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 1.80% to 5.69%. Refer to the efficient frontier section for additional details. Historical values from Jan 2012 to Sep 2022 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 19.70%
VXUS Vanguard Total International Stock ETF 80.30%
Save portfolio »

Portfolio Summary

Portfolio statistics
PortfolioExpected ReturnStandard DeviationSharpe Ratio
Provided Portfolio4.38%10.19%0.15
Maximum Sharpe Ratio5.66%14.25%0.19
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:
  • IMPORTANT: The projections or other information generated by Portfolio Visualizer regarding the likelihood of various investment outcomes are hypothetical in nature, do not reflect actual investment results and are not guarantees of future results. Results may vary with each use and over time.
  • 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. All use is subject to terms of service.
  • Investing involves risk, including possible loss of principal. Past performance is not a guarantee of future results.
  • Asset allocation and diversification strategies do not guarantee a profit or protect against a loss.
  • Hypothetical returns do not reflect trading costs, transaction fees, commissions, or actual taxes due on investment returns.
  • 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.
  • Refer to the related documentation sections for more details on terms and definitions, methodology, and data sources.
  • Portfolio optimization is a process of choosing the proportions of various assets to be held in a portfolio in such a way as to make the portfolio better than any other combination according to the selected objective function such as maximizing risk-adjusted return. 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 the total return of assets and assume that all received dividends and distributions are reinvested.
  • Compound annualized growth rate (CAGR) is the annualized geometric mean return of the portfolio. It is calculated from the portfolio start and end balance and is thus impacted by any cashflows.
  • The time-weighted rate of return (TWRR) is a measure of the compound rate of growth in a portfolio. This is calculated from the holding period returns (e.g. monthly returns), and TWRR will thus not be impacted by cashflows. If there are no external cashflows, TWRR will equal CAGR.
  • The money-weighted rate of return (MWRR) is the internal rate of return (IRR) taking into account cashflows. This is the discount rate at which the present value of cash inflows equals the present value of cash outflows.
  • Standard deviation (Stdev) is used to measure the dispersion of returns around the mean and is often used as a measure of risk. A higher standard deviation implies greater the dispersion of data points around the mean.
  • Sharpe Ratio is a measure of risk-adjusted performance of the portfolio, and it is calculated by dividing the mean monthly excess return of the portfolio over the risk-free rate by the standard deviation of excess return, and the displayed value is annualized.
  • Sortino Ratio is a measure of risk-adjusted return which is a modification of the Sharpe Ratio. While the latter is the ratio of average returns in excess of a risk-free rate divided by the standard deviation of those excess returns, the Sortino Ratio has the same denominator divided by the standard deviation of returns below the risk-free rate.
  • Treynor Ratio is a measure of risk-adjusted performance of the portfolio. It is similar to the Sharpe Ratio, but it uses portfolio beta (systematic risk) as the risk metric in the denominator.
  • Calmar Ratio is a measure of risk-adjusted performance of the portfolio. It is calculated as the annualized return over the past 36 months divided by the maximum drawdown over the past 36 months based on monthly returns.
  • Risk-free returns are calculated based on the Federal Reserve 3-Month Treasury Bill (secondary market) rates.
  • Downside deviation measures the downside volatility of the portfolio returns unlike standard deviation, which includes both upside and downside deviations. Downside deviation is calculated based on negative returns that hurt the portfolio performance.
  • Correlation measures to what degree the returns of the two assets move in relation to each other. Correlation coefficient is a numerical value between -1 and +1. If one variable goes up by a certain amount, the correlation coefficient indicates which way the other variable moves and by how much. Asset correlations are calculated based on monthly returns.
  • Skewness is a measure of the asymmetry of the probability distribution or returns from a normal Gaussian distribution shape about its mean. Negative skewness is associated with the left (typically negative returns) tail of the distribution extending further than the right tail; and positive skewness is associated with the right (typically positive returns) tail of the distribution extending further than the left tail.
  • Excess kurtosis is a measure of whether a data distribution is peaked or flat relative to a normal distribution. Distributions with high kurtosis tend to have a distinct peak near the mean, decline rather rapidly, and have heavy or fat tails.
  • A drawdown refers to the decline in value of a single investment or an investment portfolio from a relative peak value to a relative trough. A maximum drawdown (Max Drawdown) is the maximum observed loss from a peak to a trough of a portfolio before a new peak is attained. Drawdown values are calculated based on monthly returns.
  • Value at Risk (VaR) measures the scale of loss at a given confidence level. If the 5% VaR is -3% the portfolio return is expected to be greater than -3% 95% of the time and less than -3% 5% of the time. Value at Risk can be calculated directly based on historical returns based on a given percentile or analytically based on the mean and standard deviation of the returns.
  • Conditional Value at Risk (CVaR) measures the scale of the expected loss once the specific Value at Risk (VaR) breakpoint has been breached, i.e., it calculates the average tail loss by taking a weighted average between the value at risk and losses exceeding the value at risk.
