Portfolio Optimization

This portfolio optimizer tool supports the following portfolio optimization strategies:

The optimization is based on the monthly return statistics of the selected portfolio assets for the given time period. The optimization result does not predict what allocation would perform best outside the given time period, and the actual performance of portfolios constructed using the optimized asset weights may vary from the given performance goal.

The required inputs for the optimization include the time range and the portfolio assets. Portfolio asset weights and constraints are optional. You can also use the Black-Litterman model based portfolio optimization, which allows the benchmark portfolio asset weights to be optimized based on investor's views.

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Asset Groups
Min. Weight
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Portfolio Optimization Results (Mar 2010 - Dec 2020)

Portfolio optimization results with goal to maximize Sharpe ratio. The possible range of expected annual portfolio returns for the given period is 42.14% to 68.69%. Refer to the efficient frontier section for additional details.

Portfolio Allocations

Maximum Sharpe Ratio
Ticker Name Allocation
TMF Direxion Daily 20+ Yr Trsy Bull 3X ETF 47.38%
TQQQ ProShares UltraPro QQQ 52.62%
Save portfolio »

Portfolio Performance Summary

Portfolio performance statistics
MetricMaximum Sharpe Ratio
Start Balance$10,000
End Balance$497,628
CAGR43.43%
Expected Return 48.20%
Stdev26.41%
Best Year99.00%
Worst Year-10.30%
Max. Drawdown -26.24%
Sharpe Ratio (ex-ante)1.80
Sharpe Ratio (ex-post)1.49
Sortino Ratio3.05
US Stock Market Correlation0.63
   

Trailing Returns

Trailing Returns
NameAnnualized ReturnAnnualized Volatility
3 Month1 year3 year5 year10 yearFull3 year5 year
Maximum Sharpe Ratio15.14%99.00%51.48%45.18%41.54%43.43%34.37%29.94%
Trailing annualized return and volatility are for full months ending in December 2020 excluding portfolio cashflows.
Notes on results:
  • Past performance is no guarantee of future results, which may vary. All use is subject to terms of service.
  • Investing involves risk, including possible loss of principal. The value of the investments and the income derived from them may fluctuate over time.
  • All portfolio returns presented are hypothetical and backtested. Hypothetical returns do not reflect trading costs, transaction fees, or taxes.
  • Portfolio optimization determines target weights for portfolio assets based on mathematical models that can use either historical or forecasted data as inputs. Optimization results are not guarantees of future performance.
  • The results are based on information from a variety of sources we consider reliable, but we do not represent that the information is accurate or complete.
  • The results do not constitute investment advice or recommendation, are provided solely for informational purposes, and are not an offer to buy or sell any securities.
  • The results are based on the total return of assets and assume that all received dividends and distributions are reinvested.
  • Monte Carlo method was used to resample the efficient frontier inputs to mitigate the impact of input estimation errors.
  • The annual results for 2010 are based on full calendar months from March to December
  • CAGR = Compound Annual Growth Rate
  • Stdev = Annualized standard deviation of monthly returns
  • Sharpe ratio is calculated and annualized from monthly excess returns over the risk free rate (3-month treasury bill)
  • Drawdowns are calculated based on monthly returns.
  • The backtested results assume monthly rebalancing of portfolio assets to match the specified allocation.
Efficient Frontier Assets
#AssetCAGRExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1Direxion Daily 20+ Yr Trsy Bull 3X ETF (TMF)15.79%24.36%39.42%0.6040.00%100.00%
2ProShares UltraPro QQQ (TQQQ)52.68%73.17%51.82%1.4010.00%100.00%
Results based on historical returns. Ex ante Sharpe Ratio calculated using 3-month treasury bill returns as the risk-free rate (0.56% annualized).

