This portfolio optimizer tool supports the following portfolio optimization strategies:

- Mean Variance Optimization – Find the optimal risk adjusted portfolio that lies on the efficient frontier
- Minimize Conditional Value-at-Risk – Optimize the portfolio to minimize the expected tail loss
- Risk Parity – Find the portfolio that equalizes the risk contribution of portfolio assets
- Minimize Tracking Error – Find the portfolio that minimizes the tracking error against the selected benchmark
- Maximize Information Ratio – Find the portfolio that maximizes the information ratio against the selected benchmark
- Maximize Kelly Criterion – Finds the portfolio with the maximum expected geometric growth rate
- Maximize Sortino Ratio – Find the portfolio that maximizes the Sortino ratio for the given minimum acceptable return
- Maximize Omega Ratio – Find the portfolio that maximizes the Omega ratio for the given minimum acceptable return
- Minimize Maximum Drawdown – Find the portfolio with the minimum worst case drawdown with optional minimum acceptable return

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.

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.

Ticker | Name | Allocation |
---|---|---|

UPRO | ProShares UltraPro S&P500 | 0.80% |

TQQQ | ProShares UltraPro QQQ | 99.20% |

Save portfolio » |

Metric | Maximum Sharpe Ratio |
---|---|

Start Balance | $10,000 |

End Balance | $15,862 |

CAGR | 25.95% |

Expected Return | 43.18% |

Stdev | 51.01% |

Best Year | 133.58% |

Worst Year | -37.19% |

Max. Drawdown | -48.63% |

Sharpe Ratio (ex-ante) | 0.81 |

Sharpe Ratio (ex-post) | 0.67 |

Sortino Ratio | 1.01 |

US Stock Market Correlation | 0.95 |

Name | 3 Month | YTD | 1 year | Full |
---|---|---|---|---|

Maximum Sharpe Ratio | 35.06% | 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.

# | Asset | CAGR | Expected Return | Standard Deviation | Sharpe Ratio | Min. Weight | Max. Weight |
---|---|---|---|---|---|---|---|

1 | ProShares UltraPro S&P500 (UPRO) | 12.66% | 23.36% | 42.76% | 0.499 | 0.00% | 100.00% |

2 | ProShares UltraPro QQQ (TQQQ) | 26.04% | 43.35% | 51.10% | 0.809 | 0.00% | 100.00% |

3 | MicroSectors FANG+ 3X Leveraged ETN (FNGU) | 13.09% | 45.85% | 71.55% | 0.613 | 0.00% | 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). |

