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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Portfolio Optimization Results Save

Portfolio optimization results with goal to maximize Sharpe ratio. The possible range of expected annual portfolio returns based on provided parameters is 1.97% to 5.00%. Refer to the efficient frontier section for additional details. Historical values from Jan 2012 to Sep 2021 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 7.91%
VXUS Vanguard Total International Stock ETF 4.03%
BND Vanguard Total Bond Market ETF 86.77%
VNQ Vanguard Real Estate ETF 1.29%
Save portfolio »

Portfolio Summary

Portfolio statistics
PortfolioExpected ReturnStandard DeviationSharpe Ratio
Provided Portfolio4.37%9.22%0.47
Maximum Sharpe Ratio2.28%3.53%0.64
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.
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 ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1Vanguard Total Stock Market ETF (VTI)5.50%13.51%0.3940.00%100.00%
2Vanguard Total International Stock ETF (VXUS)5.70%14.14%0.3900.00%100.00%
3Vanguard Total Bond Market ETF (BND)1.80%3.30%0.5290.00%100.00%
4Vanguard Real Estate ETF (VNQ)5.00%15.29%0.3170.00%100.00%
Results based on the provided capital market expectations. Expected return is the annualized monthly arithmetic mean return. Ex-ante Sharpe Ratio calculated using the current 3-month treasury bill return as the risk-free rate.