Asset Correlations

Efficient Frontier Asset Correlations
NameTickerTMFTQQQ
Direxion Daily 20+ Yr Trsy Bull 3X ETFTMF1.00-0.39
ProShares UltraPro QQQTQQQ-0.391.00
Based on monthly returns from Mar 2010 to Dec 2020
Efficient Frontier Assets
#TMFTQQQExpected Return*Standard Deviation*Sharpe Ratio*
159.98%40.02%42.14%24.67%1.685
259.45%40.55%42.38%24.67%1.695
358.93%41.07%42.63%24.68%1.705
458.40%41.60%42.88%24.69%1.714
557.88%42.12%43.13%24.71%1.723
657.35%42.65%43.38%24.74%1.731
756.83%43.17%43.63%24.77%1.739
856.30%43.70%43.88%24.81%1.746
955.78%44.22%44.13%24.85%1.753
1055.25%44.75%44.38%24.91%1.760
1154.73%45.27%44.63%24.96%1.766
1254.20%45.80%44.89%25.03%1.771
1353.68%46.32%45.14%25.10%1.776
1453.15%46.85%45.39%25.17%1.781
1552.63%47.37%45.64%25.26%1.785
1652.10%47.90%45.90%25.35%1.789
1751.58%48.42%46.15%25.44%1.792
1851.05%48.95%46.41%25.54%1.795
1950.53%49.47%46.66%25.65%1.798
2050.00%50.00%46.92%25.76%1.800
2149.48%50.52%47.17%25.88%1.801
2248.95%51.05%47.43%26.00%1.803
2348.43%51.57%47.68%26.13%1.803
2447.90%52.10%47.94%26.27%1.804
2547.38%52.62%48.20%26.41%1.804
2646.85%53.15%48.46%26.55%1.804
2746.33%53.67%48.71%26.70%1.803
2845.80%54.20%48.97%26.86%1.803
2945.28%54.72%49.23%27.02%1.801
3044.75%55.25%49.49%27.18%1.800
3144.23%55.77%49.75%27.36%1.798
3243.70%56.30%50.01%27.53%1.796
3343.18%56.82%50.27%27.71%1.794
3442.65%57.35%50.53%27.90%1.791
3542.13%57.87%50.79%28.08%1.789
3641.60%58.40%51.05%28.28%1.786
3741.08%58.92%51.32%28.48%1.783
3840.55%59.45%51.58%28.68%1.779
3940.03%59.97%51.84%28.88%1.775
4039.50%60.50%52.11%29.10%1.772
4138.98%61.02%52.37%29.31%1.768
4238.45%61.55%52.63%29.53%1.764
4337.93%62.07%52.90%29.75%1.759
4437.40%62.60%53.16%29.98%1.755
4536.88%63.12%53.43%30.20%1.750
4636.35%63.65%53.69%30.44%1.746
4735.83%64.17%53.96%30.67%1.741
4835.30%64.70%54.23%30.91%1.736
4934.78%65.22%54.49%31.16%1.731
5034.25%65.75%54.76%31.40%1.726
5133.73%66.27%55.03%31.65%1.721
5233.20%66.80%55.30%31.91%1.716
5332.68%67.32%55.57%32.16%1.711
5432.15%67.85%55.84%32.42%1.705
5531.63%68.37%56.11%32.68%1.700
5631.10%68.90%56.38%32.94%1.694
5730.58%69.42%56.65%33.21%1.689
5830.05%69.95%56.92%33.48%1.683
5929.53%70.47%57.19%33.75%1.678
6029.00%71.00%57.46%34.03%1.672
6128.48%71.52%57.73%34.30%1.667
6227.95%72.05%58.01%34.58%1.661
6327.43%72.57%58.28%34.87%1.656
6426.90%73.10%58.55%35.15%1.650
6526.38%73.62%58.83%35.44%1.644
6625.85%74.15%59.10%35.73%1.639
6725.33%74.67%59.38%36.02%1.633
6824.80%75.20%59.65%36.31%1.628
6924.28%75.72%59.93%36.60%1.622
7023.75%76.25%60.20%36.90%1.616
7123.23%76.77%60.48%37.20%1.611
7222.70%77.30%60.76%37.50%1.605
7322.18%77.82%61.04%37.80%1.600
7421.65%78.35%61.31%38.11%1.594
7521.13%78.87%61.59%38.41%1.589
7620.60%79.40%61.87%38.72%1.583
7720.08%79.92%62.15%39.03%1.578
7819.55%80.45%62.43%39.34%1.573
7919.03%80.97%62.71%39.66%1.567
