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.

%
%
Browse…
1
%
%
%
%
%
2
%
%
%
%
%
3
%
%
%
%
%
4
%
%
%
%
%
5
%
%
%
%
%
6
%
%
%
%
%
7
%
%
%
%
%
8
%
%
%
%
%
9
%
%
%
%
%
10
%
%
%
%
%
Total
%

Asset Groups
Min. Weight
Max. Weight
A
%
%
B
%
%
C
%
%
D
%
%
E
%
%
F
%
%

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 1.99% to 4.91%. Refer to the efficient frontier section for additional details. Historical values from Jan 2012 to Jun 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 8.76%
VXUS Vanguard Total International Stock ETF 3.41%
BND Vanguard Total Bond Market ETF 86.10%
VNQ Vanguard Real Estate ETF 1.72%
Save portfolio »

Portfolio Summary

Portfolio statistics
PortfolioExpected ReturnStandard DeviationSharpe Ratio
Provided Portfolio4.37%9.07%0.47
Maximum Sharpe Ratio2.31%3.50%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 (0.14% 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%13.29%0.4030.00%100.00%
2Vanguard Total International Stock ETF (VXUS)5.70%14.14%0.3930.00%100.00%
3Vanguard Total Bond Market ETF (BND)1.80%3.28%0.5060.00%100.00%
4Vanguard Real Estate ETF (VNQ)5.00%15.45%0.3150.00%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 (0.14% 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 Jun 2020
Efficient Frontier Assets
#VTIVXUSBNDVNQExpected Return*Standard Deviation*Sharpe Ratio*
14.93%0.16%94.91%0.00%1.99%3.20%0.577
25.68%0.32%93.97%0.03%2.02%3.21%0.587
36.14%0.60%93.16%0.10%2.05%3.22%0.594
46.51%0.91%92.38%0.20%2.08%3.23%0.599
56.84%1.22%91.62%0.32%2.11%3.25%0.604
67.16%1.52%90.86%0.46%2.13%3.28%0.608
77.45%1.84%90.08%0.63%2.16%3.31%0.612
87.71%2.17%89.30%0.82%2.19%3.34%0.614
97.96%2.48%88.52%1.04%2.22%3.38%0.616
108.22%2.80%87.72%1.26%2.25%3.42%0.617
118.49%3.11%86.92%1.49%2.28%3.46%0.618
128.76%3.41%86.10%1.72%2.31%3.50%0.618
139.03%3.72%85.29%1.97%2.33%3.55%0.618
149.29%4.03%84.47%2.21%2.36%3.60%0.617
159.54%4.34%83.65%2.47%2.39%3.65%0.617
169.80%4.64%82.83%2.73%2.42%3.71%0.615
1710.06%4.95%81.99%3.00%2.45%3.77%0.614
1810.31%5.25%81.15%3.29%2.48%3.83%0.612
1910.56%5.55%80.31%3.58%2.51%3.89%0.610
2010.81%5.84%79.48%3.87%2.54%3.96%0.607
2111.05%6.13%78.64%4.18%2.57%4.02%0.605
2211.30%6.43%77.80%4.48%2.60%4.09%0.602
2311.54%6.72%76.95%4.79%2.63%4.16%0.599
2411.78%7.01%76.11%5.10%2.66%4.23%0.596
2512.02%7.30%75.27%5.42%2.69%4.30%0.593
2612.26%7.59%74.42%5.73%2.72%4.38%0.590
2712.49%7.89%73.58%6.05%2.75%4.45%0.586
2812.73%8.18%72.73%6.36%2.78%4.53%0.583
2912.97%8.46%71.88%6.69%2.81%4.61%0.580
3013.21%8.74%71.03%7.02%2.84%4.69%0.577
3113.46%9.03%70.18%7.34%2.87%4.77%0.573
3213.70%9.31%69.32%7.67%2.90%4.85%0.570
3313.95%9.60%68.46%8.00%2.93%4.93%0.567
3414.19%9.88%67.60%8.33%2.96%5.01%0.563
3514.44%10.16%66.74%8.66%2.99%5.10%0.560
3614.68%10.45%65.88%8.99%3.03%5.18%0.557
