Efficient Frontier Forecast

This tool uses mean-variance optimization to generate forward-looking efficient frontiers based on user-specified expected annual return and volatility of assets combined with historical asset correlations.

The required inputs for the efficient frontier include the portfolio assets and expected annual returns, along with volatility expectations when historical volatility is not used. 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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Efficient Frontier Results

Portfolio Allocations

Tangency Portfolio
Asset Class Allocation
US Stock Market 26.91%
Global ex-US Stock Market 24.07%
10-year Treasury 31.15%
Long Term Treasury 17.86%
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Portfolio Returns

Portfolio Statistics
PortfolioExpected ReturnExpected VolatilitySharpe Ratio
Tangency Portfolio4.02%8.35%0.47
Efficient Frontier Assets
#AssetExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1US Stock Market6.00%15.34%0.3780.00%100.00%
2Global ex-US Stock Market7.00%17.76%0.3800.00%100.00%
3Short Term Treasury0.22%2.07%0.0870.00%100.00%
4Intermediate Term Treasury0.80%4.78%0.1580.00%100.00%
510-year Treasury1.33%7.35%0.1740.00%100.00%
6Long Term Treasury1.87%10.31%0.1760.00%100.00%
Results based on the provided capital market expectations. Expected return is the annualized monthly arithmetic mean return. Ex-ante Sharpe Ratio calculated using the current 3-month treasury bill return as the risk-free rate.