Asset Correlations

Efficient Frontier Asset Correlations
NameTickerVTIVXUSBNDVNQ
Vanguard Total Stock Market ETFVTI1.000.860.060.64
Vanguard Total International Stock ETFVXUS0.861.000.120.58
Vanguard Total Bond Market ETFBND0.060.121.000.47
Vanguard Real Estate ETFVNQ0.640.580.471.00
Based on monthly returns from Jan 2012 to Sep 2021
Efficient Frontier Assets
#VTIVXUSBNDVNQExpected Return*Standard Deviation*Sharpe Ratio*
14.15%0.50%95.35%0.00%1.97%3.25%0.589
24.76%0.65%94.56%0.02%2.00%3.25%0.597
35.24%0.89%93.80%0.08%2.03%3.26%0.603
45.67%1.16%93.02%0.15%2.06%3.28%0.609
56.04%1.47%92.25%0.24%2.08%3.30%0.614
66.33%1.84%91.50%0.34%2.11%3.32%0.618
76.59%2.22%90.75%0.45%2.14%3.34%0.622
86.84%2.58%89.99%0.59%2.17%3.37%0.624
97.11%2.96%89.20%0.74%2.20%3.41%0.627
107.38%3.32%88.39%0.91%2.23%3.44%0.628
117.65%3.68%87.58%1.09%2.25%3.48%0.629
127.91%4.03%86.77%1.29%2.28%3.53%0.630
138.16%4.39%85.95%1.49%2.31%3.57%0.630
148.41%4.75%85.13%1.70%2.34%3.62%0.629
158.65%5.11%84.32%1.92%2.37%3.67%0.628
168.90%5.47%83.50%2.14%2.40%3.73%0.627
179.15%5.82%82.67%2.36%2.43%3.78%0.626
189.40%6.18%81.83%2.58%2.46%3.84%0.624
199.65%6.54%81.00%2.81%2.49%3.90%0.622
209.91%6.89%80.16%3.04%2.52%3.96%0.619
2110.16%7.24%79.33%3.27%2.55%4.03%0.617
2210.42%7.59%78.47%3.52%2.58%4.09%0.614
2310.67%7.94%77.62%3.77%2.61%4.16%0.611
2410.92%8.28%76.77%4.02%2.65%4.23%0.608
2511.18%8.61%75.92%4.29%2.68%4.31%0.604
2611.44%8.95%75.06%4.56%2.71%4.38%0.601
2711.69%9.28%74.20%4.83%2.74%4.46%0.598
2811.94%9.61%73.33%5.11%2.77%4.53%0.594
2912.20%9.95%72.47%5.39%2.80%4.61%0.591
3012.45%10.28%71.60%5.66%2.83%4.69%0.587
3112.71%10.62%70.74%5.94%2.86%4.77%0.583
3212.96%10.95%69.88%6.22%2.89%4.86%0.580
3313.21%11.28%69.01%6.50%2.92%4.94%0.576
3413.46%11.61%68.15%6.78%2.95%5.02%0.573
3513.71%11.95%67.27%7.07%2.99%5.11%0.569
3613.97%12.28%66.40%7.36%3.02%5.19%0.565
3714.22%12.61%65.52%7.65%3.05%5.28%0.562
3814.47%12.95%64.65%7.94%3.08%5.37%0.558
3914.72%13.28%63.77%8.23%3.11%5.46%0.555
4014.97%13.61%62.90%8.52%3.14%5.55%0.551
4115.22%13.95%62.02%8.82%3.18%5.64%0.548
4215.47%14.28%61.14%9.11%3.21%5.73%0.545
4315.72%14.61%60.27%9.40%3.24%5.82%0.541
4415.97%14.95%59.38%9.70%3.27%5.91%0.538
4516.23%15.29%58.49%9.99%3.30%6.01%0.535
4616.48%15.62%57.61%10.29%3.33%6.10%0.532
4716.73%15.96%56.72%10.59%3.37%6.20%0.529
4816.98%16.31%55.82%10.89%3.40%6.29%0.525
4917.24%16.64%54.93%11.20%3.43%6.39%0.522
5017.49%16.97%54.03%11.51%3.46%6.49%0.519
5117.74%17.30%53.13%11.83%3.49%6.58%0.516
5217.99%17.63%52.24%12.14%3.53%6.68%0.514
5318.25%17.96%51.34%12.45%3.56%6.78%0.511
5418.50%18.29%50.44%12.77%3.59%6.88%0.508
5518.75%18.63%49.54%13.08%3.62%6.98%0.505
5619.01%18.96%48.64%13.39%3.66%7.08%0.502
5719.26%19.29%47.75%13.71%3.69%7.18%0.500
5819.52%19.62%46.85%14.02%3.72%7.28%0.497
5919.77%19.95%45.95%14.33%3.75%7.38%0.495
6020.03%20.28%45.05%14.64%3.79%7.48%0.492
6120.28%20.61%44.15%14.96%3.82%7.58%0.490
6220.54%20.94%43.25%15.27%3.85%7.68%0.487
6320.80%21.27%42.35%15.58%3.88%7.78%0.485
6421.05%21.60%41.45%15.90%3.92%7.89%0.483
6521.31%21.94%40.55%16.21%3.95%7.99%0.481
6621.56%22.27%39.65%16.52%3.98%8.09%0.478
6721.82%22.60%38.74%16.84%4.01%8.19%0.476
6822.07%22.93%37.84%17.16%4.05%8.30%0.474
6922.32%23.26%36.94%17.47%4.08%8.40%0.472
7022.58%23.60%36.04%17.79%4.11%8.50%0.470
7122.83%23.93%35.14%18.10%4.14%8.61%0.468
7223.09%24.26%34.24%18.42%4.18%8.71%0.466
7323.34%24.59%33.33%18.73%4.21%8.82%0.464
7423.59%24.92%32.43%19.05%4.24%8.92%0.462
7523.85%25.25%31.53%19.37%4.27%9.02%0.460
7624.10%25.58%30.63%19.69%4.31%9.13%0.458
7724.35%25.92%29.73%20.00%4.34%9.23%0.457
7824.61%26.25%28.83%20.32%4.37%9.34%0.455
7924.86%26.58%27.92%20.64%4.40%9.44%0.453
8025.11%26.91%27.02%20.95%4.44%9.55%0.451
8125.37%27.24%26.12%21.27%4.47%9.65%0.450
8225.62%27.57%25.22%21.59%4.50%9.76%0.448
8325.88%27.90%24.32%21.91%4.54%9.86%0.446
8426.13%28.23%23.42%22.22%4.57%9.97%0.445
8526.38%28.56%22.52%22.54%4.60%10.08%0.443
8626.61%28.90%21.62%22.87%4.63%10.18%0.442
8726.84%29.23%20.73%23.20%4.67%10.29%0.440
8827.05%29.57%19.84%23.54%4.70%10.39%0.439
8927.24%29.90%18.95%23.91%4.73%10.49%0.437
9027.41%30.21%18.09%24.29%4.76%10.60%0.436
9127.59%30.49%17.23%24.69%4.79%10.70%0.435
9227.75%30.72%16.39%25.15%4.82%10.80%0.433
9327.86%30.91%15.58%25.66%4.85%10.89%0.432
9427.93%31.03%14.79%26.25%4.88%10.99%0.431
9527.91%31.16%14.04%26.89%4.90%11.08%0.429
9627.85%31.29%13.33%27.53%4.92%11.16%0.428
9727.68%31.60%12.66%28.07%4.95%11.24%0.427
9827.15%32.23%12.03%28.58%4.97%11.32%0.426
9926.61%32.92%11.47%29.00%4.99%11.39%0.425
10026.00%34.00%11.00%29.00%5.01%11.45%0.424
*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.