Efficient Frontier

This tool uses mean-variance optimization to calculate and plot the efficient frontier for the specified asset classes, mutual funds, ETFs or stocks for the specified time period. The efficient frontier shows the set of optimal portfolios that provide the best possible expected return for the level of risk in the portfolio. Monte Carlo method can be used for more robust optimization that resamples the optimization inputs in order to mitigate the impact of input estimation errors and improve diversification. You can also use the efficient frontier forecast tool to specify expected future returns for the assets. The required inputs for the efficient frontier include the portfolio assets. You can optionally specify the asset allocation and allocation constraints for the portfolio assets. If an asset allocation is specified, the provided portfolio will be rendered on the efficient frontier chart.

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Asset Groups
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Efficient Frontier Results (Jan 2010 - Dec 2019)

Portfolio Allocations

Tangency Portfolio
Ticker Name Allocation
UPRO ProShares UltraPro S&P500 56.16%
TMF Direxion Daily 20+ Yr Trsy Bull 3X ETF 43.84%
Save portfolio »

Portfolio Returns

Portfolio Statistics
PortfolioExpected ReturnExpected VolatilitySharpe Ratio
Tangency Portfolio33.32%19.72%1.66

Efficient Frontier Assets

Efficient Frontier Assets
#AssetCAGRExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1ProShares UltraPro S&P500 (UPRO)32.83%42.71%38.43%1.0970.00%100.00%
2Direxion Daily 20+ Yr Trsy Bull 3X ETF (TMF)13.80%22.12%39.22%0.5500.00%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

Asset Correlations
NameTickerUPROTMF
ProShares UltraPro S&P500UPRO1.00-0.50
Direxion Daily 20+ Yr Trsy Bull 3X ETFTMF-0.501.00
Based on monthly returns from Jan 2010 to Dec 2019
Efficient Frontier Points
#UPROTMFExpected Return*Standard Deviation*Sharpe Ratio*
150.68%49.32%32.19%19.37%1.633
251.18%48.82%32.29%19.37%1.638
351.67%48.33%32.39%19.38%1.642
452.17%47.83%32.50%19.40%1.646
552.67%47.33%32.60%19.42%1.650
653.17%46.83%32.70%19.44%1.653
753.67%46.33%32.81%19.48%1.656
854.17%45.83%32.91%19.51%1.658
954.66%45.34%33.01%19.56%1.659
1055.16%44.84%33.12%19.61%1.660
1155.66%44.34%33.22%19.66%1.661
1256.16%43.84%33.32%19.72%1.661
1356.66%43.34%33.43%19.79%1.661
1457.15%42.85%33.53%19.86%1.660
1557.65%42.35%33.63%19.93%1.659
1658.15%41.85%33.74%20.01%1.658
1758.65%41.35%33.84%20.10%1.656
1859.15%40.85%33.94%20.19%1.653
1959.65%40.35%34.05%20.29%1.650
2060.14%39.86%34.15%20.39%1.647
2160.64%39.36%34.26%20.50%1.644
2261.14%38.86%34.36%20.61%1.640
2361.64%38.36%34.46%20.73%1.636
2462.14%37.86%34.57%20.85%1.631
2562.63%37.37%34.67%20.98%1.626
2663.13%36.87%34.78%21.11%1.621
2763.63%36.37%34.88%21.24%1.616
2864.13%35.87%34.99%21.38%1.610
2964.63%35.37%35.09%21.53%1.604
3065.13%34.87%35.19%21.67%1.598
3165.62%34.38%35.30%21.83%1.592
3266.12%33.88%35.40%21.98%1.585
3366.62%33.38%35.51%22.14%1.578
3467.12%32.88%35.61%22.31%1.571
3567.62%32.38%35.72%22.48%1.564
3668.11%31.89%35.82%22.65%1.557
3768.61%31.39%35.93%22.82%1.550
3869.11%30.89%36.03%23.00%1.542
3969.61%30.39%36.14%23.19%1.535
4070.11%29.89%36.25%23.37%1.527
4170.61%29.39%36.35%23.56%1.519
4271.10%28.90%36.46%23.75%1.511
4371.60%28.40%36.56%23.95%1.503
4472.10%27.90%36.67%24.15%1.495
4572.60%27.40%36.77%24.35%1.487
4673.10%26.90%36.88%24.55%1.479
4773.60%26.40%36.99%24.76%1.471
4874.09%25.91%37.09%24.97%1.463
4974.59%25.41%37.20%25.18%1.455
5075.09%24.91%37.30%25.40%1.447
5175.59%24.41%37.41%25.62%1.438
5276.09%23.91%37.52%25.84%1.430
5376.58%23.42%37.62%26.06%1.422
5477.08%22.92%37.73%26.29%1.414
5577.58%22.42%37.84%26.51%1.406
5678.08%21.92%37.94%26.74%1.398
5778.58%21.42%38.05%26.98%1.390
5879.08%20.92%38.16%27.21%1.382
5979.57%20.43%38.26%27.45%1.374
6080.07%19.93%38.37%27.69%1.366
6180.57%19.43%38.48%27.93%1.358
6281.07%18.93%38.58%28.17%1.350
6381.57%18.43%38.69%28.41%1.342
6482.06%17.94%38.80%28.66%1.334
6582.56%17.44%38.90%28.91%1.326
6683.06%16.94%39.01%29.16%1.319
6783.56%16.44%39.12%29.41%1.311
6884.06%15.94%39.23%29.66%1.304
6984.56%15.44%39.33%29.92%1.296
7085.05%14.95%39.44%30.17%1.289
7185.55%14.45%39.55%30.43%1.281
7286.05%13.95%39.66%30.69%1.274
7386.55%13.45%39.77%30.95%1.267
7487.05%12.95%39.87%31.21%1.260
7587.54%12.46%39.98%31.48%1.252
7688.04%11.96%40.09%31.74%1.245
7788.54%11.46%40.20%32.01%1.238
7889.04%10.96%40.31%32.27%1.231
7989.54%10.46%40.42%32.54%1.225
8090.04%9.96%40.52%32.81%1.218
8190.53%9.47%40.63%33.08%1.211
8291.03%8.97%40.74%33.36%1.205
8391.53%8.47%40.85%33.63%1.198
8492.03%7.97%40.96%33.91%1.191
8592.53%7.47%41.07%34.18%1.185
8693.03%6.97%41.18%34.46%1.179
8793.52%6.48%41.28%34.74%1.172
8894.02%5.98%41.39%35.01%1.166
8994.52%5.48%41.50%35.29%1.160
9095.02%4.98%41.61%35.57%1.154
9195.52%4.48%41.72%35.86%1.148
9296.01%3.99%41.83%36.14%1.142
9396.51%3.49%41.94%36.42%1.136
9497.01%2.99%42.05%36.71%1.130
9597.51%2.49%42.16%36.99%1.125
9698.01%1.99%42.27%37.28%1.119
9798.51%1.49%42.38%37.56%1.113
9899.00%1.00%42.49%37.85%1.108
9999.50%0.50%42.60%38.14%1.102
100100.00%0.00%42.71%38.43%1.097
*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).
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.
  • Historical asset statistics are based on monthly returns from Jan 2010 to Dec 2019
  • The efficient frontier is based on the monthly returns, volatilities, and correlations of the specified assets
  • The displayed standard deviation and expected return in the efficient frontier are annualized from the monthly returns
  • Ex-ante Sharpe Ratio for the efficient frontier data points is calculated using historical 3-month treasury bill returns as the risk free rate