064 0.9082 0.8561
Cumulative Return 1,572.92% 1,042.09% 940.62% 971.19% 1,786.14%
Worst Drawdown 26.04% 19.80% 20.05% 20.26% 23.62%
Average Drawdown 1.18% 0.96% 1.04% 0.99% 1.38%
Average Length 17.8962 18.5793 20.7115 19.6799 19.2255
Average Recovery 9.2839 9.7621 11.5623 10.8972 9.5786
Hurst Index 0.3720 0.3481 0.3391 0.3461 0.3166
VaR −0.85% −0.68% −0.68% −0.67% −0.96%
CVaR −1.06% −1.03% −1.11% −0.99% −1.80%
Sortino Ratio 1.2038 1.3536 1.3230 1.3278 1.2442
USD 2000-2020
Return 5.61% 3.67% 3.32% 3.42% 3.95%
Standard Deviation 9.73% 5.92% 5.91% 5.89% 10.55%
Sharpe Ratio 0.5763 0.6205 0.5615 0.5813 0.3741
Cumulative Return 206.22% 109.50% 95.41% 99.48% 121.19%
Worst Drawdown 27.89% 18.92% 19.70% 19.32% 41.82%
Average Drawdown 1.07% 0.60% 0.70% 0.65% 1.54%
Average Length 18.5211 18.3409 22.0404 20.5527 31.7197
Average Recovery 9.5862 10.8750 13.2466 12.4852 21.1210
Hurst Index 0.3735 0.3941 0.3886 0.3929 0.3947
VaR −0.82% −0.43% −0.46% −0.43% −0.47%
CVaR −0.82% −0.43% −0.46% −0.43% −0.47%
Sortino Ratio 0.8579 0.9024 0.8204 0.8479 0.5834
USD 2010-2020
Return 8.73% 5.12% 4.33% 4.69% 5.91%
Standard Deviation 8.61% 4.29% 4.03% 4.03% 7.57%
Sharpe Ratio 1.0142 1.1929 1.0750 1.1620 0.7804
Cumulative Return 136.12% 66.96% 54.52% 60.06% 80.29%
Worst Drawdown 19.33% 9.43% 8.96% 9.38% 17.94%
Average Drawdown 0.80% 0.43% 0.47% 0.43% 0.83%
Average Length 10.8774 12.2158 15.0633 13.2443 13.9763
Average Recovery 5.4151 6.9263 8.6329 8.0568 8.0414
Hurst Index 0.4136 0.4648 0.4668 0.4719 0.3943
VaR −0.68% 0.00% 0.00% 0.00% −0.64%
CVaR −0.68% −0.66% −0.66% −0.66% −0.64%
Sortino Ratio 1.4008 1.6077 1.4663 1.5718 1.0945
USD → EUR 1985-2020
Return 7.12% 7.20% 6.74% 7.09% 10.18%
Standard Deviation 15.22% 14.19% 14.28% 14.25% 17.15%
Sharpe Ratio 0.4677 0.5076 0.4720 0.4975 0.5936
Cumulative Return 1,085.41% 1,120.46% 943.82% 1,073.72% 3,168.75%
Worst Drawdown 46.38% 48.67% 46.90% 49.49% 41.30%
Average Drawdown 2.85% 2.85% 2.86% 2.96% 3.00%
Average Length 43.0293 42.6893 44.8223 44.0800 30.1419
Average Recovery 18.6146 25.8010 25.5990 26.0000 17.5294
Hurst Index 0.3254 0.2773 0.3052 0.2760 0.3541
VaR −1.50% −1.40% −1.41% −1.40% −1.64%
CVaR −2.59% −2.11% −2.22% −2.11% −3.43%
Sortino Ratio 0.7538 0.8078 0.7589 0.7952 0.9212
USD → EUR 2000-2020
Return 4.14% 2.89% 3.00% 2.68% 3.35%
Standard Deviation 13.36% 12.07% 11.91% 12.09% 14.48%
Sharpe Ratio 0.3099 0.2396 0.2521 0.2217 0.2315
Cumulative Return 129.82% 79.51% 83.47% 72.03% 96.70%
Worst Drawdown 44.67% 49.70% 47.02% 51.00% 55.46%
Average Drawdown 1.95% 2.21% 1.94% 2.40% 2.63%
Average Length 47.3738 60.6786 58.5172 67.1579 59.3256
Average Recovery 20.3364 38.6667 39.8851 44.3289 28.0465
Hurst Index 0.3282 0.3040 0.3117 0.3047 0.3491
VaR −1.31% −1.21% −1.19% −1.21% −1.32%
CVaR −2.15% −1.87% −1.82% −1.86% −1.80%
Sortino Ratio 0.5236 0.4195 0.4369 0.3953 0.4220
USD → EUR 2010-2020
Return 9.48% 6.37% 7.06% 6.09% 9.79%
Standard Deviation 11.02% 8.41% 8.66% 8.44% 11.49%
Sharpe Ratio 0.8604 0.7566 0.8154 0.7217 0.8519
Cumulative Return 153.50% 88.44% 101.52% 83.43% 160.88%
Worst Drawdown 20.32% 14.94% 11.86% 15.51% 19.11%
Average Drawdown 1.48% 1.35% 1.30% 1.43% 1.87%
Average Length 20.1639 25.8854 24.0485 27.9551 22.2072
Average Recovery 10.4754 13.4583 12.2136 14.5618 10.5315
Hurst Index 0.3826 0.3763 0.3775 0.3778 0.3371
VaR −1.01% −0.77% −0.80% −0.76% −1.13%
CVaR −1.76% −1.18% −1.32% −1.14% −2.02%
Sortino Ratio 1.2438 1.1312 1.2056 1.0831 1.2422
EUR 1985-2020
Return 6.11% 6.29% 6.03% 5.75% 6.44%
Standard Deviation 7.29% 5.14% 4.84% 4.72% 7.87%
Sharpe Ratio 0.8381 1.2242 1.2474 1.2184 0.8185
Cumulative Return 743.31% 798.04% 722.17% 647.67% 842.85%
Worst Drawdown 28.97% 24.18% 19.79% 20.98% 31.20%
Average Drawdown 1.44% 1.16% 1.07% 1.04% 1.99%
Average Length 30.0356 30.4928 29.6725 30.6232 43.5590
Average Recovery 15.4377 16.6304 14.9789 15.5036 24.8564
Hurst Index 0.3340 0.2987 0.2868 0.2881 0.2943
VaR −0.74% −0.52% −0.48% −0.46% −0.79%
CVaR −1.55% −0.94% −0.78% −0.76% −1.59%
Sortino Ratio 1.1922 1.7462 1.8061 1.7683 1.1652
EUR 2000-2020
Return 3.22% 3.41% 3.14% 3.00% 3.38%
Standard Deviation 8.61% 4.70% 4.81% 4.60% 9.00%
Sharpe Ratio 0.3735 0.7254 0.6521 0.6515 0.3753
Cumulative Return 91.47% 98.77% 88.47% 83.27% 97.64%
Worst Drawdown 28.95% 10.64% 9.79% 11.50% 47.26%
Average Drawdown 1.69% 0.98% 1.15% 1.10% 1.66%
Average Length 38.0152 37.2932 42.6154 45.0090 45.6455
Average Recovery 21.4015 21.1353 21.4444 22.4595 22.9273
Hurst Index 0.3379 0.3041 0.3062 0.3048 0.3699
VaR −0.88% −0.46% −0.47% −0.45% −0.80%
CVaR −1.74% −0.72% −0.73% −0.70% −0.95%
Sortino Ratio 0.5720 1.0661 0.9684 0.9638 0.5739
EUR 2010-2020
Return 5.04% 3.40% 3.38% 3.50% 2.07%
Standard Deviation 9.61% 4.89% 4.95% 4.75% 8.71%
Sharpe Ratio 0.5245 0.6952 0.6830 0.7362 0.2379
Cumulative Return 65.63% 40.90% 40.72% 42.35% 23.43%
Worst Drawdown 23.28% 9.94% 9.85% 10.10% 21.60%
Average Drawdown 1.59% 1.34% 1.15% 1.20% 2.45%
Average Length 26.5106 46.1296 47.0943 38.9062 82.0323
Average Recovery 13.7766 28.6111 31.5849 24.1875 34.3226
Hurst Index 0.3461 0.3241 0.3263 0.3279 0.3168
VaR −1.00% −0.49% −0.49% −0.47% −0.90%
CVaR −2.19% −0.83% −0.84% −0.83% −1.65%
Sortino Ratio 0.7751 1.0099 0.9961 1.0679 0.3854

