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 1978 - Dec 2018)

Portfolio Allocations

Tangency Portfolio
Asset Class Allocation
US Stock Market 49.69%
Long Term Treasury 50.31%
Save portfolio »

Portfolio Returns

Portfolio Statistics
PortfolioExpected ReturnExpected VolatilitySharpe Ratio
Tangency Portfolio10.68%9.57%0.63

Efficient Frontier Assets

Efficient Frontier Assets
#AssetCAGRExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1US Stock Market11.17%12.46%15.14%0.5160.00%100.00%
2Long Term Treasury8.30%8.94%10.97%0.3910.00%100.00%
Results based on historical returns. Ex ante Sharpe Ratio calculated using 3-month treasury bill returns as the risk-free rate (4.65% annualized).

Asset Correlations

Asset Correlations
AssetUS Stock MarketLong Term Treasury
US Stock Market1.000.05
Long Term Treasury0.051.00
Based on provided custom correlation matrix
Efficient Frontier Points
#US Stock MarketLong Term TreasuryExpected Return*Standard Deviation*Sharpe Ratio*
133.59%66.41%10.11%9.11%0.599
234.26%65.74%10.13%9.11%0.602
334.93%65.07%10.16%9.11%0.604
435.60%64.40%10.18%9.12%0.607
536.27%63.73%10.20%9.12%0.609
636.95%63.05%10.23%9.13%0.611
737.62%62.38%10.25%9.14%0.613
838.29%61.71%10.28%9.15%0.615
938.96%61.04%10.30%9.16%0.616
1039.63%60.37%10.32%9.18%0.618
1140.30%59.70%10.35%9.19%0.620
1240.97%59.03%10.37%9.21%0.621
1341.64%58.36%10.39%9.23%0.622
1442.31%57.69%10.42%9.25%0.624
1542.98%57.02%10.44%9.27%0.625
1643.65%56.35%10.46%9.29%0.626
1744.32%55.68%10.49%9.32%0.626
1844.99%55.01%10.51%9.34%0.627
1945.67%54.33%10.54%9.37%0.628
2046.34%53.66%10.56%9.40%0.628
2147.01%52.99%10.58%9.43%0.629
2247.68%52.32%10.61%9.46%0.629
2348.35%51.65%10.63%9.50%0.629
2449.02%50.98%10.65%9.53%0.630
2549.69%50.31%10.68%9.57%0.630
2650.36%49.64%10.70%9.61%0.630
2751.03%48.97%10.72%9.65%0.630
2851.70%48.30%10.75%9.69%0.629
2952.37%47.63%10.77%9.73%0.629
3053.04%46.96%10.80%9.78%0.629
3153.72%46.28%10.82%9.82%0.628
3254.39%45.61%10.84%9.87%0.628
3355.06%44.94%10.87%9.91%0.627
3455.73%44.27%10.89%9.96%0.626
3556.40%43.60%10.91%10.01%0.626
3657.07%42.93%10.94%10.06%0.625
3757.74%42.26%10.96%10.12%0.624
3858.41%41.59%10.98%10.17%0.623
3959.08%40.92%11.01%10.22%0.622
4059.75%40.25%11.03%10.28%0.621
4160.42%39.58%11.06%10.34%0.620
4261.09%38.91%11.08%10.40%0.618
4361.76%38.24%11.10%10.46%0.617
4462.44%37.56%11.13%10.52%0.616
4563.11%36.89%11.15%10.58%0.615
4663.78%36.22%11.17%10.64%0.613
4764.45%35.55%11.20%10.70%0.612
4865.12%34.88%11.22%10.77%0.610
4965.79%34.21%11.25%10.83%0.609
5066.46%33.54%11.27%10.90%0.607
5167.13%32.87%11.29%10.97%0.606
5267.80%32.20%11.32%11.04%0.604
5368.47%31.53%11.34%11.11%0.602
5469.14%30.86%11.36%11.18%0.601
5569.81%30.19%11.39%11.25%0.599
5670.48%29.52%11.41%11.32%0.597
5771.16%28.84%11.44%11.39%0.596
5871.83%28.17%11.46%11.47%0.594
5972.50%27.50%11.48%11.54%0.592
6073.17%26.83%11.51%11.62%0.590
6173.84%26.16%11.53%11.69%0.588
6274.51%25.49%11.55%11.77%0.587
6375.18%24.82%11.58%11.85%0.585
6475.85%24.15%11.60%11.93%0.583
6576.52%23.48%11.63%12.00%0.581
6677.19%22.81%11.65%12.08%0.579
6777.86%22.14%11.67%12.17%0.577
6878.53%21.47%11.70%12.25%0.575
6979.21%20.79%11.72%12.33%0.574
7079.88%20.12%11.75%12.41%0.572
7180.55%19.45%11.77%12.49%0.570
7281.22%18.78%11.79%12.58%0.568
7381.89%18.11%11.82%12.66%0.566
7482.56%17.44%11.84%12.75%0.564
7583.23%16.77%11.86%12.83%0.562
7683.90%16.10%11.89%12.92%0.560
7784.57%15.43%11.91%13.01%0.558
7885.24%14.76%11.94%13.09%0.556
7985.91%14.09%11.96%13.18%0.555
8086.58%13.42%11.98%13.27%0.553
8187.25%12.75%12.01%13.36%0.551
8287.93%12.07%12.03%13.45%0.549
8388.60%11.40%12.06%13.54%0.547
8489.27%10.73%12.08%13.63%0.545
8589.94%10.06%12.10%13.72%0.543
8690.61%9.39%12.13%13.81%0.541
8791.28%8.72%12.15%13.91%0.539
8891.95%8.05%12.18%14.00%0.538
8992.62%7.38%12.20%14.09%0.536
9093.29%6.71%12.22%14.18%0.534
9193.96%6.04%12.25%14.28%0.532
9294.63%5.37%12.27%14.37%0.530
9395.30%4.70%12.30%14.47%0.528
9495.97%4.03%12.32%14.56%0.527
9596.65%3.35%12.34%14.66%0.525
9697.32%2.68%12.37%14.75%0.523
9797.99%2.01%12.39%14.85%0.521
9898.66%1.34%12.42%14.95%0.520
9999.33%0.67%12.44%15.04%0.518
100100.00%0.00%12.46%15.14%0.516
*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 (4.65% 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 1978 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