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 - Sep 2020)

Portfolio optimization results with goal to maximize sharpe ratio. The possible range of expected annual portfolio returns for the given period is 21.54% to 129.75%. Refer to the efficient frontier section for additional details.

Portfolio Allocations

Maximum Sharpe Ratio
Ticker Name Allocation
FNGU MicroSectors FANG+ 3X Leveraged ETN 100.00%
Save portfolio »

Portfolio Performance Summary

Portfolio performance statistics
MetricMaximum Sharpe Ratio
Start Balance$10,000
End Balance$33,002
CAGR56.48%
Expected Return 129.75%
Stdev93.24%
Best Year221.13%
Worst Year-52.70%
Max. Drawdown -61.92%
Sharpe Ratio (ex-ante)1.37
Sharpe Ratio (ex-post)0.91
Sortino Ratio1.68
US Stock Market Correlation0.83
   

Trailing Returns

Trailing Returns
Name3 MonthYTD1 yearFull
Maximum Sharpe Ratio104.50%221.13%472.49%56.48%
Trailing returns are for full months ending in September 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 September
  • 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)0.94%21.54%58.57%0.3400.00%100.00%
2ProShares UltraPro QQQ (TQQQ)34.88%66.46%66.17%0.9800.00%100.00%
3MicroSectors FANG+ 3X Leveraged ETN (FNGU)56.48%129.75%93.24%1.3740.00%100.00%
Results based on historical returns. Ex ante Sharpe Ratio calculated using 3-month treasury bill returns as the risk-free rate (1.62% annualized).

