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 1.98% to 5.20%. Refer to the efficient frontier section for additional details. Historical values from Jan 2012 to Mar 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 8.69%
VXUS Vanguard Total International Stock ETF 2.92%
BND Vanguard Total Bond Market ETF 86.59%
VNQ Vanguard Real Estate ETF 1.80%
Save portfolio »

Portfolio Summary

Portfolio statistics
PortfolioExpected ReturnStandard DeviationSharpe Ratio
Provided Portfolio4.37%9.32%0.46
Maximum Sharpe Ratio2.29%3.56%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 (0.04% 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%13.67%0.4000.00%100.00%
2Vanguard Total International Stock ETF (VXUS)5.70%14.40%0.3930.00%100.00%
3Vanguard Total Bond Market ETF (BND)1.80%3.33%0.5280.00%100.00%
4Vanguard Real Estate ETF (VNQ)5.00%15.32%0.3240.00%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 (0.04% annualized).

Asset Correlations

Efficient Frontier Asset Correlations
NameTickerVTIVXUSBNDVNQ
Vanguard Total Stock Market ETFVTI1.000.860.040.63
Vanguard Total International Stock ETFVXUS0.861.000.110.58
Vanguard Total Bond Market ETFBND0.040.111.000.46
Vanguard Real Estate ETFVNQ0.630.580.461.00
Based on monthly returns from Jan 2012 to Mar 2021
Efficient Frontier Assets
#VTIVXUSBNDVNQExpected Return*Standard Deviation*Sharpe Ratio*
14.55%0.30%95.15%0.00%1.98%3.27%0.593
25.27%0.45%94.24%0.04%2.01%3.27%0.602
35.77%0.70%93.40%0.14%2.04%3.29%0.609
46.18%0.97%92.58%0.27%2.07%3.30%0.615
56.55%1.26%91.76%0.43%2.10%3.33%0.619
66.91%1.55%90.93%0.62%2.13%3.36%0.623
77.28%1.82%90.08%0.82%2.16%3.39%0.626
87.65%2.09%89.22%1.05%2.19%3.42%0.628
97.99%2.37%88.34%1.30%2.22%3.47%0.630
108.34%2.64%87.47%1.55%2.25%3.51%0.631
118.69%2.92%86.59%1.80%2.29%3.56%0.631
129.05%3.19%85.70%2.06%2.32%3.61%0.631
139.40%3.48%84.81%2.31%2.35%3.66%0.631
149.74%3.76%83.93%2.58%2.38%3.72%0.630
1510.08%4.03%83.03%2.85%2.41%3.78%0.628
1610.43%4.31%82.14%3.12%2.45%3.84%0.626
1710.78%4.58%81.23%3.40%2.48%3.90%0.624
1811.14%4.84%80.33%3.69%2.51%3.97%0.622
1911.49%5.11%79.43%3.97%2.54%4.04%0.619
2011.83%5.38%78.52%4.26%2.57%4.11%0.616
2112.18%5.65%77.62%4.56%2.61%4.19%0.613
2212.52%5.92%76.72%4.85%2.64%4.26%0.610
2312.87%6.18%75.80%5.15%2.67%4.34%0.606
2413.21%6.45%74.89%5.45%2.70%4.42%0.603
2513.56%6.72%73.97%5.76%2.74%4.50%0.599
2613.90%6.99%73.05%6.06%2.77%4.58%0.596
2714.24%7.25%72.13%6.37%2.80%4.67%0.592
2814.58%7.52%71.21%6.69%2.83%4.75%0.588
2914.92%7.78%70.29%7.00%2.87%4.84%0.584
3015.26%8.05%69.38%7.31%2.90%4.93%0.581
3115.60%8.32%68.45%7.63%2.93%5.02%0.577
3215.93%8.58%67.53%7.95%2.97%5.11%0.573
3316.27%8.85%66.61%8.27%3.00%5.20%0.569
3416.60%9.12%65.69%8.59%3.03%5.29%0.566
3516.93%9.38%64.77%8.92%3.06%5.38%0.562
3617.27%9.65%63.84%9.25%3.10%5.48%0.558
