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 1.96% to 5.08%. Refer to the efficient frontier section for additional details. Historical values from Jan 2012 to Dec 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 7.41%
VXUS Vanguard Total International Stock ETF 3.59%
BND Vanguard Total Bond Market ETF 87.07%
VNQ Vanguard Real Estate ETF 1.93%
Save portfolio »

Portfolio Summary

Portfolio statistics
PortfolioExpected ReturnStandard DeviationSharpe Ratio
Provided Portfolio4.37%9.43%0.45
Maximum Sharpe Ratio2.27%3.54%0.62
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%13.81%0.3920.00%100.00%
2Vanguard Total International Stock ETF (VXUS)5.70%14.59%0.3850.00%100.00%
3Vanguard Total Bond Market ETF (BND)1.80%3.27%0.5240.00%100.00%
4Vanguard Real Estate ETF (VNQ)5.00%15.44%0.3180.00%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 ETFVTI1.000.860.050.63
Vanguard Total International Stock ETFVXUS0.861.000.130.58
Vanguard Total Bond Market ETFBND0.050.131.000.50
Vanguard Real Estate ETFVNQ0.630.580.501.00
Based on monthly returns from Jan 2012 to Dec 2020
Efficient Frontier Assets
#VTIVXUSBNDVNQExpected Return*Standard Deviation*Sharpe Ratio*
14.09%0.19%95.72%0.00%1.96%3.21%0.581
24.67%0.34%94.93%0.06%1.99%3.22%0.589
35.08%0.59%94.19%0.14%2.01%3.23%0.595
45.39%0.91%93.45%0.25%2.04%3.25%0.600
55.67%1.25%92.67%0.41%2.07%3.27%0.605
65.91%1.61%91.89%0.58%2.10%3.30%0.608
76.16%1.95%91.13%0.77%2.12%3.33%0.611
86.38%2.27%90.36%0.99%2.15%3.36%0.613
96.63%2.59%89.56%1.22%2.18%3.40%0.614
106.89%2.92%88.75%1.45%2.21%3.44%0.616
117.14%3.25%87.92%1.69%2.24%3.49%0.616
127.41%3.59%87.07%1.93%2.27%3.54%0.616
137.67%3.93%86.22%2.18%2.30%3.59%0.616
147.94%4.27%85.36%2.44%2.33%3.64%0.615
158.19%4.62%84.50%2.69%2.36%3.70%0.614
168.45%4.97%83.63%2.96%2.39%3.76%0.612
178.70%5.32%82.75%3.23%2.42%3.82%0.611
188.96%5.67%81.88%3.50%2.46%3.89%0.608
199.21%6.02%81.00%3.78%2.49%3.96%0.606
209.46%6.36%80.12%4.05%2.52%4.03%0.603
219.72%6.70%79.24%4.33%2.55%4.10%0.601
229.98%7.04%78.36%4.62%2.58%4.17%0.598
2310.24%7.37%77.49%4.90%2.61%4.24%0.594
2410.50%7.70%76.61%5.19%2.64%4.32%0.591
2510.76%8.04%75.72%5.48%2.68%4.40%0.588
2611.02%8.37%74.83%5.78%2.71%4.48%0.584
2711.28%8.70%73.93%6.08%2.74%4.56%0.581
2811.54%9.03%73.04%6.38%2.77%4.65%0.577
2911.80%9.36%72.15%6.69%2.80%4.73%0.574
3012.06%9.69%71.26%6.99%2.84%4.82%0.570
3112.31%10.02%70.36%7.30%2.87%4.90%0.567
3212.57%10.35%69.46%7.62%2.90%4.99%0.563
3312.83%10.68%68.56%7.93%2.93%5.08%0.559
3413.09%11.01%67.65%8.24%2.96%5.17%0.556
3513.35%11.35%66.75%8.56%3.00%5.26%0.552
3613.61%11.68%65.84%8.88%3.03%5.36%0.549
3713.86%12.00%64.94%9.20%3.06%5.45%0.545
3814.12%12.33%64.03%9.52%3.09%5.54%0.542
