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 2.14% to 5.28%. Refer to the efficient frontier section for additional details. Historical values from Jan 2012 to Dec 2019 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 26.40%
VXUS Vanguard Total International Stock ETF 26.50%
BND Vanguard Total Bond Market ETF 31.73%
VNQ Vanguard Real Estate ETF 15.37%
Save portfolio »

Portfolio Summary

Portfolio statistics
PortfolioExpected ReturnStandard DeviationSharpe Ratio
Provided Portfolio4.37%7.54%0.38
Maximum Sharpe Ratio4.29%7.39%0.37
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%11.31%0.3510.00%100.00%
2Vanguard Total International Stock ETF (VXUS)5.70%12.57%0.3310.00%100.00%
3Vanguard Total Bond Market ETF (BND)1.80%3.10%0.0860.00%100.00%
4Vanguard Real Estate ETF (VNQ)5.00%13.62%0.2550.00%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 ETFVTI1.000.81-0.120.48
Vanguard Total International Stock ETFVXUS0.811.000.030.41
Vanguard Total Bond Market ETFBND-0.120.031.000.49
Vanguard Real Estate ETFVNQ0.480.410.491.00
Based on monthly returns from Jan 2012 to Dec 2019
Efficient Frontier Assets
#VTIVXUSBNDVNQExpected Return*Standard Deviation*Sharpe Ratio*
19.26%0.06%90.68%0.00%2.14%2.88%0.210
29.94%0.21%89.81%0.04%2.17%2.88%0.221
310.47%0.43%89.01%0.10%2.20%2.89%0.230
410.89%0.69%88.24%0.17%2.23%2.91%0.239
511.22%1.03%87.50%0.26%2.26%2.92%0.247
611.48%1.39%86.77%0.35%2.28%2.94%0.254
711.69%1.78%86.05%0.47%2.31%2.97%0.261
811.88%2.18%85.33%0.60%2.34%3.00%0.268
912.06%2.59%84.61%0.74%2.36%3.02%0.274
1012.25%3.00%83.88%0.88%2.39%3.06%0.280
1112.42%3.43%83.12%1.04%2.42%3.09%0.286
1212.60%3.84%82.35%1.20%2.45%3.13%0.291
1312.80%4.25%81.57%1.38%2.47%3.17%0.297
1413.01%4.66%80.77%1.56%2.50%3.21%0.302
1513.22%5.07%79.96%1.75%2.53%3.25%0.307
1613.44%5.48%79.14%1.94%2.56%3.30%0.312
1713.66%5.89%78.31%2.14%2.59%3.35%0.316
1813.90%6.30%77.47%2.34%2.62%3.40%0.320
1914.13%6.71%76.61%2.55%2.66%3.46%0.324
2014.38%7.12%75.75%2.75%2.69%3.51%0.328
2114.62%7.52%74.89%2.96%2.72%3.57%0.332
2214.87%7.94%74.02%3.17%2.75%3.63%0.335
2315.12%8.35%73.15%3.39%2.78%3.69%0.338
2415.37%8.76%72.27%3.60%2.81%3.75%0.341
2515.62%9.16%71.39%3.82%2.85%3.82%0.343
2615.88%9.57%70.51%4.04%2.88%3.88%0.346
2716.14%9.98%69.62%4.26%2.91%3.95%0.348
2816.39%10.39%68.74%4.48%2.94%4.02%0.350
2916.64%10.80%67.85%4.71%2.97%4.09%0.352
3016.89%11.21%66.96%4.94%3.01%4.16%0.354
3117.13%11.62%66.07%5.18%3.04%4.23%0.356
3217.37%12.03%65.17%5.42%3.07%4.30%0.357
3317.62%12.44%64.27%5.67%3.10%4.38%0.359
3417.86%12.85%63.37%5.92%3.14%4.45%0.360
3518.10%13.26%62.46%6.18%3.17%4.53%0.361
3618.35%13.67%61.55%6.44%3.20%4.61%0.362
3718.59%14.07%60.63%6.70%3.24%4.69%0.363