Name | Ticker | UPRO | TQQQ | FNGU |
---|---|---|---|---|

ProShares UltraPro S&P500 | UPRO | 1.00 | 0.95 | 0.76 |

ProShares UltraPro QQQ | TQQQ | 0.95 | 1.00 | 0.89 |

MicroSectors FANG+ 3X Leveraged ETN | FNGU | 0.76 | 0.89 | 1.00 |

Based on monthly returns from Feb 2018 to Jan 2020 |

# | UPRO | TQQQ | FNGU | Expected Return^{*} | Standard Deviation^{*} | Sharpe Ratio^{*} |
---|---|---|---|---|---|---|

1 | 100.00% | 0.00% | 0.00% | 23.36% | 42.76% | 0.499 |

2 | 98.87% | 1.13% | 0.00% | 23.57% | 42.82% | 0.503 |

3 | 97.75% | 2.25% | 0.00% | 23.78% | 42.89% | 0.507 |

4 | 96.62% | 3.38% | 0.00% | 23.99% | 42.95% | 0.511 |

5 | 95.49% | 4.51% | 0.00% | 24.20% | 43.02% | 0.516 |

6 | 94.36% | 5.64% | 0.00% | 24.41% | 43.09% | 0.520 |

7 | 93.24% | 6.76% | 0.00% | 24.62% | 43.15% | 0.524 |

8 | 92.11% | 7.89% | 0.00% | 24.84% | 43.22% | 0.528 |

9 | 90.98% | 9.02% | 0.00% | 25.05% | 43.29% | 0.532 |

10 | 89.85% | 10.15% | 0.00% | 25.26% | 43.36% | 0.536 |

11 | 88.73% | 11.27% | 0.00% | 25.48% | 43.43% | 0.540 |

12 | 87.60% | 12.40% | 0.00% | 25.69% | 43.50% | 0.544 |

13 | 86.47% | 13.53% | 0.00% | 25.90% | 43.57% | 0.548 |

14 | 85.35% | 14.65% | 0.00% | 26.12% | 43.65% | 0.552 |

15 | 84.22% | 15.78% | 0.00% | 26.33% | 43.72% | 0.556 |

16 | 83.09% | 16.91% | 0.00% | 26.55% | 43.79% | 0.560 |

17 | 81.96% | 18.04% | 0.00% | 26.76% | 43.87% | 0.564 |

18 | 80.84% | 19.16% | 0.00% | 26.98% | 43.94% | 0.568 |

19 | 79.71% | 20.29% | 0.00% | 27.19% | 44.02% | 0.572 |

20 | 78.58% | 21.42% | 0.00% | 27.41% | 44.10% | 0.576 |

21 | 77.46% | 22.54% | 0.00% | 27.63% | 44.18% | 0.580 |

22 | 76.33% | 23.67% | 0.00% | 27.84% | 44.26% | 0.583 |

23 | 75.20% | 24.80% | 0.00% | 28.06% | 44.34% | 0.587 |

24 | 74.07% | 25.93% | 0.00% | 28.28% | 44.42% | 0.591 |

25 | 72.95% | 27.05% | 0.00% | 28.50% | 44.50% | 0.595 |

26 | 71.82% | 28.18% | 0.00% | 28.72% | 44.58% | 0.599 |

27 | 70.69% | 29.31% | 0.00% | 28.93% | 44.66% | 0.603 |

28 | 69.56% | 30.44% | 0.00% | 29.15% | 44.74% | 0.606 |

29 | 68.44% | 31.56% | 0.00% | 29.37% | 44.83% | 0.610 |

30 | 67.31% | 32.69% | 0.00% | 29.59% | 44.91% | 0.614 |

31 | 66.18% | 33.82% | 0.00% | 29.81% | 45.00% | 0.618 |

32 | 65.06% | 34.94% | 0.00% | 30.03% | 45.08% | 0.621 |

33 | 63.93% | 36.07% | 0.00% | 30.25% | 45.17% | 0.625 |

34 | 62.80% | 37.20% | 0.00% | 30.47% | 45.26% | 0.629 |

35 | 61.67% | 38.33% | 0.00% | 30.70% | 45.35% | 0.632 |

36 | 60.55% | 39.45% | 0.00% | 30.92% | 45.43% | 0.636 |

37 | 59.42% | 40.58% | 0.00% | 31.14% | 45.52% | 0.640 |

38 | 58.29% | 41.71% | 0.00% | 31.36% | 45.61% | 0.643 |

39 | 57.17% | 42.83% | 0.00% | 31.59% | 45.70% | 0.647 |

40 | 56.04% | 43.96% | 0.00% | 31.81% | 45.80% | 0.650 |

41 | 54.91% | 45.09% | 0.00% | 32.03% | 45.89% | 0.654 |

42 | 53.78% | 46.22% | 0.00% | 32.26% | 45.98% | 0.658 |

43 | 52.66% | 47.34% | 0.00% | 32.48% | 46.07% | 0.661 |

44 | 51.53% | 48.47% | 0.00% | 32.70% | 46.17% | 0.665 |

45 | 50.40% | 49.60% | 0.00% | 32.93% | 46.26% | 0.668 |

46 | 49.27% | 50.73% | 0.00% | 33.15% | 46.36% | 0.672 |

47 | 48.15% | 51.85% | 0.00% | 33.38% | 46.45% | 0.675 |

48 | 47.02% | 52.98% | 0.00% | 33.61% | 46.55% | 0.678 |

