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 2009 - Aug 2021)

Portfolio Allocations

Tangency Portfolio
Ticker Name Allocation
SPY SPDR S&P 500 ETF Trust 70.55%
EDV Vanguard Extended Duration Trs ETF 29.45%
Save portfolio »

Portfolio Returns

Portfolio Statistics
PortfolioExpected ReturnExpected VolatilitySharpe Ratio
Tangency Portfolio14.10%9.96%1.28

Efficient Frontier Assets

Efficient Frontier Assets
#AssetExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1SPDR S&P 500 ETF Trust (SPY)17.01%14.52%1.0560.00%100.00%
2Vanguard Extended Duration Trs ETF (EDV)7.41%20.41%0.3270.00%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
NameTickerSPYEDV
SPDR S&P 500 ETF TrustSPY1.00-0.34
Vanguard Extended Duration Trs ETFEDV-0.341.00
Based on monthly returns from Jan 2009 to Aug 2021
Efficient Frontier Points
#SPYEDVExpected Return*Standard Deviation*Sharpe Ratio*
162.45%37.55%13.32%9.68%1.247
262.65%37.35%13.34%9.69%1.249
362.85%37.15%13.35%9.69%1.250
463.05%36.95%13.37%9.69%1.252
563.24%36.76%13.39%9.69%1.254
663.44%36.56%13.41%9.69%1.255
763.64%36.36%13.43%9.69%1.257
863.84%36.16%13.45%9.69%1.258
964.03%35.97%13.47%9.70%1.260
1064.23%35.77%13.49%9.70%1.261
1164.43%35.57%13.51%9.70%1.262
1264.63%35.37%13.53%9.71%1.264
1364.82%35.18%13.55%9.71%1.265
1465.02%34.98%13.57%9.71%1.266
1565.22%34.78%13.58%9.72%1.267
1665.42%34.58%13.60%9.72%1.268
1765.61%34.39%13.62%9.73%1.269
1865.81%34.19%13.64%9.73%1.270
1966.01%33.99%13.66%9.74%1.271
2066.20%33.80%13.68%9.75%1.272
2166.40%33.60%13.70%9.75%1.273
2266.60%33.40%13.72%9.76%1.274
2366.80%33.20%13.74%9.77%1.275
2466.99%33.01%13.76%9.77%1.276
2567.19%32.81%13.78%9.78%1.276
2667.39%32.61%13.80%9.79%1.277
2767.59%32.41%13.82%9.80%1.278
2867.78%32.22%13.83%9.81%1.278
2967.98%32.02%13.85%9.82%1.279
3068.18%31.82%13.87%9.83%1.279
3168.38%31.62%13.89%9.84%1.280
3268.57%31.43%13.91%9.85%1.280
3368.77%31.23%13.93%9.86%1.281
3468.97%31.03%13.95%9.87%1.281
3569.17%30.83%13.97%9.88%1.281
3669.36%30.64%13.99%9.89%1.282
3769.56%30.44%14.01%9.90%1.282
3869.76%30.24%14.03%9.91%1.282
3969.96%30.04%14.05%9.92%1.282
4070.15%29.85%14.07%9.94%1.282
4170.35%29.65%14.08%9.95%1.282
4270.55%29.45%14.10%9.96%1.282
4370.75%29.25%14.12%9.98%1.282
4470.94%29.06%14.14%9.99%1.282
4571.14%28.86%14.16%10.00%1.282
4671.34%28.66%14.18%10.02%1.282
4771.54%28.46%14.20%10.03%1.282
4871.73%28.27%14.22%10.05%1.282
4971.93%28.07%14.24%10.06%1.281
5072.13%27.87%14.26%10.08%1.281
5172.33%27.67%14.28%10.10%1.281
5272.52%27.48%14.30%10.11%1.280
5372.72%27.28%14.32%10.13%1.280
5472.92%27.08%14.34%10.14%1.280
5573.12%26.88%14.35%10.16%1.279
5673.31%26.69%14.37%10.18%1.279
5773.51%26.49%14.39%10.20%1.278
5873.71%26.29%14.41%10.21%1.278
5973.90%26.10%14.43%10.23%1.277
6074.10%25.90%14.45%10.25%1.276
6174.30%25.70%14.47%10.27%1.276
6274.50%25.50%14.49%10.29%1.275
6374.69%25.31%14.51%10.31%1.274
6474.89%25.11%14.53%10.33%1.273
6575.09%24.91%14.55%10.35%1.273
6675.29%24.71%14.57%10.37%1.272
6775.48%24.52%14.59%10.39%1.271
6875.68%24.32%14.61%10.41%1.270
6975.88%24.12%14.63%10.43%1.269
7076.08%23.92%14.64%10.45%1.268
7176.27%23.73%14.66%10.47%1.267
7276.47%23.53%14.68%10.49%1.266
7376.67%23.33%14.70%10.52%1.265
7476.87%23.13%14.72%10.54%1.264
7577.06%22.94%14.74%10.56%1.263
7677.26%22.74%14.76%10.58%1.262
7777.46%22.54%14.78%10.61%1.261
7877.66%22.34%14.80%10.63%1.260
7977.85%22.15%14.82%10.65%1.258
8078.05%21.95%14.84%10.68%1.257
8178.25%21.75%14.86%10.70%1.256
8278.45%21.55%14.88%10.73%1.255
8378.64%21.36%14.90%10.75%1.254
8478.84%21.16%14.92%10.78%1.252
8579.04%20.96%14.94%10.80%1.251
8679.24%20.76%14.95%10.83%1.250
8779.43%20.57%14.97%10.85%1.248
8879.63%20.37%14.99%10.88%1.247
8979.83%20.17%15.01%10.90%1.245
9080.03%19.97%15.03%10.93%1.244
9180.22%19.78%15.05%10.96%1.243
9280.42%19.58%15.07%10.98%1.241
9380.62%19.38%15.09%11.01%1.240
9480.82%19.18%15.11%11.04%1.238
9581.01%18.99%15.13%11.06%1.237
9681.21%18.79%15.15%11.09%1.235
9781.41%18.59%15.17%11.12%1.233
9881.60%18.40%15.19%11.15%1.232
9981.80%18.20%15.21%11.18%1.230
10082.00%18.00%15.23%11.20%1.229
*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 2009 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