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.

%
%
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 2.15% to 5.24%. Refer to the efficient frontier section for additional details. Historical values from Jan 2012 to Nov 2019 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 30.82%
VXUS Vanguard Total International Stock ETF 31.74%
BND Vanguard Total Bond Market ETF 5.31%
VNQ Vanguard Real Estate ETF 32.13%
Save portfolio »

Portfolio Summary

Portfolio statistics
PortfolioExpected ReturnStandard DeviationSharpe Ratio
Provided Portfolio4.37%7.57%0.29
Maximum Sharpe Ratio5.20%10.00%0.30
Expected return is based on the provided capital market expectations. Ex ante Sharpe Ratio calculated using the current 1-month treasury bill return as the risk-free rate (2.18% 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 Return*Standard DeviationSharpe Ratio*Min. WeightMax. Weight
1Vanguard Total Stock Market ETF (VTI)5.50%11.36%0.2920.00%100.00%
2Vanguard Total International Stock ETF (VXUS)5.70%12.57%0.2800.00%100.00%
3Vanguard Total Bond Market ETF (BND)1.80%3.11%-0.1230.00%100.00%
4Vanguard Real Estate ETF (VNQ)5.00%13.69%0.2060.00%100.00%
*Expected return based on the provided capital market expectations. Ex ante Sharpe Ratio calculated using the current 1-month treasury bill return as the risk-free rate (2.18% annualized).