3714.93%10.73%65.02%9.33%3.06%5.27%0.553
3815.17%11.01%64.16%9.66%3.09%5.36%0.550
3915.42%11.29%63.30%9.99%3.12%5.44%0.547
4015.66%11.58%62.44%10.33%3.15%5.53%0.544
4115.91%11.85%61.58%10.66%3.18%5.62%0.541
4216.16%12.13%60.72%11.00%3.21%5.71%0.538
4316.40%12.40%59.86%11.33%3.24%5.80%0.535
4416.65%12.68%59.00%11.67%3.27%5.89%0.532
4516.89%12.95%58.14%12.01%3.30%5.98%0.529
4617.14%13.22%57.29%12.35%3.33%6.07%0.526
4717.39%13.49%56.43%12.69%3.36%6.16%0.523
4817.63%13.77%55.57%13.04%3.39%6.25%0.520
4917.87%14.04%54.70%13.38%3.42%6.34%0.518
5018.12%14.31%53.84%13.73%3.45%6.43%0.515
5118.36%14.59%52.97%14.08%3.48%6.53%0.512
5218.61%14.87%52.10%14.43%3.52%6.62%0.510
5318.85%15.14%51.22%14.79%3.55%6.72%0.507
5419.09%15.42%50.35%15.14%3.58%6.81%0.504
5519.34%15.70%49.47%15.50%3.61%6.91%0.502
5619.58%15.97%48.60%15.85%3.64%7.01%0.500
5719.82%16.25%47.72%16.21%3.67%7.10%0.497
5820.06%16.53%46.85%16.57%3.70%7.20%0.495
5920.30%16.80%45.97%16.93%3.73%7.30%0.492
6020.54%17.08%45.10%17.28%3.76%7.39%0.490
6120.78%17.36%44.22%17.64%3.80%7.49%0.488
6221.02%17.63%43.35%18.00%3.83%7.59%0.486
6321.26%17.91%42.47%18.36%3.86%7.69%0.484
6421.50%18.19%41.59%18.72%3.89%7.79%0.482
6521.74%18.46%40.72%19.08%3.92%7.89%0.479
6621.98%18.74%39.84%19.43%3.95%7.98%0.477
6722.22%19.02%38.97%19.79%3.98%8.08%0.475
6822.47%19.29%38.09%20.15%4.01%8.18%0.474
6922.71%19.57%37.22%20.51%4.05%8.28%0.472
7022.95%19.84%36.34%20.87%4.08%8.38%0.470
7123.19%20.12%35.47%21.23%4.11%8.48%0.468
7223.43%20.39%34.59%21.59%4.14%8.58%0.466
7323.67%20.67%33.72%21.94%4.17%8.68%0.464
7423.91%20.94%32.84%22.30%4.20%8.78%0.463
7524.16%21.22%31.96%22.66%4.23%8.88%0.461
7624.40%21.49%31.09%23.02%4.27%8.98%0.459
7724.64%21.77%30.21%23.38%4.30%9.08%0.458
7824.88%22.04%29.34%23.74%4.33%9.18%0.456
7925.12%22.32%28.46%24.10%4.36%9.28%0.454
8025.37%22.60%27.58%24.46%4.39%9.38%0.453
8125.61%22.87%26.70%24.81%4.42%9.49%0.451
8225.85%23.15%25.83%25.17%4.45%9.59%0.450
8326.09%23.42%24.95%25.53%4.48%9.69%0.448
8426.34%23.70%24.08%25.89%4.52%9.79%0.447
8526.56%23.96%23.21%26.27%4.55%9.89%0.446
8626.77%24.22%22.34%26.66%4.58%9.99%0.444
8726.98%24.46%21.49%27.07%4.61%10.09%0.443
8827.17%24.70%20.64%27.49%4.64%10.19%0.441
8927.31%24.94%19.80%27.95%4.67%10.29%0.440
9027.39%25.18%18.98%28.45%4.70%10.39%0.439
9127.40%25.42%18.18%29.00%4.72%10.48%0.437
9227.32%25.63%17.41%29.64%4.75%10.58%0.436
9327.21%25.80%16.66%30.34%4.78%10.67%0.434
9427.05%25.93%15.93%31.09%4.80%10.76%0.433
9526.83%26.14%15.26%31.78%4.82%10.84%0.432
9626.55%26.35%14.61%32.48%4.84%10.93%0.430
9726.07%26.79%14.02%33.12%4.86%11.00%0.429
9825.26%27.37%13.48%33.89%4.88%11.08%0.428
9924.07%28.36%12.98%34.60%4.90%11.15%0.427
10021.50%30.50%12.50%35.50%4.91%11.23%0.425
*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 (0.14% annualized).