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 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 4.92%. Refer to the efficient frontier section for additional details. Historical values from Jan 2012 to Jun 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 7.44%
VXUS Vanguard Total International Stock ETF 3.61%
BND Vanguard Total Bond Market ETF 87.11%
VNQ Vanguard Real Estate ETF 1.84%
Save portfolio »

Portfolio Summary

Portfolio statistics
PortfolioExpected ReturnStandard DeviationSharpe Ratio
Provided Portfolio4.37%9.24%0.47
Maximum Sharpe Ratio2.27%3.52%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%13.55%0.3950.00%100.00%
2Vanguard Total International Stock ETF (VXUS)5.70%14.25%0.3890.00%100.00%
3Vanguard Total Bond Market ETF (BND)1.80%3.30%0.5380.00%100.00%
4Vanguard Real Estate ETF (VNQ)5.00%15.30%0.3190.00%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 ETFVTI1.000.860.040.64
Vanguard Total International Stock ETFVXUS0.861.000.110.58
Vanguard Total Bond Market ETFBND0.040.111.000.46
Vanguard Real Estate ETFVNQ0.640.580.461.00
Based on monthly returns from Jan 2012 to Jun 2021
Efficient Frontier Assets
#VTIVXUSBNDVNQExpected Return*Standard Deviation*Sharpe Ratio*
14.42%0.21%95.38%0.00%1.97%3.24%0.599
24.98%0.45%94.54%0.02%2.00%3.24%0.608
35.40%0.74%93.77%0.09%2.03%3.25%0.614
45.70%1.05%93.04%0.21%2.05%3.27%0.619
55.95%1.36%92.33%0.36%2.08%3.29%0.623
66.19%1.67%91.60%0.53%2.11%3.31%0.627
76.40%1.99%90.88%0.72%2.13%3.34%0.629
86.60%2.32%90.15%0.93%2.16%3.37%0.631
96.81%2.64%89.41%1.14%2.19%3.40%0.633
107.02%2.97%88.64%1.37%2.21%3.44%0.634
117.23%3.29%87.88%1.60%2.24%3.48%0.635
127.44%3.61%87.11%1.84%2.27%3.52%0.635
137.66%3.93%86.33%2.09%2.30%3.56%0.635
147.87%4.25%85.54%2.33%2.32%3.61%0.634
158.10%4.58%84.74%2.59%2.35%3.66%0.633
168.32%4.91%83.93%2.85%2.38%3.71%0.632
178.55%5.23%83.11%3.11%2.41%3.77%0.630
188.78%5.55%82.29%3.38%2.44%3.82%0.628
199.01%5.87%81.47%3.65%2.47%3.88%0.626
209.24%6.18%80.65%3.93%2.50%3.94%0.624
219.48%6.50%79.83%4.20%2.53%4.01%0.621
229.70%6.81%79.01%4.48%2.56%4.07%0.619
239.93%7.12%78.18%4.77%2.59%4.14%0.616
2410.15%7.43%77.35%5.07%2.62%4.21%0.612
2510.38%7.74%76.53%5.36%2.65%4.28%0.609
2610.61%8.04%75.70%5.65%2.68%4.35%0.606
2710.84%8.35%74.87%5.95%2.71%4.42%0.603
2811.06%8.65%74.03%6.25%2.74%4.49%0.599
2911.29%8.96%73.19%6.56%2.77%4.57%0.596
3011.52%9.26%72.35%6.88%2.80%4.65%0.592
3111.74%9.56%71.51%7.19%2.83%4.72%0.588
3211.97%9.86%70.66%7.51%2.86%4.80%0.585
3312.19%10.16%69.81%7.84%2.89%4.88%0.581
3412.42%10.45%68.96%8.17%2.92%4.97%0.577
3512.64%10.75%68.11%8.50%2.95%5.05%0.574
3612.86%11.04%67.26%8.84%2.98%5.13%0.570
3713.09%11.34%66.40%9.17%3.01%5.22%0.567