3818.83%14.48%59.72%6.97%3.27%4.77%0.364
3919.07%14.88%58.81%7.23%3.30%4.85%0.365
4019.32%15.29%57.89%7.50%3.34%4.93%0.366
4119.56%15.69%56.98%7.77%3.37%5.01%0.366
4219.81%16.09%56.06%8.04%3.40%5.09%0.367
4320.05%16.50%55.14%8.31%3.44%5.17%0.368
4420.30%16.90%54.21%8.59%3.47%5.26%0.368
4520.56%17.30%53.28%8.86%3.50%5.34%0.369
4620.81%17.71%52.35%9.14%3.54%5.43%0.369
4721.06%18.11%51.42%9.41%3.57%5.51%0.370
4821.32%18.51%50.48%9.69%3.61%5.60%0.370
4921.57%18.92%49.55%9.97%3.64%5.68%0.370
5021.81%19.32%48.61%10.26%3.67%5.77%0.371
5122.06%19.72%47.68%10.54%3.71%5.86%0.371
5222.31%20.12%46.74%10.82%3.74%5.95%0.371
5322.56%20.53%45.80%11.11%3.78%6.03%0.371
5422.81%20.93%44.87%11.39%3.81%6.12%0.372
5523.06%21.33%43.93%11.67%3.84%6.21%0.372
5623.32%21.73%43.00%11.96%3.88%6.30%0.372
5723.57%22.13%42.06%12.24%3.91%6.39%0.372
5823.82%22.53%41.12%12.52%3.95%6.48%0.372
5924.08%22.93%40.19%12.80%3.98%6.57%0.372
6024.34%23.33%39.25%13.09%4.01%6.66%0.372
6124.60%23.72%38.31%13.37%4.05%6.75%0.373
6224.85%24.12%37.37%13.65%4.08%6.84%0.373
6325.11%24.52%36.43%13.94%4.12%6.93%0.373
6425.37%24.92%35.49%14.22%4.15%7.02%0.373
6525.63%25.31%34.55%14.51%4.19%7.11%0.373
6625.89%25.71%33.61%14.79%4.22%7.21%0.373
6726.14%26.10%32.67%15.08%4.25%7.30%0.373
6826.40%26.50%31.73%15.37%4.29%7.39%0.373
6926.66%26.90%30.79%15.65%4.32%7.48%0.373
7026.92%27.29%29.85%15.94%4.36%7.57%0.373
7127.18%27.69%28.91%16.22%4.39%7.67%0.373
7227.43%28.09%27.97%16.51%4.43%7.76%0.373
7327.69%28.48%27.03%16.80%4.46%7.85%0.373
7427.95%28.88%26.09%17.08%4.50%7.95%0.373
7528.21%29.27%25.14%17.37%4.53%8.04%0.373
7628.47%29.67%24.20%17.66%4.56%8.13%0.373
7728.73%30.07%23.26%17.94%4.60%8.23%0.373
7828.99%30.46%22.32%18.23%4.63%8.32%0.373
7929.25%30.86%21.38%18.52%4.67%8.41%0.372
8029.51%31.25%20.44%18.80%4.70%8.51%0.372
8129.77%31.64%19.50%19.09%4.74%8.60%0.372
8230.03%32.04%18.55%19.38%4.77%8.69%0.372
8330.27%32.43%17.62%19.68%4.81%8.79%0.372
8430.51%32.83%16.68%19.98%4.84%8.88%0.372
8530.72%33.22%15.76%20.30%4.87%8.97%0.372
8630.92%33.62%14.84%20.63%4.91%9.07%0.372
8731.11%33.99%13.93%20.98%4.94%9.16%0.372
8831.26%34.36%13.05%21.33%4.97%9.25%0.372
8931.40%34.75%12.18%21.67%5.00%9.33%0.372
9031.54%35.15%11.33%21.99%5.04%9.42%0.372
9131.60%35.60%10.50%22.30%5.07%9.50%0.372
9231.57%36.12%9.71%22.60%5.09%9.58%0.371
9331.41%36.71%8.96%22.92%5.12%9.66%0.371
9431.09%37.45%8.26%23.20%5.15%9.74%0.371
9530.71%38.25%7.61%23.44%5.17%9.81%0.371
9630.30%39.16%7.00%23.54%5.20%9.88%0.371
9729.99%40.05%6.42%23.54%5.22%9.95%0.371
9829.31%41.24%5.91%23.55%5.24%10.01%0.370
9928.39%42.48%5.43%23.71%5.26%10.08%0.370
10027.00%44.50%5.00%23.50%5.28%10.15%0.369
*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).