Portfolio Optimization

This portfolio optimizer tool supports the following portfolio optimization strategies:

The optimization is based on the monthly return statistics of the selected portfolio assets for the given time period. The optimization result does not predict what allocation would perform best outside the given time period, and the actual performance of portfolios constructed using the optimized asset weights may vary from the given performance goal.

The required inputs for the optimization include the time range and the portfolio assets. Portfolio asset weights and constraints are optional. You can also use the Black-Litterman model based portfolio optimization, which allows the benchmark portfolio asset weights to be optimized based on investor's views.

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Asset Groups
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Portfolio Optimization Results

Portfolio optimization results with goal to maximize sharpe ratio. The possible range of expected annual portfolio returns based on provided parameters is 2.17% to 5.12%. Refer to the efficient frontier section for additional details. Historical values from Jan 2012 to Feb 2020 were used for non-user supplied parameters based on the selected time period and available data for the portfolio assets.

Portfolio Allocations

Provided Portfolio
Ticker Name Allocation
VTI Vanguard Total Stock Market ETF 40.00%
VXUS Vanguard Total International Stock ETF 20.00%
BND Vanguard Total Bond Market ETF 30.00%
VNQ Vanguard Real Estate ETF 10.00%
Save portfolio »
Maximum Sharpe Ratio
Ticker Name Allocation
VTI Vanguard Total Stock Market ETF 23.65%
VXUS Vanguard Total International Stock ETF 20.62%
BND Vanguard Total Bond Market ETF 39.84%
VNQ Vanguard Real Estate ETF 15.90%
Save portfolio »

Portfolio Summary

Portfolio statistics
PortfolioExpected ReturnStandard DeviationSharpe Ratio
Provided Portfolio4.37%7.71%0.37
Maximum Sharpe Ratio3.97%6.70%0.36
Expected return is based on the provided capital market expectations. Ex ante Sharpe Ratio calculated using the current 3-month treasury bill return as the risk-free rate (1.53% 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.
  • The results are based on combining user provided forecast model parameters with historical monthly return statistics of the portfolio assets
  • Monte Carlo method was used to resample the efficient frontier inputs to mitigate the impact of input estimation errors.
Efficient Frontier Assets
#AssetExpected Return*Standard DeviationSharpe Ratio*Min. WeightMax. Weight
1Vanguard Total Stock Market ETF (VTI)5.50%11.65%0.3400.00%100.00%
2Vanguard Total International Stock ETF (VXUS)5.70%12.77%0.3260.00%100.00%
3Vanguard Total Bond Market ETF (BND)1.80%3.17%0.0840.00%100.00%
4Vanguard Real Estate ETF (VNQ)5.00%13.76%0.2520.00%100.00%
*Expected return based on the provided capital market expectations. Ex ante Sharpe Ratio calculated using the current 3-month treasury bill return as the risk-free rate (1.53% annualized).