Asset Correlations

Asset Correlations
AssetUS Stock MarketGlobal ex-US Stock MarketShort Term TreasuryIntermediate Term Treasury10-year TreasuryLong Term Treasury
US Stock Market1.000.72-0.11-0.09-0.11-0.10
Global ex-US Stock Market0.721.00-0.07-0.08-0.11-0.10
Short Term Treasury-0.11-0.071.000.900.820.67
Intermediate Term Treasury-0.09-0.080.901.000.970.87
10-year Treasury-0.11-0.110.820.971.000.93
Long Term Treasury-0.10-0.100.670.870.931.00
Based on monthly returns from Jan 1986 to Sep 2021
Efficient Frontier Points
#US Stock MarketGlobal ex-US Stock MarketShort Term TreasuryIntermediate Term Treasury10-year TreasuryLong Term TreasuryExpected Return*Standard Deviation*Sharpe Ratio*
12.75%0.43%96.83%0.00%0.00%0.00%0.40%2.01%0.180
23.29%0.95%95.77%0.00%0.00%0.00%0.47%2.02%0.211
33.83%1.47%94.71%0.00%0.00%0.00%0.53%2.04%0.241
44.37%1.99%93.65%0.00%0.00%0.00%0.60%2.08%0.268
54.91%2.51%92.59%0.00%0.00%0.00%0.66%2.12%0.292
65.45%3.03%91.53%0.00%0.00%0.00%0.73%2.18%0.314
75.99%3.55%90.47%0.00%0.00%0.00%0.79%2.25%0.333
86.53%4.07%89.41%0.00%0.00%0.00%0.86%2.33%0.350
97.06%4.59%88.35%0.00%0.00%0.00%0.92%2.41%0.364
107.60%5.11%87.29%0.00%0.00%0.00%0.99%2.51%0.376
118.11%5.59%86.03%0.00%0.00%0.28%1.05%2.61%0.386
128.53%6.00%84.35%0.00%0.00%1.12%1.12%2.72%0.395
138.95%6.41%82.67%0.00%0.00%1.97%1.18%2.82%0.402
149.38%6.82%80.99%0.00%0.00%2.81%1.25%2.94%0.409
159.80%7.22%79.32%0.00%0.00%3.66%1.31%3.05%0.415
1610.23%7.63%77.64%0.00%0.00%4.50%1.38%3.17%0.420
1710.65%8.04%75.96%0.00%0.00%5.35%1.44%3.28%0.425
1811.07%8.45%74.28%0.00%0.00%6.19%1.51%3.40%0.429
1911.50%8.86%72.60%0.00%0.00%7.04%1.57%3.52%0.432
2011.92%9.27%70.93%0.00%0.00%7.88%1.64%3.65%0.435
2112.34%9.68%69.25%0.00%0.00%8.73%1.70%3.77%0.438
2212.77%10.09%67.57%0.00%0.00%9.58%1.77%3.89%0.441
2313.19%10.49%65.89%0.00%0.00%10.42%1.84%4.02%0.443
2413.62%10.90%64.22%0.00%0.00%11.27%1.90%4.15%0.445
2514.04%11.31%62.54%0.00%0.00%12.11%1.97%4.27%0.447
2614.46%11.71%60.57%0.00%0.79%12.47%2.03%4.40%0.449
2714.87%12.11%58.35%0.00%2.25%12.42%2.10%4.53%0.450
2815.28%12.51%56.14%0.00%3.71%12.37%2.16%4.66%0.452
2915.70%12.90%53.92%0.00%5.16%12.31%2.23%4.79%0.453
3016.11%13.30%51.71%0.00%6.62%12.26%2.30%4.92%0.454
3116.52%13.70%49.49%0.00%8.08%12.21%2.36%5.05%0.455
3216.94%14.09%47.28%0.00%9.54%12.16%2.43%5.18%0.456
3317.35%14.49%45.06%0.00%11.00%12.11%2.49%5.31%0.457
3417.76%14.89%42.84%0.00%12.45%12.05%2.56%5.44%0.458
3518.18%15.28%40.63%0.00%13.91%12.00%2.63%5.57%0.459
3618.59%15.68%38.41%0.00%15.37%11.95%2.69%5.70%0.460
3719.00%16.07%36.20%0.00%16.83%11.90%2.76%5.83%0.460
3819.42%16.47%33.98%0.00%18.29%11.85%2.82%5.96%0.461
3919.83%16.87%31.77%0.00%19.74%11.79%2.89%6.09%0.462
4020.24%17.26%29.55%0.00%21.20%11.74%2.96%6.22%0.462
4120.66%17.66%27.33%0.00%22.66%11.69%3.02%6.36%0.463
4221.07%18.06%25.12%0.00%24.12%11.64%3.09%6.49%0.463
4321.48%18.45%22.90%0.00%25.58%11.58%3.15%6.62%0.464
4421.89%18.85%20.69%0.00%27.04%11.53%3.22%6.75%0.464
4522.31%19.25%18.47%0.00%28.49%11.48%3.29%6.88%0.465
4622.72%19.64%16.26%0.00%29.95%11.43%3.35%7.02%0.465
4723.13%20.04%14.04%0.00%31.41%11.38%3.42%7.15%0.466
