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
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Portfolio Optimization Results (Feb 2018 - Jan 2020)

Portfolio optimization results with goal to maximize sharpe ratio. The possible range of expected annual portfolio returns for the given period is 23.36% to 45.84%. Refer to the efficient frontier section for additional details.

Portfolio Allocations

Maximum Sharpe Ratio
Ticker Name Allocation
UPRO ProShares UltraPro S&P500 0.80%
TQQQ ProShares UltraPro QQQ 99.20%
Save portfolio »

Portfolio Performance Summary

Portfolio performance statistics
MetricMaximum Sharpe Ratio
Start Balance$10,000
End Balance$15,862
CAGR25.95%
Expected Return 43.18%
Stdev51.01%
Best Year133.58%
Worst Year-37.19%
Max. Drawdown -48.63%
Sharpe Ratio (ex-ante)0.81
Sharpe Ratio (ex-post)0.67
Sortino Ratio1.01
US Stock Market Correlation0.95
   

Trailing Returns

Trailing Returns
Name3 MonthYTD1 yearFull
Maximum Sharpe Ratio35.06%8.12%99.02%25.95%
Trailing returns are for full months ending in January 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.
  • The annual results for 2018 are based on full calendar months from February to December
  • The annual results for 2020 are based on full calendar months from January to January
  • 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
1ProShares UltraPro S&P500 (UPRO)12.66%23.36%42.76%0.4990.00%100.00%
2ProShares UltraPro QQQ (TQQQ)26.04%43.35%51.10%0.8090.00%100.00%
3MicroSectors FANG+ 3X Leveraged ETN (FNGU)13.09%45.85%71.55%0.6130.00%100.00%
Results based on historical returns. Ex ante Sharpe Ratio calculated using 3-month treasury bill returns as the risk-free rate (2.02% annualized).