Monthly Correlations

Efficient Frontier Asset Correlations
NameTickerVTIVXUSBNDVNQ
Vanguard Total Stock Market ETFVTI1.000.81-0.120.48
Vanguard Total International Stock ETFVXUS0.811.000.030.42
Vanguard Total Bond Market ETFBND-0.120.031.000.49
Vanguard Real Estate ETFVNQ0.480.420.491.00
Based on monthly returns from Jan 2012 to Nov 2019
Efficient Frontier Assets
#VTIVXUSBNDVNQExpected Return*Standard Deviation*Sharpe Ratio*
19.48%0.06%90.45%0.00%2.15%2.89%-0.012
210.29%0.21%89.45%0.04%2.18%2.90%0.001
310.86%0.45%88.58%0.12%2.22%2.91%0.012
411.31%0.72%87.76%0.22%2.25%2.93%0.022
511.69%0.99%86.97%0.35%2.28%2.95%0.032
612.01%1.31%86.19%0.49%2.30%2.98%0.041
712.28%1.64%85.42%0.65%2.33%3.00%0.050
812.54%1.98%84.65%0.83%2.36%3.04%0.059
912.78%2.32%83.88%1.02%2.39%3.07%0.067
1012.98%2.67%83.11%1.23%2.42%3.11%0.075
1113.20%3.02%82.33%1.45%2.44%3.14%0.083
1213.41%3.38%81.55%1.67%2.47%3.18%0.091
1313.63%3.72%80.76%1.90%2.50%3.23%0.099
1413.86%4.05%79.95%2.14%2.53%3.27%0.106
1514.09%4.39%79.12%2.39%2.56%3.32%0.114
1614.33%4.73%78.29%2.65%2.59%3.37%0.121
1714.58%5.06%77.45%2.92%2.62%3.42%0.128
1814.83%5.39%76.60%3.18%2.65%3.48%0.135
1915.07%5.73%75.76%3.45%2.68%3.53%0.141
2015.32%6.06%74.90%3.72%2.71%3.59%0.147
2115.57%6.40%74.04%3.99%2.74%3.65%0.154
2215.82%6.74%73.17%4.27%2.77%3.71%0.159
2316.08%7.06%72.29%4.56%2.80%3.77%0.165
2416.34%7.39%71.41%4.85%2.84%3.84%0.171
2516.60%7.71%70.53%5.16%2.87%3.90%0.176
2616.86%8.02%69.65%5.46%2.90%3.97%0.181
2717.12%8.34%68.76%5.77%2.93%4.04%0.186
2817.38%8.66%67.87%6.08%2.96%4.11%0.190
2917.65%8.98%66.97%6.40%2.99%4.18%0.195
3017.91%9.30%66.08%6.71%3.03%4.25%0.199
3118.18%9.61%65.18%7.03%3.06%4.32%0.203
3218.44%9.93%64.28%7.35%3.09%4.40%0.207
3318.71%10.25%63.37%7.67%3.12%4.47%0.211
3418.98%10.57%62.47%7.98%3.16%4.55%0.214
3519.25%10.89%61.56%8.30%3.19%4.62%0.218
3619.52%11.21%60.65%8.63%3.22%4.70%0.221
3719.78%11.53%59.74%8.95%3.25%4.78%0.224
3820.05%11.85%58.82%9.27%3.29%4.86%0.227
3920.32%12.17%57.91%9.60%3.32%4.94%0.230
4020.59%12.49%57.00%9.92%3.35%5.02%0.233
4120.86%12.81%56.08%10.25%3.38%5.10%0.236
4221.13%13.14%55.17%10.57%3.42%5.18%0.239
4321.40%13.45%54.25%10.90%3.45%5.26%0.241
4421.67%13.77%53.33%11.23%3.48%5.34%0.244
4521.94%14.09%52.42%11.55%3.52%5.43%0.246
4622.21%14.41%51.50%11.88%3.55%5.51%0.248
4722.48%14.73%50.58%12.21%3.58%5.59%0.250
4822.75%15.05%49.66%12.54%3.62%5.68%0.253
4923.02%15.36%48.74%12.87%3.65%5.76%0.255
5023.29%15.68%47.82%13.20%3.68%5.84%0.257
5123.57%16.00%46.90%13.54%3.71%5.93%0.258
5223.84%16.31%45.98%13.87%3.75%6.02%0.260
5324.11%16.63%45.06%14.20%3.78%6.10%0.262
5424.38%16.94%44.14%14.54%3.81%6.19%0.264
5524.65%17.26%43.22%14.87%3.85%6.27%0.265
5624.92%17.57%42.29%15.21%3.88%6.36%0.267
5725.19%17.89%41.37%15.55%3.91%6.45%0.269
5825.47%18.20%40.45%15.89%3.95%6.53%0.270
5925.74%18.51%39.52%16.23%3.98%6.62%0.271
6026.01%18.82%38.58%16.58%4.01%6.71%0.273
6126.28%19.14%37.65%16.93%4.05%6.80%0.274
6226.56%19.45%36.71%17.29%4.08%6.89%0.276
6326.83%19.76%35.77%17.64%4.11%6.98%0.277
6427.10%20.07%34.83%18.00%4.15%7.07%0.278
6527.38%20.38%33.89%18.35%4.18%7.16%0.279
6627.65%20.69%32.95%18.71%4.22%7.25%0.281
6727.93%21.00%32.01%19.06%4.25%7.34%0.282
6828.20%21.31%31.07%19.42%4.28%7.43%0.283
6928.48%21.62%30.12%19.78%4.32%7.52%0.284
7028.75%21.93%29.18%20.13%4.35%7.62%0.285
7129.03%22.24%28.24%20.49%4.39%7.71%0.286
7229.30%22.55%27.30%20.84%4.42%7.80%0.287
7329.57%22.86%26.36%21.20%4.45%7.89%0.288
7429.85%23.18%25.40%21.58%4.49%7.98%0.289
7530.12%23.49%24.44%21.95%4.52%8.08%0.290
7630.40%23.80%23.47%22.33%4.56%8.17%0.291
7730.67%24.11%22.51%22.71%4.59%8.27%0.291
7830.95%24.42%21.55%23.08%4.63%8.36%0.292
7931.23%24.73%20.59%23.46%4.66%8.46%0.293
8031.50%25.04%19.63%23.83%4.70%8.55%0.294
8131.78%25.35%18.66%24.21%4.73%8.65%0.295
8232.05%25.66%17.71%24.59%4.76%8.74%0.296
8332.30%25.97%16.75%24.98%4.80%8.83%0.296
8432.55%26.28%15.80%25.37%4.83%8.93%0.297
8532.77%26.59%14.86%25.78%4.87%9.02%0.298
8632.99%26.89%13.93%26.20%4.90%9.11%0.298
8733.19%27.17%13.01%26.63%4.93%9.21%0.299
8833.35%27.44%12.10%27.10%4.97%9.30%0.299
8933.45%27.68%11.23%27.64%5.00%9.38%0.300
9033.45%27.98%10.38%28.19%5.03%9.47%0.300
9133.38%28.31%9.55%28.76%5.05%9.55%0.301
9233.26%28.62%8.76%29.36%5.08%9.63%0.301
9333.12%28.92%7.99%29.97%5.11%9.71%0.301
9432.91%29.29%7.24%30.56%5.13%9.79%0.302
9532.49%29.83%6.54%31.14%5.16%9.86%0.302
9631.89%30.61%5.89%31.61%5.18%9.93%0.302
9730.82%31.74%5.31%32.13%5.20%10.00%0.302
9829.38%33.17%4.82%32.63%5.22%10.06%0.302
9927.90%34.57%4.40%33.14%5.24%10.12%0.302
10026.00%35.50%4.00%34.50%5.25%10.18%0.301
*Ex-ante values shown for portfolio return and volatility. Ex ante Sharpe Ratio calculated using the current 1-month treasury bill return as the risk-free rate (2.18% annualized).