3914.38%12.65%63.13%9.84%3.13%5.64%0.539
4014.64%12.98%62.22%10.16%3.16%5.73%0.535
4114.91%13.30%61.31%10.48%3.19%5.83%0.532
4215.17%13.62%60.40%10.81%3.22%5.93%0.529
4315.43%13.94%59.49%11.13%3.26%6.03%0.525
4415.69%14.27%58.57%11.46%3.29%6.13%0.522
4515.95%14.60%57.66%11.79%3.32%6.23%0.519
4616.22%14.93%56.74%12.12%3.36%6.33%0.516
4716.48%15.26%55.82%12.44%3.39%6.43%0.513
4816.74%15.59%54.90%12.77%3.42%6.53%0.510
4917.00%15.92%53.98%13.10%3.45%6.63%0.507
5017.26%16.24%53.06%13.43%3.49%6.73%0.505
5117.53%16.57%52.15%13.75%3.52%6.84%0.502
5217.79%16.90%51.23%14.08%3.55%6.94%0.499
5318.05%17.23%50.31%14.41%3.59%7.04%0.496
5418.32%17.56%49.39%14.73%3.62%7.15%0.494
5518.58%17.89%48.47%15.06%3.65%7.25%0.491
5618.84%18.22%47.55%15.39%3.69%7.35%0.489
5719.11%18.55%46.63%15.71%3.72%7.46%0.486
5819.37%18.88%45.71%16.04%3.75%7.56%0.484
5919.64%19.20%44.79%16.37%3.78%7.67%0.482
6019.90%19.53%43.87%16.70%3.82%7.78%0.479
6120.17%19.86%42.95%17.03%3.85%7.88%0.477
6220.43%20.19%42.03%17.35%3.88%7.99%0.475
6320.70%20.52%41.11%17.68%3.92%8.10%0.473
6420.96%20.84%40.19%18.01%3.95%8.20%0.471
6521.23%21.17%39.27%18.34%3.98%8.31%0.469
6621.49%21.50%38.34%18.67%4.02%8.42%0.467
6721.76%21.82%37.42%19.00%4.05%8.52%0.465
6822.02%22.15%36.50%19.33%4.08%8.63%0.463
6922.29%22.47%35.58%19.66%4.12%8.74%0.461
7022.56%22.80%34.66%19.99%4.15%8.85%0.459
7122.82%23.13%33.74%20.31%4.18%8.96%0.457
7223.09%23.45%32.82%20.64%4.22%9.06%0.455
7323.35%23.78%31.89%20.97%4.25%9.17%0.453
7423.62%24.11%30.97%21.30%4.28%9.28%0.452
7523.88%24.43%30.05%21.63%4.32%9.39%0.450
7624.15%24.76%29.13%21.96%4.35%9.50%0.448
7724.41%25.09%28.20%22.29%4.38%9.61%0.447
7824.68%25.42%27.28%22.62%4.42%9.72%0.445
7924.94%25.74%26.36%22.95%4.45%9.83%0.444
8025.21%26.07%25.44%23.28%4.48%9.94%0.442
8125.47%26.40%24.51%23.61%4.52%10.05%0.441
8225.74%26.73%23.59%23.94%4.55%10.16%0.439
8326.00%27.05%22.67%24.28%4.58%10.27%0.438
8426.27%27.38%21.75%24.61%4.62%10.38%0.436
8526.53%27.71%20.82%24.94%4.65%10.49%0.435
8626.80%28.03%19.90%25.27%4.68%10.60%0.433
8727.06%28.36%18.98%25.60%4.72%10.71%0.432
8827.31%28.67%18.07%25.94%4.75%10.82%0.431
8927.57%28.99%17.16%26.28%4.78%10.93%0.429
9027.82%29.30%16.25%26.63%4.82%11.04%0.428
9128.08%29.60%15.34%26.98%4.85%11.15%0.427
9228.27%29.89%14.45%27.39%4.88%11.25%0.426
9328.39%30.18%13.58%27.85%4.91%11.36%0.424
9428.48%30.46%12.74%28.31%4.94%11.46%0.423
9528.55%30.74%11.93%28.78%4.97%11.56%0.422
9628.59%31.00%11.16%29.25%5.00%11.65%0.421
9728.33%31.39%10.44%29.84%5.02%11.74%0.420
9827.68%32.10%9.75%30.47%5.05%11.83%0.419
9926.71%33.18%9.10%31.02%5.07%11.91%0.418
10026.00%33.00%8.50%32.50%5.08%11.99%0.417
*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).