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 1998 - Dec 2018)

Portfolio Allocations

Tangency Portfolio
Asset Class Allocation
Gold 2.52%
US Stock Market 4.91%
Total US Bond Market 86.22%
US Small Cap Value 6.34%
Save portfolio »

Portfolio Returns

Portfolio Statistics
PortfolioExpected ReturnExpected VolatilitySharpe Ratio
Tangency Portfolio5.20%3.49%0.93

Efficient Frontier Assets

Efficient Frontier Assets
#AssetCAGRExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1Gold7.02%8.48%16.65%0.3930.00%100.00%
2US Stock Market6.78%8.05%15.35%0.3980.00%100.00%
3Total US Bond Market4.53%4.59%3.38%0.7830.00%100.00%
4Global ex-US Stock Market4.54%6.11%17.17%0.2420.00%100.00%
5US Large Cap Value6.45%7.69%15.19%0.3790.00%100.00%
6US Small Cap Value8.20%10.07%18.41%0.4410.00%100.00%
7Emerging Markets6.67%9.64%23.27%0.3310.00%100.00%
8REIT8.10%10.41%20.34%0.4160.00%100.00%
9US Small Cap7.71%9.77%19.42%0.4030.00%100.00%
Results based on historical returns. Ex ante Sharpe Ratio calculated using 3-month treasury bill returns as the risk-free rate (1.94% annualized).

