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
SPY SPDR S&P 500 ETF Trust 62.72%
EDV Vanguard Extended Duration Trs ETF 36.80%
UPRO ProShares UltraPro S&P500 0.14%
TMF Direxion Daily 20+ Yr Trsy Bull 3X ETF 0.34%
Save portfolio »

Portfolio Returns

Portfolio Statistics
PortfolioExpected ReturnExpected VolatilitySharpe Ratio
Tangency Portfolio14.49%8.39%1.56

Efficient Frontier Assets

Efficient Frontier Assets
#AssetExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1SPDR S&P 500 ETF Trust (SPY)16.01%13.74%1.0500.00%100.00%
2Vanguard Extended Duration Trs ETF (EDV)11.77%19.39%0.5500.00%100.00%
3ProShares UltraPro S&P500 (UPRO)48.06%43.26%0.9100.00%100.00%
4Direxion 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
NameTickerSPYEDVUPROTMF
SPDR S&P 500 ETF TrustSPY1.00-0.461.00-0.44
Vanguard Extended Duration Trs ETFEDV-0.461.00-0.450.99
ProShares UltraPro S&P500UPRO1.00-0.451.00-0.44
Direxion Daily 20+ Yr Trsy Bull 3X ETFTMF-0.440.99-0.441.00
Based on monthly returns from Jan 2010 to Aug 2021
Efficient Frontier Points
#SPYEDVUPROTMFExpected Return*Standard Deviation*Sharpe Ratio*
161.57%38.43%0.00%0.00%14.36%8.33%1.558
262.72%36.80%0.14%0.34%14.49%8.39%1.560
363.23%35.39%0.39%0.99%14.66%8.50%1.557
463.50%34.05%0.72%1.73%14.85%8.63%1.553
563.62%32.65%1.12%2.61%15.07%8.79%1.547
663.64%31.22%1.55%3.58%15.31%8.96%1.542
763.55%29.85%2.02%4.57%15.55%9.13%1.536
863.39%28.53%2.53%5.56%15.81%9.31%1.530
963.13%27.27%3.07%6.54%16.07%9.50%1.524
1062.73%26.12%3.66%7.49%16.34%9.69%1.518
1162.06%25.31%4.36%8.27%16.62%9.89%1.512
1261.05%24.91%5.17%8.87%16.90%10.09%1.506
1359.86%24.70%6.05%9.39%17.19%10.30%1.500
1458.56%24.63%6.97%9.84%17.49%10.51%1.495
1557.20%24.63%7.92%10.26%17.78%10.72%1.489
1655.78%24.70%8.89%10.64%18.08%10.93%1.484
1754.33%24.79%9.86%11.01%18.38%11.14%1.479
1852.86%24.91%10.85%11.38%18.69%11.35%1.474
1951.33%25.10%11.85%11.72%18.99%11.56%1.470
2049.77%25.35%12.86%12.03%19.29%11.77%1.465
2148.17%25.62%13.88%12.32%19.59%11.99%1.461
2246.54%25.95%14.92%12.59%19.90%12.20%1.457
2344.88%26.30%15.97%12.85%20.21%12.41%1.452
2443.21%26.67%17.02%13.10%20.52%12.63%1.448
2541.54%27.04%18.08%13.34%20.83%12.84%1.445
2639.86%27.42%19.14%13.59%21.14%13.06%1.441
2738.19%27.78%20.20%13.83%21.45%13.27%1.437
2836.54%28.13%21.25%14.08%21.77%13.49%1.434
2934.93%28.45%22.28%14.34%22.07%13.70%1.430
3033.35%28.71%23.31%14.63%22.39%13.91%1.427
3131.80%28.92%24.32%14.96%22.70%14.13%1.424
3230.34%29.02%25.32%15.32%23.02%14.34%1.421
3328.92%29.06%26.32%15.70%23.34%14.56%1.418
3427.59%28.99%27.28%16.13%23.66%14.78%1.415
3526.33%28.83%28.23%16.61%23.98%15.00%1.412
3625.15%28.55%29.15%17.15%24.30%15.22%1.409
3724.04%28.17%30.05%17.75%24.63%15.44%1.406
3822.97%27.73%30.93%18.37%24.96%15.66%1.403
