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 2.00% to 5.04%. Refer to the efficient frontier section for additional details. Historical values from Jan 2012 to Aug 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 8.03%
VXUS Vanguard Total International Stock ETF 4.13%
BND Vanguard Total Bond Market ETF 86.18%
VNQ Vanguard Real Estate ETF 1.66%
Save portfolio »

Portfolio Summary

Portfolio statistics
PortfolioExpected ReturnStandard DeviationSharpe Ratio
Provided Portfolio4.37%9.10%0.47
Maximum Sharpe Ratio2.30%3.51%0.63
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 (0.09% 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 ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1Vanguard Total Stock Market ETF (VTI)5.50%13.41%0.4030.00%100.00%
2Vanguard Total International Stock ETF (VXUS)5.70%14.12%0.3970.00%100.00%
3Vanguard Total Bond Market ETF (BND)1.80%3.30%0.5190.00%100.00%
4Vanguard Real Estate ETF (VNQ)5.00%15.33%0.3200.00%100.00%
Results 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 (0.09% annualized).

Asset Correlations

Efficient Frontier Asset Correlations
NameTickerVTIVXUSBNDVNQ
Vanguard Total Stock Market ETFVTI1.000.850.020.61
Vanguard Total International Stock ETFVXUS0.851.000.100.56
Vanguard Total Bond Market ETFBND0.020.101.000.49
Vanguard Real Estate ETFVNQ0.610.560.491.00
Based on monthly returns from Jan 2012 to Aug 2020
Efficient Frontier Assets
#VTIVXUSBNDVNQExpected Return*Standard Deviation*Sharpe Ratio*
15.22%0.37%94.41%0.00%2.00%3.22%0.595
25.84%0.55%93.58%0.04%2.03%3.22%0.603
36.22%0.85%92.82%0.10%2.06%3.24%0.610
46.46%1.22%92.11%0.21%2.09%3.25%0.614
56.66%1.60%91.40%0.34%2.11%3.28%0.618
66.85%1.97%90.68%0.50%2.14%3.30%0.621
77.02%2.36%89.95%0.66%2.17%3.33%0.624
87.20%2.73%89.22%0.85%2.19%3.36%0.626
97.39%3.09%88.49%1.04%2.22%3.39%0.628
107.59%3.44%87.74%1.23%2.25%3.43%0.629
117.81%3.79%86.96%1.45%2.28%3.47%0.630
128.03%4.13%86.18%1.66%2.30%3.51%0.630
138.26%4.47%85.40%1.87%2.33%3.56%0.630
148.49%4.81%84.60%2.10%2.36%3.61%0.630
158.73%5.16%83.79%2.32%2.39%3.66%0.629
168.97%5.51%82.96%2.56%2.42%3.71%0.628
179.22%5.85%82.13%2.80%2.45%3.77%0.626
189.47%6.20%81.30%3.04%2.48%3.83%0.625
199.71%6.54%80.45%3.29%2.51%3.89%0.622
209.97%6.88%79.60%3.55%2.54%3.95%0.620
2110.22%7.22%78.75%3.81%2.57%4.02%0.618
2210.48%7.56%77.89%4.07%2.60%4.09%0.615
2310.74%7.90%77.03%4.34%2.63%4.16%0.612
2411.00%8.23%76.16%4.61%2.66%4.23%0.609
2511.26%8.57%75.30%4.87%2.70%4.30%0.606
2611.52%8.91%74.43%5.14%2.73%4.37%0.603
2711.78%9.24%73.56%5.42%2.76%4.45%0.600
2812.03%9.57%72.70%5.70%2.79%4.53%0.596
2912.29%9.90%71.83%5.98%2.82%4.61%0.593
3012.54%10.23%70.95%6.27%2.85%4.69%0.589
3112.80%10.57%70.08%6.56%2.88%4.77%0.586
3213.05%10.90%69.20%6.84%2.91%4.85%0.582
3313.31%11.24%68.32%7.13%2.95%4.93%0.579
3413.56%11.57%67.44%7.43%2.98%5.02%0.575