Asset Correlations

Asset Correlations
AssetGoldUS Stock MarketTotal US Bond MarketGlobal ex-US Stock MarketUS Large Cap ValueUS Small Cap ValueEmerging MarketsREITUS Small Cap
Gold1.000.030.340.20-0.000.040.260.120.08
US Stock Market0.031.00-0.100.870.940.880.790.580.90
Total US Bond Market0.34-0.101.000.00-0.10-0.07-0.000.18-0.10
Global ex-US Stock Market0.200.870.001.000.830.770.890.560.79
US Large Cap Value-0.000.94-0.100.831.000.870.740.610.81
US Small Cap Value0.040.88-0.070.770.871.000.720.720.94
Emerging Markets0.260.79-0.000.890.740.721.000.500.76
REIT0.120.580.180.560.610.720.501.000.64
US Small Cap0.080.90-0.100.790.810.940.760.641.00
Based on provided custom correlation matrix
Efficient Frontier Points
#GoldUS Stock MarketTotal US Bond MarketGlobal ex-US Stock MarketUS Large Cap ValueUS Small Cap ValueEmerging MarketsREITUS Small CapExpected Return*Standard Deviation*Sharpe Ratio*
10.00%3.43%93.27%0.00%3.29%0.00%0.00%0.00%0.00%4.81%3.22%0.892
20.00%4.07%92.02%0.00%3.17%0.00%0.00%0.00%0.73%4.86%3.22%0.906
30.00%3.20%91.11%0.00%3.47%0.00%0.00%0.00%2.22%4.92%3.25%0.916
40.31%4.03%90.21%0.00%2.34%1.62%0.00%0.00%1.49%4.98%3.29%0.923
50.85%5.13%89.23%0.00%1.08%3.39%0.00%0.00%0.33%5.03%3.33%0.928
61.39%5.38%88.25%0.00%0.43%4.55%0.00%0.00%0.00%5.09%3.37%0.932
71.95%5.29%87.26%0.00%0.03%5.47%0.00%0.00%0.00%5.14%3.43%0.933
82.52%4.91%86.22%0.00%0.00%6.34%0.00%0.00%0.00%5.20%3.49%0.934
93.10%4.51%85.17%0.00%0.00%7.22%0.00%0.00%0.00%5.25%3.55%0.933
103.68%4.10%84.13%0.00%0.00%8.09%0.00%0.00%0.00%5.31%3.62%0.930
114.25%3.70%83.08%0.00%0.00%8.97%0.00%0.00%0.00%5.36%3.69%0.927
124.83%3.29%82.03%0.00%0.00%9.84%0.00%0.00%0.00%5.42%3.77%0.923
135.41%2.89%80.99%0.00%0.00%10.72%0.00%0.00%0.00%5.47%3.85%0.918
145.99%2.49%79.94%0.00%0.00%11.59%0.00%0.00%0.00%5.53%3.93%0.912
156.56%2.08%78.89%0.00%0.00%12.46%0.00%0.00%0.00%5.59%4.02%0.906
167.14%1.68%77.84%0.00%0.00%13.34%0.00%0.00%0.00%5.64%4.11%0.899
177.72%1.27%76.80%0.00%0.00%14.21%0.00%0.00%0.00%5.70%4.21%0.892
188.30%0.87%75.75%0.00%0.00%15.09%0.00%0.00%0.00%5.75%4.31%0.885
198.87%0.46%74.70%0.00%0.00%15.96%0.00%0.00%0.00%5.81%4.41%0.877
209.43%0.09%73.65%0.00%0.00%16.74%0.00%0.08%0.00%5.86%4.51%0.869
219.98%0.00%72.52%0.00%0.00%17.15%0.00%0.35%0.00%5.92%4.62%0.861
2210.52%0.00%71.35%0.00%0.00%17.49%0.00%0.63%0.00%5.97%4.72%0.854
2311.07%0.00%70.18%0.00%0.00%17.84%0.00%0.91%0.00%6.03%4.83%0.846
2411.62%0.00%69.01%0.00%0.00%18.18%0.00%1.19%0.00%6.09%4.94%0.838
2512.16%0.00%67.84%0.00%0.00%18.52%0.00%1.47%0.00%6.14%5.06%0.830
2612.71%0.00%66.68%0.00%0.00%18.86%0.00%1.75%0.00%6.20%5.17%0.823
2713.26%0.00%65.51%0.00%0.00%19.21%0.00%2.03%0.00%6.25%5.29%0.815
2813.80%0.00%64.34%0.00%0.00%19.55%0.00%2.31%0.00%6.31%5.41%0.808
2914.35%0.00%63.17%0.00%0.00%19.89%0.00%2.59%0.00%6.37%5.52%0.801
3014.90%0.00%62.00%0.00%0.00%20.23%0.00%2.87%0.00%6.42%5.64%0.793
3115.44%0.00%60.83%0.00%0.00%20.58%0.00%3.15%0.00%6.48%5.77%0.787
3215.99%0.00%59.66%0.00%0.00%20.92%0.00%3.43%0.00%6.53%5.89%0.780
3316.54%0.00%58.50%0.00%0.00%21.26%0.00%3.71%0.00%6.59%6.01%0.773
3417.08%0.00%57.33%0.00%0.00%21.60%0.00%3.99%0.00%6.65%6.14%0.767
3517.63%0.00%56.16%0.00%0.00%21.94%0.00%4.27%0.00%6.70%6.26%0.760
3618.17%0.00%54.99%0.00%0.00%22.29%0.00%4.55%0.00%6.76%6.39%0.754
3718.72%0.00%53.82%0.00%0.00%22.63%0.00%4.83%0.00%6.81%6.51%0.748
3819.27%0.00%52.65%0.00%0.00%22.97%0.00%5.11%0.00%6.87%6.64%0.742
3919.81%0.00%51.48%0.00%0.00%23.31%0.00%5.39%0.00%6.93%6.77%0.736
4020.36%0.00%50.32%0.00%0.00%23.66%0.00%5.67%0.00%6.98%6.90%0.731
4120.91%0.00%49.15%0.00%0.00%24.00%0.00%5.95%0.00%7.04%7.03%0.725
4221.45%0.00%47.98%0.00%0.00%24.34%0.00%6.23%0.00%7.10%7.16%0.720
4322.00%0.00%46.81%0.00%0.00%24.68%0.00%6.51%0.00%7.15%7.29%0.715
4422.55%0.00%45.64%0.00%0.00%25.03%0.00%6.79%0.00%7.21%7.42%0.710
4523.09%0.00%44.47%0.00%0.00%25.37%0.00%7.07%0.00%7.26%7.55%0.705