4823.55%20.44%11.83%0.00%32.87%11.32%3.49%7.28%0.466
4923.96%20.83%9.61%0.00%34.33%11.27%3.55%7.41%0.466
5024.37%21.23%7.39%0.00%35.78%11.22%3.62%7.55%0.467
5124.79%21.63%5.18%0.00%37.24%11.17%3.69%7.68%0.467
5225.20%22.02%2.96%0.00%38.70%11.12%3.75%7.81%0.467
5325.61%22.42%0.75%0.00%40.16%11.06%3.82%7.95%0.467
5426.04%22.93%0.00%0.00%38.29%12.74%3.89%8.08%0.468
5526.48%23.50%0.00%0.00%34.72%15.30%3.95%8.22%0.468
5626.91%24.07%0.00%0.00%31.15%17.86%4.02%8.35%0.468
5727.35%24.64%0.00%0.00%27.59%20.42%4.09%8.49%0.468
5827.78%25.21%0.00%0.00%24.02%22.98%4.15%8.63%0.468
5928.22%25.78%0.00%0.00%20.45%25.54%4.22%8.78%0.467
6028.65%26.35%0.00%0.00%16.89%28.11%4.29%8.92%0.467
6129.09%26.92%0.00%0.00%13.32%30.67%4.36%9.07%0.467
6229.53%27.49%0.00%0.00%9.76%33.23%4.42%9.21%0.466
6329.96%28.06%0.00%0.00%6.19%35.79%4.49%9.36%0.466
6430.40%28.63%0.00%0.00%2.62%38.35%4.56%9.51%0.465
6530.81%29.32%0.00%0.00%0.00%39.87%4.62%9.66%0.464
6631.17%30.34%0.00%0.00%0.00%38.49%4.69%9.82%0.464
6731.52%31.36%0.00%0.00%0.00%37.11%4.76%9.98%0.463
6831.88%32.38%0.00%0.00%0.00%35.74%4.83%10.15%0.461
6932.23%33.40%0.00%0.00%0.00%34.36%4.89%10.32%0.460
7032.59%34.42%0.00%0.00%0.00%32.99%4.96%10.49%0.458
7132.94%35.44%0.00%0.00%0.00%31.61%5.03%10.67%0.457
7233.30%36.46%0.00%0.00%0.00%30.24%5.09%10.86%0.455
7333.66%37.48%0.00%0.00%0.00%28.86%5.16%11.05%0.453
7434.01%38.50%0.00%0.00%0.00%27.49%5.23%11.24%0.451
7534.37%39.52%0.00%0.00%0.00%26.11%5.30%11.43%0.449
7634.72%40.54%0.00%0.00%0.00%24.73%5.37%11.63%0.447
7735.08%41.56%0.00%0.00%0.00%23.36%5.43%11.83%0.445
7835.44%42.58%0.00%0.00%0.00%21.98%5.50%12.04%0.443
7935.79%43.60%0.00%0.00%0.00%20.61%5.57%12.24%0.440
8036.15%44.62%0.00%0.00%0.00%19.23%5.64%12.45%0.438
8136.50%45.64%0.00%0.00%0.00%17.86%5.70%12.67%0.436
8236.86%46.66%0.00%0.00%0.00%16.48%5.77%12.88%0.434
8337.21%47.68%0.00%0.00%0.00%15.10%5.84%13.10%0.431
8437.57%48.70%0.00%0.00%0.00%13.73%5.91%13.32%0.429
8537.93%49.72%0.00%0.00%0.00%12.35%5.98%13.54%0.427
8638.28%50.74%0.00%0.00%0.00%10.98%6.04%13.76%0.424
8738.64%51.76%0.00%0.00%0.00%9.60%6.11%13.99%0.422
8838.99%52.78%0.00%0.00%0.00%8.23%6.18%14.22%0.420
8939.35%53.80%0.00%0.00%0.00%6.85%6.25%14.45%0.418
9039.70%54.82%0.00%0.00%0.00%5.47%6.32%14.68%0.416
9140.06%55.84%0.00%0.00%0.00%4.10%6.38%14.91%0.413
9240.42%56.86%0.00%0.00%0.00%2.72%6.45%15.14%0.411
9340.77%57.88%0.00%0.00%0.00%1.35%6.52%15.38%0.409
9440.98%59.02%0.00%0.00%0.00%0.00%6.59%15.62%0.407
9534.15%65.85%0.00%0.00%0.00%0.00%6.66%15.88%0.405
9627.32%72.68%0.00%0.00%0.00%0.00%6.73%16.18%0.401
9720.49%79.51%0.00%0.00%0.00%0.00%6.79%16.52%0.397
9813.66%86.34%0.00%0.00%0.00%0.00%6.86%16.90%0.391
996.83%93.17%0.00%0.00%0.00%0.00%6.93%17.31%0.386
1000.00%100.00%0.00%0.00%0.00%0.00%7.00%17.76%0.380
*Ex-ante values shown for portfolio return and volatility. Ex-ante Sharpe Ratio calculated using the current 3-month treasury bill return 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 1986 to Sep 2021
  • 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 forecast is calculated using the current 3-month treasury bill return as the risk free rate (0.04% annualized)