Asset Correlations

Efficient Frontier Asset Correlations
NameTickerUPROTQQQFNGU
ProShares UltraPro S&P500UPRO1.000.950.82
ProShares UltraPro QQQTQQQ0.951.000.92
MicroSectors FANG+ 3X Leveraged ETNFNGU0.820.921.00
Based on monthly returns from Feb 2018 to Sep 2020
Efficient Frontier Assets
#UPROTQQQFNGUExpected Return*Standard Deviation*Sharpe Ratio*
1100.00%0.00%0.00%21.54%58.57%0.340
297.93%2.07%0.00%22.35%58.66%0.353
395.85%4.15%0.00%23.16%58.76%0.367
493.78%6.22%0.00%23.97%58.86%0.380
591.71%8.29%0.00%24.79%58.96%0.393
689.64%10.36%0.00%25.62%59.07%0.406
787.56%12.44%0.00%26.45%59.18%0.420
885.49%14.51%0.00%27.28%59.29%0.433
983.42%16.58%0.00%28.12%59.41%0.446
1081.34%18.66%0.00%28.97%59.52%0.459
1179.27%20.73%0.00%29.82%59.64%0.473
1277.20%22.80%0.00%30.68%59.77%0.486
1375.12%24.88%0.00%31.54%59.89%0.499
1473.05%26.95%0.00%32.40%60.02%0.513
1570.98%29.02%0.00%33.27%60.15%0.526
1668.91%31.09%0.00%34.15%60.29%0.540
1766.83%33.17%0.00%35.03%60.43%0.553
1864.76%35.24%0.00%35.92%60.57%0.566
1962.69%37.31%0.00%36.81%60.71%0.580
2060.61%39.39%0.00%37.71%60.85%0.593
2158.54%41.46%0.00%38.61%61.00%0.606
2256.47%43.53%0.00%39.52%61.15%0.620
2354.39%45.61%0.00%40.43%61.30%0.633
2452.32%47.68%0.00%41.35%61.46%0.646
2550.25%49.75%0.00%42.28%61.62%0.660
2648.18%51.82%0.00%43.21%61.78%0.673
2746.10%53.90%0.00%44.14%61.94%0.686
2844.03%55.97%0.00%45.08%62.11%0.700
2941.96%58.04%0.00%46.03%62.27%0.713
3039.88%60.12%0.00%46.98%62.44%0.726
3137.81%62.19%0.00%47.94%62.62%0.740
3235.74%64.26%0.00%48.91%62.79%0.753
3333.67%66.33%0.00%49.88%62.97%0.766
3431.59%68.41%0.00%50.85%63.15%0.780
3529.52%70.48%0.00%51.83%63.33%0.793
3627.45%72.55%0.00%52.82%63.52%0.806
3725.37%74.63%0.00%53.81%63.70%0.819
3823.30%76.70%0.00%54.81%63.89%0.833
3921.23%78.77%0.00%55.82%64.08%0.846
4019.15%80.85%0.00%56.83%64.28%0.859
4117.08%82.92%0.00%57.85%64.47%0.872
4215.01%84.99%0.00%58.87%64.67%0.885
4312.94%87.06%0.00%59.90%64.87%0.898
4410.86%89.14%0.00%60.93%65.07%0.911
458.79%91.21%0.00%61.98%65.28%0.925
466.72%93.28%0.00%63.02%65.49%0.938
474.64%95.36%0.00%64.08%65.69%0.951
482.57%97.43%0.00%65.14%65.91%0.964
490.50%99.50%0.00%66.20%66.12%0.977
500.00%98.50%1.50%67.28%66.47%0.988
510.00%96.53%3.47%68.36%66.86%0.998
520.00%94.56%5.44%69.44%67.27%1.008
530.00%92.59%7.41%70.53%67.68%1.018
540.00%90.62%9.38%71.63%68.10%1.028
550.00%88.65%11.35%72.74%68.53%1.038
560.00%86.68%13.32%73.85%68.96%1.047
570.00%84.71%15.29%74.97%69.40%1.057
580.00%82.74%17.26%76.09%69.85%1.066
590.00%80.77%19.23%77.22%70.30%1.075
600.00%78.80%21.20%78.36%70.76%1.084
610.00%76.83%23.17%79.50%71.23%1.093
620.00%74.86%25.14%80.65%71.70%1.102
630.00%72.89%27.11%81.81%72.18%1.111
640.00%70.92%29.08%82.98%72.66%1.120
650.00%68.95%31.05%84.15%73.16%1.128
660.00%66.98%33.02%85.33%73.65%1.136
670.00%65.01%34.99%86.51%74.15%1.145
680.00%63.04%36.96%87.70%74.66%1.153
690.00%61.07%38.93%88.90%75.18%1.161
700.00%59.10%40.90%90.11%75.69%1.169
710.00%57.13%42.87%91.32%76.22%1.177
720.00%55.16%44.84%92.54%76.75%1.185
730.00%53.19%46.81%93.77%77.28%1.192
740.00%51.22%48.78%95.01%77.82%1.200
750.00%49.25%50.75%96.25%78.36%1.208
760.00%47.28%52.72%97.50%78.91%1.215
770.00%45.31%54.69%98.75%79.46%1.222
780.00%43.34%56.66%100.02%80.02%1.230
790.00%41.37%58.63%101.29%80.58%1.237
800.00%39.40%60.60%102.57%81.15%1.244
810.00%37.43%62.57%103.85%81.72%1.251
820.00%35.46%64.54%105.15%82.29%1.258
830.00%33.49%66.51%106.45%82.87%1.265
840.00%31.52%68.48%107.76%83.45%1.272
850.00%29.55%70.45%109.07%84.04%1.279
860.00%27.58%72.42%110.39%84.63%1.285