I pesi ottimali più recenti dei Two funds e di tutti gli altri Lazy portfolios possono essere consultati al seguente link (per avere accesso è necessario sottoscrivere un abbonamento PRO): Lazy portfolios modello.

Vai agli altri Lazy portfolios (link in basso) o all'articolo principale sui Lazy portfolios:

13.3.1 World Bond

13.3.2 World Stocks

13.3.3 Two funds portfolios

13.3.4 Warren Buffett

13.3.5 Simple Path to Wealth

13.3.6 Couch Potato

13.3.7 Three Funds Bogleheads

13.3.8 Second Grader's Starter

13.3.9 Talmud

13.3.10 Margaritaville

13.3.11 Andrew Tobias

13.3.12 Gyroscopic Investing Desert

13.3.13 Permanent

13.3.14 Core Four

13.3.15 Bogleheads Four Funds

13.3.16 No Brainer

13.3.17 Larry

13.3.18 Golden Butterfly

13.3.19 All Weather

13.3.20 Ivy

13.3.21 Dynamic 60/40 Income

13.3.22 Dynamic 40/60 Income

13.3.23 Five Asset

13.3.24 David Swensen Lazy Portfolio

13.3.25 Coffee House

13.3.26 Rob Arnott

13.3.27 Ultimate Buy and Hold Strategy

13.3.28 Ultimate Buy & Hold

13.3.29 Dedalo Three

13.3.30 Dedalo Four

13.3.31 Dedalo Eleven

BASIC

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Disclaimer

Tutti i tipi di investimento sono rischiosi. Il livello di rischio può essere più o meno alto e i rendimenti possono variare al rialzo o al ribasso. Ogni investimento è soggetto al rischio di perdita.
I rendimenti passati non sono indicativi di quelli futuri.