4623.64%0.00%43.31%0.00%0.00%25.71%0.00%7.35%0.00%7.32%7.68%0.700
4724.19%0.00%42.14%0.00%0.00%26.05%0.00%7.62%0.00%7.38%7.82%0.695
4824.73%0.00%40.97%0.00%0.00%26.39%0.00%7.90%0.00%7.43%7.95%0.691
4925.28%0.00%39.80%0.00%0.00%26.74%0.00%8.18%0.00%7.49%8.08%0.686
5025.83%0.00%38.63%0.00%0.00%27.08%0.00%8.46%0.00%7.55%8.22%0.682
5126.37%0.00%37.46%0.00%0.00%27.42%0.00%8.74%0.00%7.60%8.35%0.678
5226.92%0.00%36.29%0.00%0.00%27.76%0.00%9.02%0.00%7.66%8.48%0.674
5327.47%0.00%35.13%0.00%0.00%28.11%0.00%9.30%0.00%7.72%8.62%0.670
5428.01%0.00%33.96%0.00%0.00%28.45%0.00%9.58%0.00%7.77%8.75%0.666
5528.56%0.00%32.79%0.00%0.00%28.79%0.00%9.86%0.00%7.83%8.89%0.662
5629.11%0.00%31.62%0.00%0.00%29.13%0.00%10.14%0.00%7.89%9.03%0.659
5729.65%0.00%30.45%0.00%0.00%29.48%0.00%10.42%0.00%7.94%9.16%0.655
5830.20%0.00%29.28%0.00%0.00%29.82%0.00%10.70%0.00%8.00%9.30%0.651
5930.74%0.00%28.11%0.00%0.00%30.16%0.00%10.98%0.00%8.06%9.44%0.648
6031.29%0.00%26.95%0.00%0.00%30.50%0.00%11.26%0.00%8.11%9.57%0.645
6131.84%0.00%25.78%0.00%0.00%30.84%0.00%11.54%0.00%8.17%9.71%0.641
6232.38%0.00%24.61%0.00%0.00%31.19%0.00%11.82%0.00%8.23%9.85%0.638
6332.93%0.00%23.44%0.00%0.00%31.53%0.00%12.10%0.00%8.28%9.98%0.635
6433.48%0.00%22.27%0.00%0.00%31.87%0.00%12.38%0.00%8.34%10.12%0.632
6534.02%0.00%21.10%0.00%0.00%32.21%0.00%12.66%0.00%8.40%10.26%0.629
6634.57%0.00%19.94%0.00%0.00%32.56%0.00%12.94%0.00%8.45%10.40%0.626
6735.12%0.00%18.77%0.00%0.00%32.90%0.00%13.22%0.00%8.51%10.54%0.623
6835.66%0.00%17.60%0.00%0.00%33.24%0.00%13.50%0.00%8.57%10.67%0.621
6936.21%0.00%16.43%0.00%0.00%33.58%0.00%13.78%0.00%8.63%10.81%0.618
7036.76%0.00%15.26%0.00%0.00%33.93%0.00%14.06%0.00%8.68%10.95%0.615
7137.30%0.00%14.09%0.00%0.00%34.27%0.00%14.34%0.00%8.74%11.09%0.613
7237.85%0.00%12.92%0.00%0.00%34.61%0.00%14.62%0.00%8.80%11.23%0.610
7338.40%0.00%11.76%0.00%0.00%34.95%0.00%14.90%0.00%8.85%11.37%0.608
7438.94%0.00%10.59%0.00%0.00%35.29%0.00%15.18%0.00%8.91%11.51%0.606
7539.49%0.00%9.42%0.00%0.00%35.64%0.00%15.46%0.00%8.97%11.65%0.603
7640.04%0.00%8.25%0.00%0.00%35.98%0.00%15.74%0.00%9.03%11.79%0.601
7740.58%0.00%7.08%0.00%0.00%36.32%0.00%16.02%0.00%9.08%11.93%0.599
7841.13%0.00%5.91%0.00%0.00%36.66%0.00%16.29%0.00%9.14%12.07%0.596
7941.68%0.00%4.74%0.00%0.00%37.01%0.00%16.57%0.00%9.20%12.21%0.594
8042.22%0.00%3.58%0.00%0.00%37.35%0.00%16.85%0.00%9.25%12.35%0.592
8142.77%0.00%2.41%0.00%0.00%37.69%0.00%17.13%0.00%9.31%12.49%0.590
8243.31%0.00%1.24%0.00%0.00%38.03%0.00%17.41%0.00%9.37%12.63%0.588
8343.86%0.00%0.07%0.00%0.00%38.38%0.00%17.69%0.00%9.43%12.77%0.586
8441.06%0.00%0.00%0.00%0.00%38.57%0.00%20.37%0.00%9.48%12.93%0.583
8538.04%0.00%0.00%0.00%0.00%38.76%0.00%23.20%0.00%9.54%13.12%0.579
8635.02%0.00%0.00%0.00%0.00%38.95%0.00%26.02%0.00%9.60%13.36%0.573
8732.00%0.00%0.00%0.00%0.00%39.14%0.00%28.85%0.00%9.66%13.63%0.566
8828.99%0.00%0.00%0.00%0.00%39.33%0.00%31.68%0.00%9.71%13.94%0.558
8925.97%0.00%0.00%0.00%0.00%39.52%0.00%34.51%0.00%9.77%14.28%0.548
9022.95%0.00%0.00%0.00%0.00%39.71%0.00%37.34%0.00%9.83%14.64%0.539
9119.93%0.00%0.00%0.00%0.00%39.90%0.00%40.17%0.00%9.89%15.04%0.528
9216.91%0.00%0.00%0.00%0.00%40.09%0.00%42.99%0.00%9.94%15.45%0.518
9313.90%0.00%0.00%0.00%0.00%40.28%0.00%45.82%0.00%10.00%15.90%0.507
9410.88%0.00%0.00%0.00%0.00%40.47%0.00%48.65%0.00%10.06%16.36%0.496
957.86%0.00%0.00%0.00%0.00%40.66%0.00%51.48%0.00%10.12%16.84%0.485
964.84%0.00%0.00%0.00%0.00%40.85%0.00%54.31%0.00%10.18%17.35%0.475
971.82%0.00%0.00%0.00%0.00%41.04%0.00%57.13%0.00%10.23%17.86%0.464
980.00%0.00%0.00%0.00%0.00%34.36%0.00%65.64%0.00%10.29%18.42%0.453
990.00%0.00%0.00%0.00%0.00%17.18%0.00%82.82%0.00%10.35%19.24%0.437
1000.00%0.00%0.00%0.00%0.00%0.00%0.00%100.00%0.00%10.41%20.34%0.416
*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 (1.94% 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 1998 to Dec 2018
  • 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