49 | 45.89% | 54.11% | 0.00% | 33.83% | 46.65% | 0.682 |

50 | 44.77% | 55.23% | 0.00% | 34.06% | 46.75% | 0.685 |

51 | 43.64% | 56.36% | 0.00% | 34.29% | 46.84% | 0.689 |

52 | 42.51% | 57.49% | 0.00% | 34.51% | 46.94% | 0.692 |

53 | 41.38% | 58.62% | 0.00% | 34.74% | 47.04% | 0.696 |

54 | 40.26% | 59.74% | 0.00% | 34.97% | 47.14% | 0.699 |

55 | 39.13% | 60.87% | 0.00% | 35.20% | 47.24% | 0.702 |

56 | 38.00% | 62.00% | 0.00% | 35.43% | 47.35% | 0.706 |

57 | 36.88% | 63.12% | 0.00% | 35.66% | 47.45% | 0.709 |

58 | 35.75% | 64.25% | 0.00% | 35.88% | 47.55% | 0.712 |

59 | 34.62% | 65.38% | 0.00% | 36.11% | 47.65% | 0.715 |

60 | 33.49% | 66.51% | 0.00% | 36.34% | 47.76% | 0.719 |

61 | 32.37% | 67.63% | 0.00% | 36.58% | 47.86% | 0.722 |

62 | 31.24% | 68.76% | 0.00% | 36.81% | 47.97% | 0.725 |

63 | 30.11% | 69.89% | 0.00% | 37.04% | 48.07% | 0.728 |

64 | 28.98% | 71.02% | 0.00% | 37.27% | 48.18% | 0.732 |

65 | 27.86% | 72.14% | 0.00% | 37.50% | 48.29% | 0.735 |

66 | 26.73% | 73.27% | 0.00% | 37.73% | 48.39% | 0.738 |

67 | 25.60% | 74.40% | 0.00% | 37.97% | 48.50% | 0.741 |

68 | 24.48% | 75.52% | 0.00% | 38.20% | 48.61% | 0.744 |

69 | 23.35% | 76.65% | 0.00% | 38.43% | 48.72% | 0.747 |

70 | 22.22% | 77.78% | 0.00% | 38.67% | 48.83% | 0.750 |

71 | 21.09% | 78.91% | 0.00% | 38.90% | 48.94% | 0.754 |

72 | 19.97% | 80.03% | 0.00% | 39.13% | 49.05% | 0.757 |

73 | 18.84% | 81.16% | 0.00% | 39.37% | 49.16% | 0.760 |

74 | 17.71% | 82.29% | 0.00% | 39.60% | 49.27% | 0.763 |

75 | 16.59% | 83.41% | 0.00% | 39.84% | 49.39% | 0.766 |

76 | 15.46% | 84.54% | 0.00% | 40.08% | 49.50% | 0.769 |

77 | 14.33% | 85.67% | 0.00% | 40.31% | 49.61% | 0.772 |

78 | 13.20% | 86.80% | 0.00% | 40.55% | 49.73% | 0.775 |

79 | 12.08% | 87.92% | 0.00% | 40.79% | 49.84% | 0.778 |

80 | 10.95% | 89.05% | 0.00% | 41.02% | 49.96% | 0.781 |

81 | 9.82% | 90.18% | 0.00% | 41.26% | 50.07% | 0.784 |

82 | 8.69% | 91.31% | 0.00% | 41.50% | 50.19% | 0.787 |

83 | 7.57% | 92.43% | 0.00% | 41.74% | 50.30% | 0.790 |

84 | 6.44% | 93.56% | 0.00% | 41.98% | 50.42% | 0.792 |

85 | 5.31% | 94.69% | 0.00% | 42.22% | 50.54% | 0.795 |

86 | 4.19% | 95.81% | 0.00% | 42.46% | 50.66% | 0.798 |

87 | 3.06% | 96.94% | 0.00% | 42.70% | 50.77% | 0.801 |

88 | 1.93% | 98.07% | 0.00% | 42.94% | 50.89% | 0.804 |

89 | 0.80% | 99.20% | 0.00% | 43.18% | 51.01% | 0.807 |

90 | 0.00% | 97.21% | 2.79% | 43.42% | 51.45% | 0.805 |

91 | 0.00% | 87.49% | 12.51% | 43.66% | 52.82% | 0.788 |

92 | 0.00% | 77.77% | 22.23% | 43.90% | 54.36% | 0.770 |

93 | 0.00% | 68.05% | 31.95% | 44.14% | 56.07% | 0.751 |

94 | 0.00% | 58.33% | 41.67% | 44.39% | 57.93% | 0.731 |

95 | 0.00% | 48.61% | 51.39% | 44.63% | 59.93% | 0.711 |

96 | 0.00% | 38.89% | 61.11% | 44.87% | 62.05% | 0.691 |

97 | 0.00% | 29.16% | 70.84% | 45.12% | 64.29% | 0.670 |

98 | 0.00% | 19.44% | 80.56% | 45.36% | 66.62% | 0.651 |

99 | 0.00% | 9.72% | 90.28% | 45.60% | 69.05% | 0.631 |

100 | 0.00% | 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). |

Year | Inflation | Maximum Sharpe Ratio Return | Maximum Sharpe Ratio Balance | ProShares UltraPro S&P500 (UPRO) | ProShares UltraPro QQQ (TQQQ) |
---|---|---|---|---|---|