3513.81%11.90%66.56%7.72%3.01%5.10%0.572
3614.06%12.23%65.69%8.02%3.04%5.19%0.568
3714.31%12.57%64.80%8.31%3.07%5.28%0.565
3814.57%12.90%63.92%8.61%3.10%5.37%0.562
3914.82%13.23%63.04%8.91%3.14%5.45%0.558
4015.08%13.55%62.16%9.21%3.17%5.54%0.555
4115.34%13.88%61.27%9.51%3.20%5.63%0.552
4215.59%14.20%60.39%9.81%3.23%5.73%0.548
4315.85%14.53%59.51%10.12%3.26%5.82%0.545
4416.10%14.85%58.62%10.42%3.29%5.91%0.542
4516.36%15.18%57.74%10.72%3.33%6.00%0.539
4616.61%15.50%56.85%11.03%3.36%6.10%0.536
4716.87%15.83%55.97%11.33%3.39%6.19%0.533
4817.12%16.15%55.08%11.64%3.42%6.28%0.530
4917.38%16.48%54.20%11.94%3.45%6.38%0.527
5017.63%16.80%53.31%12.25%3.48%6.47%0.524
5117.88%17.13%52.43%12.56%3.52%6.57%0.522
5218.14%17.45%51.54%12.87%3.55%6.67%0.519
5318.39%17.78%50.66%13.18%3.58%6.76%0.516
5418.64%18.10%49.77%13.49%3.61%6.86%0.514
5518.89%18.43%48.89%13.80%3.64%6.96%0.511
5619.14%18.75%48.00%14.11%3.68%7.05%0.508
5719.40%19.08%47.11%14.42%3.71%7.15%0.506
5819.65%19.40%46.22%14.73%3.74%7.25%0.503
5919.91%19.72%45.34%15.04%3.77%7.35%0.501
6020.16%20.04%44.45%15.35%3.80%7.45%0.499
6120.42%20.37%43.56%15.66%3.84%7.55%0.496
6220.67%20.69%42.67%15.97%3.87%7.65%0.494
6320.93%21.01%41.78%16.28%3.90%7.75%0.492
6421.18%21.33%40.90%16.59%3.93%7.84%0.490
6521.44%21.66%40.01%16.90%3.96%7.94%0.488
6621.69%21.98%39.12%17.21%4.00%8.05%0.486
6721.95%22.30%38.23%17.53%4.03%8.15%0.483
6822.20%22.62%37.34%17.84%4.06%8.25%0.481
6922.46%22.94%36.45%18.15%4.09%8.35%0.479
7022.71%23.26%35.56%18.47%4.12%8.45%0.478
7122.97%23.58%34.67%18.78%4.16%8.55%0.476
7223.23%23.90%33.78%19.09%4.19%8.65%0.474
7323.48%24.22%32.89%19.41%4.22%8.75%0.472
7423.74%24.54%32.00%19.72%4.25%8.86%0.470
7524.00%24.86%31.11%20.03%4.29%8.96%0.468
7624.25%25.18%30.22%20.35%4.32%9.06%0.467
7724.51%25.50%29.33%20.66%4.35%9.16%0.465
7824.77%25.82%28.44%20.98%4.38%9.26%0.463
7925.03%26.14%27.55%21.29%4.41%9.37%0.462
8025.28%26.45%26.66%21.60%4.45%9.47%0.460
8125.54%26.77%25.77%21.92%4.48%9.57%0.458
8225.80%27.09%24.88%22.23%4.51%9.68%0.457
8326.05%27.41%23.99%22.55%4.54%9.78%0.455
8426.31%27.73%23.10%22.86%4.58%9.88%0.454
8526.56%28.05%22.21%23.18%4.61%9.99%0.452
8626.82%28.37%21.32%23.49%4.64%10.09%0.451
8727.07%28.69%20.44%23.81%4.67%10.19%0.450
8827.30%29.00%19.55%24.14%4.70%10.30%0.448
8927.53%29.32%18.67%24.48%4.74%10.40%0.447
9027.75%29.63%17.78%24.83%4.77%10.50%0.445
9127.98%29.91%16.91%25.20%4.80%10.60%0.444
9228.18%30.21%16.04%25.57%4.83%10.71%0.443
9328.36%30.54%15.19%25.92%4.86%10.81%0.442
9428.42%30.89%14.37%26.32%4.89%10.90%0.440
9528.29%31.31%13.59%26.81%4.92%11.00%0.439
9627.99%31.79%12.87%27.35%4.94%11.08%0.438
9727.47%32.41%12.14%27.98%4.97%11.17%0.437
9826.68%33.15%11.36%28.81%5.00%11.27%0.435
9926.05%33.97%10.65%29.33%5.02%11.36%0.434
10026.50%34.00%10.00%29.50%5.04%11.43%0.433
*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 (0.09% annualized).