8018.50%81.50%62.99%39.97%1.562
8117.98%82.02%63.27%40.29%1.557
8217.45%82.55%63.55%40.60%1.551
8316.93%83.07%63.84%40.92%1.546
8416.40%83.60%64.12%41.24%1.541
8515.88%84.12%64.40%41.57%1.536
8615.35%84.65%64.68%41.89%1.531
8714.83%85.17%64.97%42.21%1.526
8814.30%85.70%65.25%42.54%1.521
8913.78%86.22%65.54%42.87%1.516
9013.25%86.75%65.82%43.19%1.511
9112.73%87.27%66.11%43.52%1.506
9212.20%87.80%66.39%43.85%1.501
9311.68%88.32%66.68%44.19%1.496
9411.15%88.85%66.97%44.52%1.492
9510.63%89.37%67.25%44.85%1.487
9610.10%89.90%67.54%45.19%1.482
979.58%90.42%67.83%45.52%1.478
989.05%90.95%68.12%45.86%1.473
998.53%91.47%68.41%46.20%1.469
1008.00%92.00%68.70%46.54%1.464
*Ex-ante values shown for portfolio return and volatility. Ex ante Sharpe Ratio calculated using historical 3-month treasury bill returns as the risk-free rate (0.56% annualized).
Annual returns for the configured portfolios
YearInflationMaximum Sharpe Ratio ReturnMaximum Sharpe Ratio BalanceDirexion Daily 20+ Yr Trsy Bull 3X ETF (TMF)ProShares UltraPro QQQ (TQQQ)
20101.12%54.24%$15,42410.27%65.62%
20112.96%48.59%$22,918109.14%-8.05%
20121.74%34.57%$30,8400.60%52.29%
20131.50%30.05%$40,108-39.01%139.73%
20140.76%78.03%$71,40697.34%57.09%
20150.73%8.06%$77,162-13.73%17.23%
20162.07%10.44%$85,217-2.52%11.38%
20172.11%68.02%$143,17822.73%118.06%
20181.91%-10.30%$128,434-11.01%-19.80%
20192.29%94.70%$250,06334.74%133.83%
20201.36%99.00%$497,62841.60%110.05%
Annual return for 2010 is from 03/01/2010 to 12/31/2010
Monthly returns for the configured portfolios
YearMonthMaximum Sharpe Ratio ReturnDirexion Daily 20+ Yr Trsy Bull 3X ETF (TMF)ProShares UltraPro QQQ (TQQQ)
201039.75%-6.73%24.58%
201047.93%9.96%6.09%
20105-4.19%16.54%-22.85%
20106-2.01%16.73%-18.88%
201079.62%-3.90%21.80%
201084.33%25.94%-15.12%
2010918.42%-9.02%43.14%
2010103.86%-13.57%19.55%
201011-3.61%-6.03%-1.43%
2010122.29%-11.63%14.81%
20111-0.24%-9.40%8.01%
201126.94%4.49%9.14%
20113-1.50%-0.55%-2.35%
201147.63%6.57%8.58%
201152.64%10.36%-4.31%
20116-7.19%-7.39%-7.01%
201178.62%13.28%4.43%
201182.67%27.34%-19.54%
2011912.06%41.35%-14.31%
20111010.50%-12.87%31.54%
201111-3.02%4.89%-10.15%
2011122.99%9.46%-2.83%
2012113.42%-1.50%26.86%
201226.83%-7.95%20.14%
201231.97%-13.02%15.46%
201244.54%14.37%-4.30%
201252.93%28.90%-20.45%
201262.42%-5.78%9.79%
201276.62%11.43%2.28%
201286.29%-4.61%16.09%
20129-2.60%-7.87%2.14%
201210-9.23%-2.13%-15.63%
2012113.53%3.90%3.19%
201212-4.71%-7.80%-1.93%
20131-0.51%-9.58%7.65%
201321.92%3.39%0.59%
201333.76%-1.77%8.74%
2013410.40%14.25%6.94%
20135-3.67%-19.65%10.71%
20136-9.12%-10.33%-8.02%
201377.09%-7.41%20.14%
20138-3.01%-4.47%-1.69%
201398.57%1.53%14.91%
2013109.69%4.12%14.70%
2013111.56%-8.19%10.34%
2013121.81%-6.01%8.86%
201415.88%19.47%-6.36%
201428.88%1.63%15.40%
20143-3.57%1.76%-8.37%
201441.75%5.96%-2.03%