2018 | 1.36% | -37.19% | $6,281 | -36.68% | -37.20% |

2019 | 2.29% | 133.58% | $14,671 | 102.31% | 133.83% |

2020 | 0.39% | 8.12% | $15,862 | -0.91% | 8.19% |

Annual returns for 2018 and 2020 are based on partial years |

Year | Month | Maximum Sharpe Ratio Return | Maximum Sharpe Ratio Balance | ProShares UltraPro S&P500 (UPRO) | ProShares UltraPro QQQ (TQQQ) |
---|---|---|---|---|---|

2018 | 2 | -6.22% | $9,378 | -13.53% | -6.16% |

2018 | 3 | -13.38% | $8,123 | -8.69% | -13.42% |

2018 | 4 | -0.42% | $8,088 | -0.14% | -0.42% |

2018 | 5 | 16.91% | $9,456 | 6.46% | 17.00% |

2018 | 6 | 2.18% | $9,662 | 1.29% | 2.18% |

2018 | 7 | 7.59% | $10,395 | 10.73% | 7.56% |

2018 | 8 | 17.63% | $12,228 | 9.09% | 17.69% |

2018 | 9 | -1.58% | $12,034 | 1.20% | -1.60% |

2018 | 10 | -26.56% | $8,838 | -20.78% | -26.61% |

2018 | 11 | -2.85% | $8,586 | 4.28% | -2.91% |

2018 | 12 | -26.84% | $6,281 | -26.25% | -26.84% |

2019 | 1 | 26.89% | $7,970 | 23.89% | 26.92% |

2019 | 2 | 8.58% | $8,654 | 9.28% | 8.57% |

2019 | 3 | 11.00% | $9,606 | 4.85% | 11.05% |

2019 | 4 | 16.60% | $11,201 | 11.81% | 16.64% |

2019 | 5 | -23.97% | $8,516 | -18.89% | -24.01% |

2019 | 6 | 22.99% | $10,473 | 21.37% | 23.00% |

2019 | 7 | 6.18% | $11,121 | 3.80% | 6.20% |

2019 | 8 | -7.78% | $10,256 | -6.62% | -7.79% |

2019 | 9 | 1.91% | $10,452 | 5.30% | 1.88% |

2019 | 10 | 12.37% | $11,745 | 5.70% | 12.43% |

2019 | 11 | 12.18% | $13,176 | 10.73% | 12.20% |

2019 | 12 | 11.35% | $14,671 | 8.38% | 11.37% |

2020 | 1 | 8.12% | $15,862 | -0.91% | 8.19% |

Metric | Maximum 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 Correlation | 0.95 |

Beta^{(*)} | 3.31 |

Alpha (annualized) | 6.29% |

R^{2} | 90.05% |

Sharpe Ratio | 0.67 |

Sortino Ratio | 1.01 |

Treynor Ratio (%) | 10.41 |

Active Return | 17.57% |

Tracking Error | 37.41% |

Information Ratio | 0.47 |

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 Rate | 43.10% |

Perpetual Withdrawal Rate | 19.00% |

Positive Periods | 15 out of 24 (62.50%) |

Gain/Loss Ratio | 1.00 |

^{*} US stock market is used as the benchmark for calculations. Value-at-risk metrics are based on monthly values. |

Rank | Start | End | Length | Recovery By | Recovery Time | Underwater Period | Drawdown |
---|---|---|---|---|---|---|---|

1 | Sep 2018 | Dec 2018 | 4 months | Nov 2019 | 11 months | 1 year 3 months | -48.63% |

2 | Feb 2018 | Apr 2018 | 3 months | Jul 2018 | 3 months | 6 months | -19.12% |

Ticker | Name | CAGR | Stdev | Best Year | Worst Year | Max. Drawdown | Sharpe Ratio | Sortino Ratio | US Mkt Correlation |
---|---|---|---|---|---|---|---|---|---|

UPRO | ProShares UltraPro S&P500 | 12.66% | 42.76% | 102.31% | -36.68% | -39.08% | 0.45 | 0.64 | 1.00 |

TQQQ | ProShares UltraPro QQQ | 26.04% | 51.10% | 133.83% | -37.20% | -48.71% | 0.68 | 1.01 | 0.95 |

Ticker | Name | UPRO | TQQQ | Maximum Sharpe Ratio |
---|---|---|---|---|

UPRO | ProShares UltraPro S&P500 | 1.00 | 0.95 | 0.95 |

TQQQ | ProShares UltraPro QQQ | 0.95 | 1.00 | 1.00 |

Ticker | Name | Maximum Sharpe Ratio |
---|---|---|

UPRO | ProShares UltraPro S&P500 | 0.64% |

TQQQ | ProShares UltraPro QQQ | 99.36% |