Asset Correlations

Efficient Frontier Asset Correlations
NameTickerUPROTQQQFNGU
ProShares UltraPro S&P500UPRO1.000.950.76
ProShares UltraPro QQQTQQQ0.951.000.89
MicroSectors FANG+ 3X Leveraged ETNFNGU0.760.891.00
Based on monthly returns from Feb 2018 to Jan 2020
Efficient Frontier Assets
#UPROTQQQFNGUExpected Return*Standard Deviation*Sharpe Ratio*
1100.00%0.00%0.00%23.36%42.76%0.499
298.87%1.13%0.00%23.57%42.82%0.503
397.75%2.25%0.00%23.78%42.89%0.507
496.62%3.38%0.00%23.99%42.95%0.511
595.49%4.51%0.00%24.20%43.02%0.516
694.36%5.64%0.00%24.41%43.09%0.520
793.24%6.76%0.00%24.62%43.15%0.524
892.11%7.89%0.00%24.84%43.22%0.528
990.98%9.02%0.00%25.05%43.29%0.532
1089.85%10.15%0.00%25.26%43.36%0.536
1188.73%11.27%0.00%25.48%43.43%0.540
1287.60%12.40%0.00%25.69%43.50%0.544
1386.47%13.53%0.00%25.90%43.57%0.548
1485.35%14.65%0.00%26.12%43.65%0.552
1584.22%15.78%0.00%26.33%43.72%0.556
1683.09%16.91%0.00%26.55%43.79%0.560
1781.96%18.04%0.00%26.76%43.87%0.564
1880.84%19.16%0.00%26.98%43.94%0.568
1979.71%20.29%0.00%27.19%44.02%0.572
2078.58%21.42%0.00%27.41%44.10%0.576
2177.46%22.54%0.00%27.63%44.18%0.580
2276.33%23.67%0.00%27.84%44.26%0.583
2375.20%24.80%0.00%28.06%44.34%0.587
2474.07%25.93%0.00%28.28%44.42%0.591
2572.95%27.05%0.00%28.50%44.50%0.595
2671.82%28.18%0.00%28.72%44.58%0.599
2770.69%29.31%0.00%28.93%44.66%0.603
2869.56%30.44%0.00%29.15%44.74%0.606
2968.44%31.56%0.00%29.37%44.83%0.610
3067.31%32.69%0.00%29.59%44.91%0.614
3166.18%33.82%0.00%29.81%45.00%0.618
3265.06%34.94%0.00%30.03%45.08%0.621
3363.93%36.07%0.00%30.25%45.17%0.625
3462.80%37.20%0.00%30.47%45.26%0.629
3561.67%38.33%0.00%30.70%45.35%0.632
3660.55%39.45%0.00%30.92%45.43%0.636
3759.42%40.58%0.00%31.14%45.52%0.640
3858.29%41.71%0.00%31.36%45.61%0.643
3957.17%42.83%0.00%31.59%45.70%0.647
4056.04%43.96%0.00%31.81%45.80%0.650
4154.91%45.09%0.00%32.03%45.89%0.654
4253.78%46.22%0.00%32.26%45.98%0.658
4352.66%47.34%0.00%32.48%46.07%0.661
4451.53%48.47%0.00%32.70%46.17%0.665
4550.40%49.60%0.00%32.93%46.26%0.668
4649.27%50.73%0.00%33.15%46.36%0.672
4748.15%51.85%0.00%33.38%46.45%0.675
4847.02%52.98%0.00%33.61%46.55%0.678
4945.89%54.11%0.00%33.83%46.65%0.682
5044.77%55.23%0.00%34.06%46.75%0.685
5143.64%56.36%0.00%34.29%46.84%0.689
5242.51%57.49%0.00%34.51%46.94%0.692
5341.38%58.62%0.00%34.74%47.04%0.696
5440.26%59.74%0.00%34.97%47.14%0.699
5539.13%60.87%0.00%35.20%47.24%0.702
5638.00%62.00%0.00%35.43%47.35%0.706
5736.88%63.12%0.00%35.66%47.45%0.709
5835.75%64.25%0.00%35.88%47.55%0.712
5934.62%65.38%0.00%36.11%47.65%0.715
6033.49%66.51%0.00%36.34%47.76%0.719
6132.37%67.63%0.00%36.58%47.86%0.722
6231.24%68.76%0.00%36.81%47.97%0.725
6330.11%69.89%0.00%37.04%48.07%0.728
6428.98%71.02%0.00%37.27%48.18%0.732
6527.86%72.14%0.00%37.50%48.29%0.735
6626.73%73.27%0.00%37.73%48.39%0.738
6725.60%74.40%0.00%37.97%48.50%0.741
6824.48%75.52%0.00%38.20%48.61%0.744
6923.35%76.65%0.00%38.43%48.72%0.747
7022.22%77.78%0.00%38.67%48.83%0.750
7121.09%78.91%0.00%38.90%48.94%0.754
7219.97%80.03%0.00%39.13%49.05%0.757
7318.84%81.16%0.00%39.37%49.16%0.760
7417.71%82.29%0.00%39.60%49.27%0.763
7516.59%83.41%0.00%39.84%49.39%0.766
7615.46%84.54%0.00%40.08%49.50%0.769
7714.33%85.67%0.00%40.31%49.61%0.772
7813.20%86.80%0.00%40.55%49.73%0.775
7912.08%87.92%0.00%40.79%49.84%0.778
8010.95%89.05%0.00%41.02%49.96%0.781
819.82%90.18%0.00%41.26%50.07%0.784
828.69%91.31%0.00%41.50%50.19%0.787
837.57%92.43%0.00%41.74%50.30%0.790
846.44%93.56%0.00%41.98%50.42%0.792
855.31%94.69%0.00%42.22%50.54%0.795
864.19%95.81%0.00%42.46%50.66%0.798
873.06%96.94%0.00%42.70%50.77%0.801