2014511.27%8.79%13.50%
201464.50%-1.00%9.46%
201472.37%1.61%3.05%
2014814.97%14.42%15.47%
20149-4.61%-6.65%-2.78%
2014107.28%8.06%6.58%
20141111.83%9.08%14.30%
2014120.49%9.38%-7.51%
2015111.04%31.01%-6.95%
201523.50%-17.87%22.74%
20153-2.71%2.57%-7.46%
20154-2.17%-10.30%5.16%
20155-0.41%-7.91%6.35%
20156-9.94%-12.49%-7.65%
2015713.38%13.40%13.35%
20158-12.50%-2.75%-21.28%
20159-1.86%5.10%-8.13%
20151018.77%-1.73%37.23%
201511-0.59%-2.71%1.31%
201512-4.17%-2.41%-5.77%
20161-2.71%17.74%-21.13%
201620.95%8.71%-6.04%
2016310.73%-0.64%20.97%
20164-6.17%-2.39%-9.56%
201657.64%1.86%12.84%
201665.94%21.23%-7.83%
2016714.73%6.07%22.52%
20168-0.12%-3.58%2.99%
201690.79%-4.78%5.80%
201610-8.74%-13.32%-4.61%
201611-10.75%-23.91%1.10%
2016120.90%-0.99%2.60%
201719.00%1.49%15.76%
201729.14%4.41%13.39%
201731.86%-2.35%5.64%
201746.35%4.43%8.07%
201758.46%5.17%11.43%
20176-3.31%1.98%-8.07%
201775.46%-2.43%12.56%
201787.45%10.13%5.04%
20179-4.01%-7.29%-1.06%
2017106.98%-0.53%13.74%
2017113.72%1.73%5.50%
2017123.01%5.04%1.18%
201819.95%-9.77%27.70%
20182-7.78%-9.57%-6.16%
20183-3.06%8.44%-13.42%
20184-3.40%-6.71%-0.42%
2018511.44%5.27%17.00%
201861.85%1.49%2.18%
201871.75%-4.70%7.56%
2018810.90%3.36%17.69%
20189-5.00%-8.77%-1.60%
201810-18.32%-9.11%-26.61%
2018110.72%4.76%-2.91%
201812-5.63%17.93%-26.84%
2019114.36%0.41%26.92%
201922.37%-4.52%8.57%
2019313.87%17.00%11.05%
201945.65%-6.56%16.64%
20195-2.64%21.11%-24.01%
2019613.00%1.90%23.00%
201973.41%0.32%6.20%
2019812.53%35.11%-7.79%
20199-3.31%-9.07%1.88%
2019104.59%-4.11%12.43%
2019115.47%-2.01%12.20%
2019121.23%-10.05%11.37%
2020115.59%23.80%8.19%
20202-0.86%17.91%-17.77%
20203-14.42%11.91%-38.13%
2020425.72%2.68%46.45%
202056.74%-6.48%18.63%
202069.72%0.54%17.98%
2020717.93%13.13%22.25%
2020811.45%-14.89%35.17%
20209-8.92%2.15%-18.88%
202010-10.31%-10.35%-10.28%
20201120.19%4.24%34.54%
2020126.82%-2.32%15.05%
Portfolio return and risk metrics
MetricMaximum Sharpe Ratio
Arithmetic Mean (monthly)3.33%
Arithmetic Mean (annualized)48.20%
Geometric Mean (monthly)3.05%
Geometric Mean (annualized)43.43%
Volatility (monthly)7.62%
Volatility (annualized)26.41%
Downside Deviation (monthly)3.71%
Max. Drawdown-26.24%
US Market Correlation0.63
Beta(*)1.13
Alpha (annualized)23.68%
R239.37%
Sharpe Ratio1.49
Sortino Ratio3.05
Treynor Ratio (%)34.92
Calmar Ratio1.96
Active Return29.21%
Tracking Error20.65%
Information Ratio1.41
Skewness-0.02
Excess Kurtosis0.14
Historical Value-at-Risk (5%)-9.18%
Analytical Value-at-Risk (5%)-9.16%
Conditional Value-at-Risk (5%)-12.21%
Upside Capture Ratio (%)178.82
Downside Capture Ratio (%)58.29
Safe Withdrawal Rate41.90%
Perpetual Withdrawal Rate28.71%
Positive Periods87 out of 130 (66.92%)
Gain/Loss Ratio1.48
* US stock market is used as the benchmark for calculations. Value-at-risk metrics are based on monthly values.