Monthly Correlations

Efficient Frontier Asset Correlations
NameTickerVTIVXUSBNDVNQ
Vanguard Total Stock Market ETFVTI1.000.81-0.170.50
Vanguard Total International Stock ETFVXUS0.811.00-0.030.43
Vanguard Total Bond Market ETFBND-0.17-0.031.000.43
Vanguard Real Estate ETFVNQ0.500.430.431.00
Based on monthly returns from Jan 2012 to Feb 2020
Efficient Frontier Assets
#VTIVXUSBNDVNQExpected Return*Standard Deviation*Sharpe Ratio*
19.96%0.10%89.94%0.00%2.17%2.90%0.218
210.59%0.26%89.11%0.04%2.20%2.90%0.229
310.96%0.55%88.39%0.10%2.22%2.91%0.237
411.20%0.88%87.72%0.20%2.25%2.93%0.244
511.40%1.23%87.07%0.31%2.27%2.94%0.251
611.58%1.59%86.41%0.42%2.30%2.96%0.257
711.71%1.98%85.76%0.55%2.32%2.98%0.263
811.85%2.36%85.11%0.68%2.34%3.01%0.269
911.98%2.75%84.44%0.82%2.37%3.03%0.275
1012.12%3.14%83.76%0.98%2.39%3.06%0.281
1112.25%3.52%83.08%1.15%2.42%3.09%0.286
1212.38%3.91%82.37%1.34%2.44%3.13%0.291
1312.53%4.29%81.65%1.53%2.47%3.17%0.296
1412.69%4.65%80.92%1.74%2.50%3.20%0.300
1512.87%5.02%80.16%1.95%2.52%3.25%0.305
1613.06%5.38%79.39%2.17%2.55%3.29%0.309
1713.25%5.75%78.61%2.39%2.58%3.34%0.314
1813.43%6.10%77.82%2.64%2.61%3.39%0.317
1913.63%6.44%77.03%2.90%2.64%3.44%0.321
2013.84%6.79%76.22%3.15%2.67%3.49%0.324
2114.05%7.13%75.40%3.42%2.70%3.55%0.328
2214.26%7.47%74.58%3.69%2.73%3.60%0.331
2314.46%7.81%73.76%3.97%2.75%3.66%0.333
2414.66%8.15%72.94%4.25%2.78%3.72%0.336
2514.87%8.48%72.12%4.53%2.81%3.78%0.338
2615.07%8.82%71.29%4.82%2.84%3.84%0.341
2715.28%9.15%70.46%5.11%2.87%3.91%0.343
2815.51%9.48%69.61%5.40%2.90%3.97%0.345
2915.73%9.81%68.76%5.69%2.93%4.04%0.346
3015.96%10.13%67.91%5.99%2.96%4.11%0.348
3116.20%10.45%67.06%6.29%3.00%4.18%0.349
3216.43%10.78%66.20%6.60%3.03%4.25%0.351
3316.66%11.10%65.34%6.90%3.06%4.32%0.352
3416.88%11.43%64.48%7.20%3.09%4.39%0.353
3517.11%11.76%63.62%7.51%3.12%4.47%0.354
3617.34%12.09%62.76%7.81%3.15%4.54%0.355
3717.57%12.41%61.90%8.12%3.18%4.62%0.356
3817.80%12.74%61.04%8.42%3.21%4.69%0.357
3918.04%13.06%60.17%8.73%3.24%4.77%0.358
4018.27%13.39%59.31%9.04%3.27%4.85%0.359
4118.51%13.71%58.44%9.35%3.30%4.92%0.359
4218.74%14.03%57.57%9.66%3.34%5.00%0.360
4318.98%14.35%56.71%9.96%3.37%5.08%0.360
4419.21%14.67%55.84%10.27%3.40%5.16%0.361
4519.45%15.00%54.97%10.58%3.43%5.24%0.361
4619.70%15.32%54.09%10.89%3.46%5.32%0.362
4719.94%15.65%53.21%11.20%3.49%5.41%0.362
4820.18%15.99%52.32%11.51%3.52%5.49%0.362
4920.42%16.33%51.44%11.82%3.56%5.57%0.363
5020.66%16.66%50.55%12.13%3.59%5.66%0.363
5120.91%17.00%49.66%12.44%3.62%5.74%0.363
5221.15%17.33%48.77%12.75%3.65%5.83%0.363
5321.40%17.66%47.88%13.06%3.68%5.91%0.364
5421.64%17.99%46.98%13.38%3.72%6.00%0.364
5521.89%18.32%46.09%13.69%3.75%6.08%0.364
5622.14%18.65%45.20%14.01%3.78%6.17%0.364
5722.39%18.98%44.31%14.32%3.81%6.26%0.364
5822.64%19.31%43.41%14.64%3.84%6.34%0.364
5922.89%19.64%42.52%14.95%3.88%6.43%0.364
6023.14%19.97%41.62%15.27%3.91%6.52%0.364
6123.40%20.29%40.73%15.58%3.94%6.61%0.364
6223.65%20.62%39.84%15.90%3.97%6.70%0.364
6323.90%20.95%38.94%16.21%4.01%6.79%0.364
6424.15%21.28%38.04%16.53%4.04%6.87%0.364
6524.40%21.60%37.14%16.85%4.07%6.96%0.364
6624.66%21.93%36.23%17.18%4.10%7.05%0.364
6724.91%22.26%35.32%17.51%4.14%7.15%0.364
6825.16%22.59%34.41%17.84%4.17%7.24%0.364
6925.41%22.92%33.50%18.17%4.20%7.33%0.364
7025.66%23.25%32.59%18.50%4.24%7.42%0.364
7125.91%23.58%31.68%18.83%4.27%7.51%0.364
7226.17%23.91%30.77%19.16%4.30%7.60%0.364
7326.42%24.23%29.85%19.49%4.33%7.70%0.364
7426.67%24.56%28.94%19.82%4.37%7.79%0.364
7526.92%24.89%28.03%20.15%4.40%7.88%0.364
7627.17%25.22%27.12%20.49%4.43%7.97%0.363
7727.43%25.55%26.21%20.82%4.47%8.07%0.363
7827.68%25.88%25.29%21.15%4.50%8.16%0.363
7927.93%26.21%24.38%21.48%4.53%8.25%0.363
8028.17%26.54%23.47%21.82%4.56%8.35%0.363
8128.40%26.87%22.57%22.16%4.60%8.44%0.363
8228.64%27.20%21.66%22.50%4.63%8.53%0.363
8328.88%27.53%20.75%22.84%4.66%8.63%0.363
8429.12%27.86%19.85%23.18%4.70%8.72%0.363
8529.34%28.18%18.94%23.53%4.73%8.81%0.362
8629.56%28.49%18.05%23.90%4.76%8.90%0.362
8729.75%28.79%17.17%24.29%4.79%9.00%0.362
8829.90%29.08%16.30%24.71%4.82%9.09%0.362
8930.01%29.40%15.45%25.15%4.85%9.17%0.362
9030.09%29.72%14.60%25.59%4.88%9.26%0.362
9130.16%30.05%13.77%26.03%4.91%9.35%0.361
9230.12%30.42%12.97%26.49%4.94%9.43%0.361
9330.03%30.80%12.19%26.99%4.97%9.51%0.361
9429.91%31.24%11.44%27.40%5.00%9.59%0.361
9529.71%31.73%10.75%27.81%5.02%9.67%0.361
9629.46%32.19%10.10%28.26%5.04%9.74%0.360
9729.07%32.83%9.51%28.58%5.07%9.80%0.360
9828.37%33.81%8.97%28.85%5.09%9.86%0.360
9927.73%34.95%8.47%28.86%5.11%9.93%0.360
10026.50%36.50%8.00%29.00%5.13%9.99%0.360
*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 (1.53% annualized).