3921.97%27.19%31.80%19.04%25.29%15.88%1.400
4021.01%26.60%32.65%19.74%25.62%16.10%1.398
4120.08%25.97%33.49%20.46%25.95%16.32%1.395
4219.20%25.25%34.32%21.23%26.28%16.55%1.393
4318.35%24.48%35.14%22.03%26.62%16.77%1.390
4417.52%23.69%35.94%22.84%26.95%16.99%1.388
4516.70%22.88%36.74%23.67%27.29%17.22%1.385
4615.90%22.05%37.54%24.51%27.63%17.44%1.383
4715.13%21.18%38.32%25.36%27.96%17.66%1.381
4814.39%20.28%39.10%26.24%28.30%17.89%1.379
4913.67%19.36%39.86%27.11%28.64%18.11%1.377
5012.94%18.43%40.63%27.99%28.97%18.33%1.374
5112.22%17.51%41.40%28.87%29.31%18.55%1.372
5211.51%16.60%42.16%29.73%29.65%18.78%1.370
5310.81%15.68%42.93%30.59%29.99%19.00%1.368
5410.12%14.74%43.69%31.45%30.33%19.22%1.367
559.43%13.80%44.44%32.33%30.67%19.44%1.365
568.76%12.84%45.19%33.20%31.00%19.66%1.363
578.10%11.91%45.95%34.05%31.34%19.88%1.361
587.45%11.01%46.70%34.85%31.68%20.10%1.359
596.81%10.15%47.46%35.58%32.01%20.31%1.358
606.23%9.33%48.21%36.23%32.33%20.52%1.356
615.69%8.57%48.96%36.78%32.64%20.73%1.354
625.18%7.88%49.72%37.21%32.95%20.93%1.352
634.71%7.24%50.48%37.58%33.25%21.13%1.350
644.30%6.64%51.24%37.82%33.54%21.32%1.349
653.92%6.10%52.01%37.97%33.83%21.52%1.346
663.57%5.56%52.78%38.09%34.11%21.72%1.344
673.25%5.02%53.52%38.20%34.39%21.92%1.342
682.96%4.54%54.25%38.24%34.65%22.11%1.339
692.69%4.10%55.00%38.21%34.92%22.31%1.336
702.45%3.72%55.76%38.06%35.18%22.51%1.333
712.24%3.38%56.54%37.84%35.44%22.72%1.329
722.05%3.05%57.33%37.57%35.69%22.94%1.325
731.87%2.74%58.12%37.27%35.95%23.17%1.321
741.69%2.46%58.93%36.93%36.21%23.40%1.316
751.50%2.21%59.74%36.54%36.47%23.64%1.310
761.35%1.98%60.58%36.10%36.73%23.90%1.305
771.21%1.77%61.43%35.59%37.00%24.17%1.298
781.08%1.56%62.30%35.06%37.26%24.45%1.291
790.98%1.37%63.19%34.46%37.53%24.75%1.284
800.90%1.21%64.07%33.83%37.79%25.05%1.276
810.81%1.07%64.92%33.19%38.04%25.35%1.268
820.74%0.94%65.79%32.53%38.30%25.67%1.260
830.66%0.81%66.67%31.86%38.56%26.00%1.251
840.59%0.69%67.56%31.15%38.82%26.35%1.242
850.52%0.59%68.48%30.41%39.09%26.71%1.233
860.46%0.51%69.41%29.62%39.35%27.08%1.223
870.40%0.43%70.33%28.84%39.62%27.46%1.213
880.35%0.36%71.24%28.05%39.88%27.85%1.203
890.30%0.29%72.15%27.26%40.14%28.24%1.193
900.25%0.23%73.03%26.48%40.40%28.64%1.184
910.21%0.18%73.93%25.69%40.65%29.04%1.174
920.17%0.13%74.84%24.85%40.91%29.46%1.163
930.13%0.10%75.75%24.02%41.17%29.88%1.153
940.10%0.07%76.59%23.25%41.41%30.28%1.144
950.07%0.04%77.40%22.49%41.64%30.67%1.135
960.06%0.01%78.27%21.66%41.88%31.09%1.125
970.04%0.00%79.25%20.71%42.16%31.58%1.114
980.02%0.00%80.32%19.66%42.46%32.13%1.102
990.01%0.00%81.29%18.69%42.73%32.63%1.091
1000.00%0.00%82.00%18.00%42.93%32.99%1.083
*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