Drawdowns for Maximum Sharpe Ratio

Drawdowns for Maximum Sharpe Ratio (worst 10)
RankStartEndLengthRecovery ByRecovery TimeUnderwater PeriodDrawdown
1Sep 2018Dec 20184 monthsApr 20194 months8 months-26.24%
2Oct 2016Nov 20162 monthsApr 20175 months7 months-18.55%
3Sep 2020Oct 20202 monthsDec 20202 months4 months-18.31%
4Mar 2015Sep 20157 monthsMar 20166 months1 year 1 month-16.89%
5Feb 2020Mar 20202 monthsApr 20201 month3 months-15.16%
6Feb 2018Apr 20183 monthsAug 20184 months7 months-13.65%
7Sep 2012Jan 20135 monthsApr 20133 months8 months-13.24%
8May 2013Jun 20132 monthsOct 20134 months6 months-12.46%
9Jun 2011Jun 20111 monthJul 20111 month2 months-7.19%
10Apr 2016Apr 20161 monthMay 20161 month2 months-6.17%
Worst 10 drawdowns included above

Portfolio Assets

Performance statistics for portfolio components
TickerNameCAGRStdevBest YearWorst YearMax. DrawdownSharpe RatioSortino RatioUS Mkt Correlation
TMFDirexion Daily 20+ Yr Trsy Bull 3X ETF15.79%39.42%109.14%-39.01%-49.74%0.541.04-0.46
TQQQProShares UltraPro QQQ52.68%51.82%139.73%-19.80%-49.12%1.071.950.92

Monthly Correlations

Correlations for the portfolio assets
TickerNameTMFTQQQMaximum Sharpe Ratio
TMFDirexion Daily 20+ Yr Trsy Bull 3X ETF1.00-0.390.31
TQQQProShares UltraPro QQQ-0.391.000.76

Portfolio Risk Decomposition

Portfolio risk decomposition
TickerNameMaximum Sharpe Ratio
TMFDirexion Daily 20+ Yr Trsy Bull 3X ETF21.70%
TQQQProShares UltraPro QQQ78.30%

Annual Asset Returns

Rolling returns summary
Roll PeriodAverageHighLow
1 year43.13%106.87%-10.30%
3 years35.81%53.77%18.51%
5 years35.04%52.35%25.16%
7 years35.76%46.62%27.29%
10 years40.27%43.61%36.43%