870.00%25.61%74.39%111.73%85.22%1.292
880.00%23.64%76.36%113.07%85.82%1.299
890.00%21.67%78.33%114.41%86.42%1.305
900.00%19.70%80.30%115.77%87.02%1.312
910.00%17.73%82.27%117.13%87.63%1.318
920.00%15.76%84.24%118.50%88.24%1.325
930.00%13.79%86.21%119.88%88.85%1.331
940.00%11.82%88.18%121.26%89.47%1.337
950.00%9.85%90.15%122.66%90.09%1.343
960.00%7.88%92.12%124.06%90.72%1.350
970.00%5.91%94.09%125.47%91.34%1.356
980.00%3.94%96.06%126.89%91.97%1.362
990.00%1.97%98.03%128.32%92.60%1.368
1000.00%0.00%100.00%129.75%93.24%1.374
*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 (1.62% annualized).
Annual returns for the configured portfolios
YearInflationMaximum Sharpe Ratio ReturnMaximum Sharpe Ratio BalanceMicroSectors FANG+ 3X Leveraged ETN (FNGU)
20181.36%-52.70%$4,730-52.70%
20192.29%117.25%$10,277117.25%
20201.29%221.13%$33,002221.13%
Annual returns for 2018 and 2020 are based on partial years
Monthly returns for the configured portfolios
YearMonthMaximum Sharpe Ratio ReturnMaximum Sharpe Ratio BalanceMicroSectors FANG+ 3X Leveraged ETN (FNGU)
201824.00%$10,4004.00%
20183-22.35%$8,076-22.35%
201848.64%$8,7738.64%
2018524.25%$10,90024.25%
2018613.97%$12,42313.97%
20187-14.76%$10,589-14.76%
2018816.04%$12,28716.04%
20189-13.24%$10,660-13.24%
201810-24.56%$8,041-24.56%
201811-15.38%$6,804-15.38%
201812-30.48%$4,730-30.48%
2019139.41%$6,59539.41%
201920.64%$6,6360.64%
2019310.45%$7,33010.45%
2019413.34%$8,30813.34%
20195-40.00%$4,985-40.00%
2019623.65%$6,16323.65%
2019710.84%$6,83110.84%
20198-12.90%$5,950-12.90%
20199-3.12%$5,765-3.12%
20191018.00%$6,80218.00%
20191122.35%$8,32322.35%
20191223.47%$10,27723.47%
2020124.44%$12,78924.44%
20202-5.95%$12,027-5.95%
20203-43.12%$6,841-43.12%
2020459.84%$10,93559.84%
2020519.20%$13,03419.20%
2020623.81%$16,13723.81%
2020743.74%$23,19643.74%
2020873.49%$40,24273.49%
20209-17.99%$33,002-17.99%
Portfolio return and risk metrics
MetricMaximum Sharpe Ratio
Arithmetic Mean (monthly)7.18%
Arithmetic Mean (annualized)129.75%
Geometric Mean (monthly)3.80%
Geometric Mean (annualized)56.48%
Volatility (monthly)26.92%
Volatility (annualized)93.24%
Downside Deviation (monthly)14.42%
Max. Drawdown-61.92%
US Market Correlation0.83
Beta(*)3.98
Alpha (annualized)46.67%
R268.18%
Sharpe Ratio0.91
Sortino Ratio1.68
Treynor Ratio (%)21.22
Active Return48.10%
Tracking Error78.05%
Information Ratio0.62
Skewness0.26
Excess Kurtosis0.18
Historical Value-at-Risk (5%)-41.09%
Analytical Value-at-Risk (5%)-37.09%
Conditional Value-at-Risk (5%)-43.12%
Upside Capture Ratio (%)697.41
Downside Capture Ratio (%)275.64
Safe Withdrawal Rate31.73%
Perpetual Withdrawal Rate43.59%
Positive Periods20 out of 32 (62.50%)
Gain/Loss Ratio1.17
* 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
1Jul 2018Dec 20186 monthsJan 20201 year 1 month1 year 7 months-61.92%
2Feb 2020Mar 20202 monthsMay 20202 months4 months-46.51%
3Mar 2018Mar 20181 monthMay 20182 months3 months-22.35%
4Sep 2020Sep 20201 month-17.99%

Portfolio Assets

Performance statistics for portfolio components
TickerNameCAGRStdevBest YearWorst YearMax. DrawdownSharpe RatioSortino RatioUS Mkt Correlation
FNGUMicroSectors FANG+ 3X Leveraged ETN56.48%93.24%221.13%-52.70%-61.92%0.911.680.83

Monthly Correlations

Correlations for the portfolio assets
TickerNameFNGUMaximum Sharpe Ratio
FNGUMicroSectors FANG+ 3X Leveraged ETN1.001.00

Portfolio Risk Decomposition

Portfolio risk decomposition
TickerNameMaximum Sharpe Ratio
FNGUMicroSectors FANG+ 3X Leveraged ETN100.00%

Annual Asset Returns