3717.60%9.92%62.91%9.58%3.13%5.57%0.555
3817.93%10.18%61.98%9.91%3.16%5.67%0.551
3918.26%10.45%61.05%10.25%3.20%5.77%0.547
4018.59%10.72%60.11%10.58%3.23%5.87%0.544
4118.92%10.99%59.18%10.92%3.26%5.96%0.540
4219.24%11.25%58.25%11.25%3.30%6.06%0.537
4319.57%11.52%57.32%11.59%3.33%6.16%0.534
4419.90%11.79%56.39%11.93%3.36%6.26%0.530
4520.23%12.06%55.45%12.26%3.40%6.37%0.527
4620.56%12.32%54.52%12.60%3.43%6.47%0.524
4720.88%12.59%53.59%12.94%3.46%6.57%0.521
4821.21%12.86%52.66%13.27%3.50%6.67%0.518
4921.54%13.13%51.72%13.61%3.53%6.78%0.515
5021.86%13.40%50.79%13.95%3.56%6.88%0.512
5122.19%13.66%49.86%14.29%3.60%6.98%0.509
5222.51%13.93%48.92%14.64%3.63%7.09%0.506
5322.84%14.20%47.99%14.98%3.66%7.19%0.504
5423.16%14.46%47.05%15.32%3.70%7.30%0.501
5523.49%14.73%46.12%15.66%3.73%7.40%0.498
5623.81%14.99%45.19%16.01%3.76%7.51%0.496
5724.14%15.26%44.25%16.35%3.80%7.62%0.493
5824.46%15.53%43.32%16.69%3.83%7.72%0.491
5924.79%15.79%42.38%17.03%3.86%7.83%0.488
6025.12%16.06%41.44%17.38%3.90%7.94%0.486
6125.44%16.33%40.51%17.72%3.93%8.04%0.484
6225.77%16.59%39.57%18.06%3.96%8.15%0.481
6326.10%16.86%38.64%18.41%4.00%8.26%0.479
6426.42%17.13%37.70%18.75%4.03%8.37%0.477
6526.75%17.39%36.76%19.09%4.07%8.48%0.475
6627.08%17.66%35.83%19.44%4.10%8.59%0.473
6727.40%17.92%34.89%19.78%4.13%8.69%0.471
6827.73%18.19%33.95%20.12%4.17%8.80%0.469
6928.06%18.45%33.02%20.47%4.20%8.91%0.467
7028.39%18.72%32.08%20.81%4.23%9.02%0.465
7128.72%18.98%31.14%21.15%4.27%9.13%0.463
7229.05%19.25%30.20%21.50%4.30%9.24%0.461
7329.38%19.51%29.26%21.84%4.33%9.35%0.459
7429.71%19.77%28.32%22.19%4.37%9.46%0.457
7530.05%20.04%27.39%22.53%4.40%9.57%0.456
7630.38%20.30%26.45%22.87%4.44%9.68%0.454
7730.71%20.57%25.51%23.22%4.47%9.80%0.452
7831.04%20.83%24.57%23.56%4.50%9.91%0.451
7931.37%21.10%23.63%23.90%4.54%10.02%0.449
8031.70%21.36%22.69%24.24%4.57%10.13%0.447
8132.03%21.62%21.76%24.59%4.61%10.24%0.446
8232.36%21.89%20.82%24.93%4.64%10.35%0.444
8332.70%22.15%19.88%25.27%4.67%10.46%0.443
8433.03%22.41%18.94%25.62%4.71%10.58%0.441
8533.36%22.68%18.00%25.96%4.74%10.69%0.440
8633.69%22.94%17.06%26.30%4.77%10.80%0.438
8734.02%23.21%16.13%26.65%4.81%10.91%0.437
8834.35%23.47%15.19%26.99%4.84%11.02%0.436
8934.64%23.74%14.26%27.36%4.88%11.13%0.434
9034.92%24.00%13.33%27.75%4.91%11.25%0.433
9135.19%24.26%12.41%28.13%4.94%11.36%0.432
9235.40%24.56%11.50%28.54%4.97%11.46%0.430
9335.58%24.83%10.61%28.98%5.01%11.57%0.429
9435.69%25.11%9.74%29.47%5.04%11.68%0.428
9535.79%25.41%8.89%29.91%5.07%11.78%0.427
9635.79%25.80%8.05%30.37%5.10%11.88%0.426
9735.60%26.29%7.21%30.89%5.13%11.98%0.425
9835.22%26.84%6.42%31.52%5.15%12.08%0.423
9934.89%27.49%5.67%31.94%5.18%12.17%0.422
10034.50%28.00%5.00%32.50%5.21%12.25%0.422
*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 (0.04% annualized).