3813.32%11.65%65.53%9.51%3.04%5.30%0.563
3913.54%11.95%64.66%9.85%3.07%5.39%0.559
4013.77%12.25%63.79%10.19%3.10%5.48%0.556
4114.00%12.55%62.91%10.53%3.13%5.57%0.552
4214.23%12.85%62.04%10.88%3.16%5.66%0.549
4314.46%13.16%61.17%11.22%3.19%5.75%0.545
4414.69%13.46%60.29%11.56%3.22%5.84%0.542
4514.92%13.76%59.42%11.90%3.26%5.94%0.539
4615.15%14.06%58.55%12.25%3.29%6.03%0.535
4715.38%14.35%57.67%12.59%3.32%6.12%0.532
4815.61%14.65%56.80%12.94%3.35%6.22%0.529
4915.84%14.95%55.92%13.29%3.38%6.31%0.526
5016.08%15.25%55.05%13.63%3.41%6.40%0.523
5116.31%15.54%54.17%13.98%3.44%6.50%0.520
5216.54%15.84%53.30%14.32%3.47%6.59%0.517
5316.77%16.14%52.42%14.67%3.50%6.69%0.514
5417.01%16.43%51.54%15.02%3.54%6.79%0.511
5517.24%16.73%50.66%15.37%3.57%6.88%0.509
5617.47%17.03%49.79%15.71%3.60%6.98%0.506
5717.70%17.33%48.91%16.06%3.63%7.08%0.503
5817.93%17.63%48.03%16.41%3.66%7.18%0.501
5918.17%17.92%47.15%16.76%3.69%7.27%0.498
6018.40%18.22%46.27%17.11%3.72%7.37%0.495
6118.63%18.52%45.40%17.46%3.76%7.47%0.493
6218.86%18.82%44.52%17.80%3.79%7.57%0.490
6319.09%19.11%43.64%18.15%3.82%7.67%0.488
6419.33%19.41%42.76%18.50%3.85%7.77%0.486
6519.56%19.71%41.88%18.85%3.88%7.87%0.483
6619.79%20.01%41.00%19.20%3.91%7.97%0.481
6720.02%20.30%40.13%19.55%3.94%8.07%0.479
6820.26%20.60%39.25%19.90%3.98%8.17%0.477
6920.49%20.90%38.37%20.25%4.01%8.27%0.475
7020.72%21.19%37.49%20.59%4.04%8.37%0.473
7120.96%21.49%36.61%20.94%4.07%8.47%0.471
7221.19%21.79%35.73%21.29%4.10%8.57%0.469
7321.42%22.08%34.85%21.64%4.13%8.67%0.467
7421.66%22.38%33.97%21.99%4.16%8.77%0.465
7521.89%22.68%33.08%22.36%4.20%8.88%0.463
7622.12%22.97%32.18%22.73%4.23%8.98%0.461
7722.35%23.27%31.28%23.10%4.26%9.09%0.459
7822.59%23.57%30.38%23.47%4.29%9.19%0.457
7922.82%23.86%29.48%23.84%4.33%9.30%0.455
8023.05%24.16%28.58%24.21%4.36%9.40%0.453
8123.29%24.46%27.68%24.58%4.39%9.51%0.452
8223.52%24.75%26.78%24.95%4.42%9.61%0.450
8323.75%25.05%25.88%25.32%4.45%9.72%0.448
8423.99%25.35%24.98%25.69%4.49%9.82%0.447
8524.22%25.64%24.08%26.06%4.52%9.93%0.445
8624.45%25.94%23.18%26.43%4.55%10.03%0.443
8724.68%26.23%22.28%26.80%4.58%10.14%0.442
8824.89%26.53%21.39%27.19%4.62%10.24%0.440
8925.08%26.83%20.50%27.59%4.65%10.35%0.439
9025.26%27.12%19.61%28.01%4.68%10.45%0.437
9125.38%27.39%18.74%28.49%4.71%10.56%0.436
9225.46%27.63%17.89%29.01%4.74%10.66%0.434
9325.54%27.81%17.06%29.59%4.77%10.76%0.433
9425.53%27.95%16.26%30.26%4.79%10.86%0.431
9525.33%28.14%15.50%31.03%4.82%10.95%0.430
9624.83%28.57%14.81%31.79%4.84%11.04%0.428
9724.25%29.11%14.16%32.48%4.86%11.12%0.427
9823.42%30.00%13.56%33.02%4.89%11.20%0.426
9922.32%31.26%13.01%33.41%4.91%11.27%0.425
10021.50%32.50%12.50%33.50%4.93%11.34%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.