  • Beta is a measure of systematic risk and measures the volatility of a particular investment relative to the market or its benchmark. Alpha measures the active return of the investment compared to the market benchmark return. R-squared is the percentage of a portfolio's movements that can be explained by movements in the selected benchmark index.
  • Active return is the investment return minus the return of its benchmark. For periods longer than 12 months this is displayed as annualized value, i.e., annualized investment return minus annualized benchmark return.
  • Tracking error, also known as active risk, is the standard deviation of active return. This is displayed as annualized value based on the standard deviation of monthly active returns.
  • Information ratio is the active return divided by the tracking error. It measures whether the investment outperformed its benchmark consistently.
  • Gain/Loss ratio is a measure of downside risk, and it is calculated as the average positive return in up periods divided by the average negative return in down periods.
  • Upside Capture Ratio measures how well the fund performed relative to the benchmark when the market was up, and Downside Capture Ratio measures how well the fund performed relative to the benchmark when the market was down. An upside capture ratio greater than 100 would indicate that the fund outperformed its benchmark when the market was up, and a downside capture ratio below 100 would indicate that the fund lost less than its benchmark when the market was down. To calculate upside capture ratio a new series from the portfolio returns is constructed by dropping all time periods where the benchmark return is less than equal to zero. The up capture is then the quotient of the annualized return of the resulting manager series, divided by the annualized return of the resulting benchmark series. The downside capture ratio is calculated analogously.
  • All risk measures for the portfolio and portfolio assets are calculated based on monthly returns.
  • The results are based on combining user provided forecast model parameters with historical monthly return statistics of the portfolio assets.
Efficient Frontier Assets
#AssetExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1Vanguard Total Stock Market ETF (VTI)5.50%14.60%0.1790.00%100.00%
2Vanguard Total International Stock ETF (VXUS)5.70%14.56%0.1930.00%100.00%
3Vanguard Total Bond Market ETF (BND)1.80%4.04%-0.2680.00%100.00%
4Vanguard Real Estate ETF (VNQ)5.00%16.60%0.1280.00%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 ETFVTI1.000.860.280.71
Vanguard Total International Stock ETFVXUS0.861.000.280.62
Vanguard Total Bond Market ETFBND0.280.281.000.51
Vanguard Real Estate ETFVNQ0.710.620.511.00
Based on monthly returns from Jan 2012 to Sep 2022
Efficient Frontier Assets
#VTIVXUSBNDVNQExpected Return*Standard Deviation*Sharpe Ratio*
10.00%0.00%100.00%0.00%1.80%4.04%-0.268
20.98%0.08%98.94%0.00%1.84%4.04%-0.258
31.31%0.78%97.91%0.00%1.88%4.05%-0.248
41.63%1.48%96.89%0.00%1.92%4.06%-0.238
51.96%2.18%95.86%0.00%1.96%4.08%-0.227
62.29%2.88%94.83%0.00%2.00%4.10%-0.216
72.62%3.57%93.80%0.00%2.04%4.13%-0.205
82.95%4.27%92.78%0.00%2.08%4.16%-0.194
93.28%4.97%91.75%0.00%2.12%4.20%-0.183
103.61%5.67%90.72%0.00%2.15%4.24%-0.172
113.94%6.37%89.70%0.00%2.19%4.28%-0.161
124.27%7.06%88.67%0.00%2.23%4.33%-0.150
134.60%7.76%87.64%0.00%2.27%4.38%-0.140
144.93%8.46%86.62%0.00%2.31%4.44%-0.129
155.25%9.16%85.59%0.00%2.35%4.49%-0.118
165.58%9.85%84.56%0.00%2.39%4.56%-0.108
