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 - Aug 2021)

Portfolio Allocations

Tangency Portfolio
Ticker Name Allocation
UPRO ProShares UltraPro S&P500 53.52%
TMF Direxion Daily 20+ Yr Trsy Bull 3X ETF 46.48%
Save portfolio »

Portfolio Returns

Portfolio Statistics
PortfolioExpected ReturnExpected VolatilitySharpe Ratio
Tangency Portfolio35.15%22.32%1.34

Efficient Frontier Assets

Efficient Frontier Assets
#AssetExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1ProShares UltraPro S&P500 (UPRO)48.06%43.26%0.9100.00%100.00%
2Direxion Daily 20+ Yr Trsy Bull 3X ETF (TMF)21.57%39.20%0.4890.00%100.00%
Results based on historical returns. Expected return is the annualized monthly arithmetic mean return. Ex-ante Sharpe Ratio calculated using 3-month treasury bill returns as the risk-free rate.

Asset Correlations

Asset Correlations
NameTickerUPROTMF
ProShares UltraPro S&P500UPRO1.00-0.44
Direxion Daily 20+ Yr Trsy Bull 3X ETFTMF-0.441.00
Based on monthly returns from Jan 2010 to Aug 2021
Efficient Frontier Points
#UPROTMFExpected Return*Standard Deviation*Sharpe Ratio*
146.85%53.15%33.39%21.79%1.314
247.22%52.78%33.49%21.79%1.317
347.59%52.41%33.58%21.80%1.320
447.96%52.04%33.68%21.81%1.323
548.33%51.67%33.78%21.82%1.326
648.70%51.30%33.88%21.84%1.328
749.07%50.93%33.97%21.86%1.331
849.44%50.56%34.07%21.88%1.333
949.81%50.19%34.17%21.91%1.335
1050.19%49.81%34.27%21.94%1.336
1150.56%49.44%34.36%21.97%1.338
1250.93%49.07%34.46%22.00%1.339
1351.30%48.70%34.56%22.04%1.340
1451.67%48.33%34.66%22.08%1.341
1552.04%47.96%34.76%22.12%1.342
1652.41%47.59%34.86%22.17%1.343
1752.78%47.22%34.95%22.22%1.343
1853.15%46.85%35.05%22.27%1.343
1953.52%46.48%35.15%22.32%1.343
2053.89%46.11%35.25%22.38%1.343
2154.26%45.74%35.35%22.44%1.343
2254.63%45.37%35.45%22.50%1.342
2355.00%45.00%35.55%22.57%1.342
2455.37%44.63%35.64%22.64%1.341
2555.74%44.26%35.74%22.71%1.340
2656.11%43.89%35.84%22.79%1.339
2756.48%43.52%35.94%22.86%1.338
2856.85%43.15%36.04%22.94%1.336
2957.22%42.78%36.14%23.03%1.335
3057.59%42.41%36.24%23.11%1.333
3157.96%42.04%36.34%23.20%1.331
3258.33%41.67%36.44%23.29%1.329
3358.70%41.30%36.54%23.38%1.327
3459.07%40.93%36.64%23.48%1.325
3559.44%40.56%36.74%23.57%1.323
3659.81%40.19%36.84%23.67%1.320
3760.18%39.82%36.94%23.78%1.318
3860.55%39.45%37.04%23.88%1.315
3960.92%39.08%37.14%23.99%1.312
4061.29%38.71%37.23%24.10%1.309
4161.66%38.34%37.33%24.21%1.307
4262.03%37.97%37.43%24.32%1.303
4362.40%37.60%37.54%24.44%1.300
4462.77%37.23%37.64%24.56%1.297
4563.14%36.86%37.74%24.68%1.294
4663.51%36.49%37.84%24.80%1.290
4763.88%36.12%37.94%24.92%1.287
4864.25%35.75%38.04%25.05%1.283
4964.62%35.38%38.14%25.18%1.280
5064.99%35.01%38.24%25.31%1.276
5165.36%34.64%38.34%25.44%1.272
5265.73%34.27%38.44%25.58%1.269
5366.10%33.90%38.54%25.71%1.265
5466.47%33.53%38.64%25.85%1.261
5566.84%33.16%38.74%25.99%1.257
5667.21%32.79%38.84%26.14%1.253
5767.58%32.42%38.94%26.28%1.249
5867.95%32.05%39.04%26.43%1.245
5968.32%31.68%39.15%26.57%1.241
6068.69%31.31%39.25%26.72%1.237
6169.06%30.94%39.35%26.87%1.233
6269.43%30.57%39.45%27.02%1.228
6369.80%30.20%39.55%27.18%1.224
6470.17%29.83%39.65%27.33%1.220
6570.54%29.46%39.75%27.49%1.216
6670.91%29.09%39.86%27.65%1.212
6771.28%28.72%39.96%27.81%1.207
6871.65%28.35%40.06%27.97%1.203
6972.02%27.98%40.16%28.13%1.199
7072.40%27.60%40.26%28.30%1.194
7172.77%27.23%40.36%28.47%1.190
7273.14%26.86%40.47%28.63%1.186
7373.51%26.49%40.57%28.80%1.181
7473.88%26.12%40.67%28.97%1.177
7574.25%25.75%40.77%29.14%1.173
7674.62%25.38%40.88%29.32%1.168
7774.99%25.01%40.98%29.49%1.164
7875.36%24.64%41.08%29.66%1.159
7975.73%24.27%41.18%29.84%1.155
8076.10%23.90%41.29%30.02%1.151
8176.47%23.53%41.39%30.20%1.146
8276.84%23.16%41.49%30.38%1.142
8377.21%22.79%41.59%30.56%1.138
8477.58%22.42%41.70%30.74%1.134
8577.95%22.05%41.80%30.92%1.129
8678.32%21.68%41.90%31.11%1.125
8778.69%21.31%42.01%31.29%1.121
8879.06%20.94%42.11%31.48%1.116
8979.43%20.57%42.21%31.67%1.112
9079.80%20.20%42.32%31.85%1.108
9180.17%19.83%42.42%32.04%1.104
9280.54%19.46%42.52%32.23%1.100
9380.91%19.09%42.63%32.43%1.095
9481.28%18.72%42.73%32.62%1.091
9581.65%18.35%42.83%32.81%1.087
9682.02%17.98%42.94%33.00%1.083
9782.39%17.61%43.04%33.20%1.079
9882.76%17.24%43.14%33.40%1.075
9983.13%16.87%43.25%33.59%1.071
10083.50%16.50%43.35%33.79%1.067
*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.
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 Aug 2021
  • The efficient frontier is based on the monthly returns, volatilities, and correlations of the specified assets
  • Monte Carlo method was used to resample the efficient frontier inputs to mitigate the impact of input estimation errors
  • 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