881.93%98.07%0.00%42.94%50.89%0.804
890.80%99.20%0.00%43.18%51.01%0.807
900.00%97.21%2.79%43.42%51.45%0.805
910.00%87.49%12.51%43.66%52.82%0.788
920.00%77.77%22.23%43.90%54.36%0.770
930.00%68.05%31.95%44.14%56.07%0.751
940.00%58.33%41.67%44.39%57.93%0.731
950.00%48.61%51.39%44.63%59.93%0.711
960.00%38.89%61.11%44.87%62.05%0.691
970.00%29.16%70.84%45.12%64.29%0.670
980.00%19.44%80.56%45.36%66.62%0.651
990.00%9.72%90.28%45.60%69.05%0.631
1000.00%0.00%100.00%45.85%71.55%0.613
*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 (2.02% annualized).
Annual returns for the configured portfolios
YearInflationMaximum Sharpe Ratio ReturnMaximum Sharpe Ratio BalanceProShares UltraPro S&P500 (UPRO)ProShares UltraPro QQQ (TQQQ)
20181.36%-37.19%$6,281-36.68%-37.20%
20192.29%133.58%$14,671102.31%133.83%
20200.39%8.12%$15,862-0.91%8.19%
Annual returns for 2018 and 2020 are based on partial years
Monthly returns for the configured portfolios
YearMonthMaximum Sharpe Ratio ReturnMaximum Sharpe Ratio BalanceProShares UltraPro S&P500 (UPRO)ProShares UltraPro QQQ (TQQQ)
20182-6.22%$9,378-13.53%-6.16%
20183-13.38%$8,123-8.69%-13.42%
20184-0.42%$8,088-0.14%-0.42%
2018516.91%$9,4566.46%17.00%
201862.18%$9,6621.29%2.18%
201877.59%$10,39510.73%7.56%
2018817.63%$12,2289.09%17.69%
20189-1.58%$12,0341.20%-1.60%
201810-26.56%$8,838-20.78%-26.61%
201811-2.85%$8,5864.28%-2.91%
201812-26.84%$6,281-26.25%-26.84%
2019126.89%$7,97023.89%26.92%
201928.58%$8,6549.28%8.57%
2019311.00%$9,6064.85%11.05%
2019416.60%$11,20111.81%16.64%
20195-23.97%$8,516-18.89%-24.01%
2019622.99%$10,47321.37%23.00%
201976.18%$11,1213.80%6.20%
20198-7.78%$10,256-6.62%-7.79%
201991.91%$10,4525.30%1.88%
20191012.37%$11,7455.70%12.43%
20191112.18%$13,17610.73%12.20%
20191211.35%$14,6718.38%11.37%
202018.12%$15,862-0.91%8.19%
Portfolio return and risk metrics
MetricMaximum Sharpe Ratio
Arithmetic Mean (monthly)3.04%
Arithmetic Mean (annualized)43.18%
Geometric Mean (monthly)1.94%
Geometric Mean (annualized)25.95%
Volatility (monthly)14.73%
Volatility (annualized)51.01%
Downside Deviation (monthly)9.77%
Max. Drawdown-48.63%
US Market Correlation0.95
Beta(*)3.31
Alpha (annualized)6.29%
R290.05%
Sharpe Ratio0.67
Sortino Ratio1.01
Treynor Ratio (%)10.41
Active Return17.57%
Tracking Error37.41%
Information Ratio0.47
Skewness-0.69
Excess Kurtosis-0.05
Historical Value-at-Risk (5%)-26.77%
Analytical Value-at-Risk (5%)-20.68%
Conditional Value-at-Risk (5%)-26.84%
Upside Capture Ratio (%)437.40
Downside Capture Ratio (%)287.08
Safe Withdrawal Rate43.10%
Perpetual Withdrawal Rate19.00%
Positive Periods15 out of 24 (62.50%)
Gain/Loss Ratio1.00
* 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
RankStartEndLengthRecovery ByRecovery TimeUnderwater PeriodDrawdown
1Sep 2018Dec 20184 monthsNov 201911 months1 year 3 months-48.63%
2Feb 2018Apr 20183 monthsJul 20183 months6 months-19.12%

Portfolio Assets

Performance statistics for portfolio components
TickerNameCAGRStdevBest YearWorst YearMax. DrawdownSharpe RatioSortino RatioUS Mkt Correlation
UPROProShares UltraPro S&P50012.66%42.76%102.31%-36.68%-39.08%0.450.641.00
TQQQProShares UltraPro QQQ26.04%51.10%133.83%-37.20%-48.71%0.681.010.95

Monthly Correlations

Correlations for the portfolio assets
TickerNameUPROTQQQMaximum Sharpe Ratio
UPROProShares UltraPro S&P5001.000.950.95
TQQQProShares UltraPro QQQ0.951.001.00

Portfolio Risk Decomposition

Portfolio risk decomposition
TickerNameMaximum Sharpe Ratio
UPROProShares UltraPro S&P5000.64%
TQQQProShares UltraPro QQQ99.36%

Annual Asset Returns