175.91%10.55%83.53%0.00%2.43%4.62%-0.098
186.24%11.25%82.51%0.00%2.47%4.69%-0.088
196.57%11.95%81.48%0.00%2.51%4.76%-0.079
206.90%12.65%80.45%0.00%2.55%4.84%-0.069
217.23%13.34%79.43%0.00%2.59%4.92%-0.060
227.56%14.04%78.40%0.00%2.63%5.00%-0.051
237.89%14.74%77.37%0.00%2.67%5.08%-0.043
248.22%15.44%76.35%0.00%2.71%5.17%-0.034
258.54%16.14%75.32%0.00%2.75%5.25%-0.026
268.87%16.83%74.29%0.00%2.78%5.34%-0.019
279.20%17.53%73.27%0.00%2.82%5.43%-0.011
289.53%18.23%72.24%0.00%2.86%5.53%-0.004
299.86%18.93%71.21%0.00%2.90%5.62%0.003
3010.19%19.63%70.18%0.00%2.94%5.72%0.010
3110.52%20.32%69.16%0.00%2.98%5.82%0.017
3210.85%21.02%68.13%0.00%3.02%5.92%0.023
3311.18%21.72%67.10%0.00%3.06%6.02%0.029
3411.51%22.42%66.08%0.00%3.10%6.13%0.035
3511.84%23.12%65.05%0.00%3.14%6.23%0.041
3612.16%23.81%64.02%0.00%3.18%6.34%0.047
3712.49%24.51%63.00%0.00%3.22%6.45%0.052
3812.82%25.21%61.97%0.00%3.26%6.56%0.057
3913.15%25.91%60.94%0.00%3.30%6.66%0.062
4013.48%26.60%59.91%0.00%3.34%6.78%0.067
4113.81%27.30%58.89%0.00%3.38%6.89%0.071
4214.14%28.00%57.86%0.00%3.42%7.00%0.076
4314.47%28.70%56.83%0.00%3.45%7.11%0.080
4414.80%29.40%55.81%0.00%3.49%7.23%0.084
4515.13%30.09%54.78%0.00%3.53%7.34%0.088
4615.46%30.79%53.75%0.00%3.57%7.46%0.092
4715.78%31.49%52.73%0.00%3.61%7.58%0.096
4816.11%32.19%51.70%0.00%3.65%7.70%0.100
4916.44%32.89%50.67%0.00%3.69%7.81%0.103
5016.77%33.58%49.64%0.00%3.73%7.93%0.107
5117.10%34.28%48.62%0.00%3.77%8.05%0.110
5217.43%34.98%47.59%0.00%3.81%8.17%0.113
5317.76%35.68%46.56%0.00%3.85%8.30%0.116
5418.09%36.38%45.54%0.00%3.89%8.42%0.119
5518.42%37.07%44.51%0.00%3.93%8.54%0.122
5618.75%37.77%43.48%0.00%3.97%8.66%0.125
5719.07%38.47%42.46%0.00%4.01%8.78%0.128
5819.40%39.17%41.43%0.00%4.05%8.91%0.130
5919.73%39.86%40.40%0.00%4.08%9.03%0.133
6019.90%40.54%39.34%0.22%4.12%9.16%0.135
6120.06%41.21%38.28%0.45%4.16%9.28%0.138
6220.22%41.88%37.23%0.68%4.20%9.41%0.140
6320.38%42.55%36.17%0.91%4.24%9.53%0.143
6420.54%43.22%35.11%1.14%4.28%9.66%0.145
6520.69%43.89%34.05%1.37%4.32%9.78%0.147
6620.85%44.56%32.99%1.60%4.36%9.91%0.149
6721.01%45.23%31.93%1.83%4.40%10.04%0.151
6821.17%45.90%30.87%2.05%4.44%10.16%0.153
6921.33%46.58%29.81%2.28%4.48%10.29%0.155
7021.49%47.25%28.75%2.51%4.52%10.42%0.157
7121.65%47.92%27.69%2.74%4.56%10.54%0.159
7221.81%48.59%26.63%2.97%4.60%10.67%0.161
7321.97%49.26%25.57%3.20%4.64%10.80%0.162
7422.13%49.93%24.51%3.43%4.68%10.93%0.164
7522.29%50.60%23.45%3.66%4.72%11.06%0.166
7622.45%51.27%22.39%3.89%4.75%11.18%0.167
7722.61%51.94%21.33%4.12%4.79%11.31%0.169
7822.77%52.61%20.28%4.34%4.83%11.44%0.170
7922.93%53.29%19.22%4.57%4.87%11.57%0.172
8023.08%53.96%18.16%4.80%4.91%11.70%0.173
8123.24%54.63%17.10%5.03%4.95%11.83%0.175
8223.40%55.30%16.04%5.26%4.99%11.96%0.176
8323.56%55.97%14.98%5.49%5.03%12.09%0.178
8423.72%56.64%13.92%5.72%5.07%12.22%0.179
8523.88%57.31%12.86%5.95%5.11%12.35%0.180
8624.04%57.98%11.80%6.18%5.15%12.48%0.181
8724.20%58.65%10.74%6.41%5.19%12.61%0.183
8824.36%59.32%9.68%6.64%5.23%12.74%0.184
8924.52%60.00%8.62%6.86%5.27%12.87%0.185
9024.68%60.67%7.56%7.09%5.31%13.00%0.186
9124.84%61.34%6.50%7.32%5.35%13.13%0.187
9225.00%62.01%5.44%7.55%5.38%13.26%0.189
9325.16%62.68%4.38%7.78%5.42%13.39%0.190
9425.32%63.35%3.33%8.01%5.46%13.52%0.191
9525.47%64.02%2.27%8.24%5.50%13.65%0.192
9625.63%64.69%1.21%8.47%5.54%13.79%0.193
9725.79%65.36%0.15%8.70%5.58%13.92%0.194
9825.33%70.65%0.00%4.02%5.62%14.06%0.195
9919.70%80.30%0.00%0.00%5.66%14.25%0.195
1000.01%99.99%0.00%0.00%5.70%14.56%0.193
*Annualized 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.