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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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 1.93% to 4.99%. Refer to the efficient frontier section for additional details. Historical values from Jan 2012 to Apr 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 7.50%
VXUS Vanguard Total International Stock ETF 9.27%
BND Vanguard Total Bond Market ETF 77.71%
VNQ Vanguard Real Estate ETF 5.52%
Save portfolio »

Portfolio Summary

Portfolio statistics
PortfolioExpected ReturnStandard DeviationSharpe Ratio
Provided Portfolio4.37%9.54%0.40
Maximum Sharpe Ratio2.61%4.59%0.46
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.
  • 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%13.92%0.3490.00%100.00%
2Vanguard Total International Stock ETF (VXUS)5.70%14.13%0.3570.00%100.00%
3Vanguard Total Bond Market ETF (BND)1.80%3.67%0.3470.00%100.00%
4Vanguard Real Estate ETF (VNQ)5.00%15.76%0.2780.00%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 ETFVTI1.000.850.160.67
Vanguard Total International Stock ETFVXUS0.851.000.180.59
Vanguard Total Bond Market ETFBND0.160.181.000.43
Vanguard Real Estate ETFVNQ0.670.590.431.00
Based on monthly returns from Jan 2012 to Apr 2022
Efficient Frontier Assets
#VTIVXUSBNDVNQExpected Return*Standard Deviation*Sharpe Ratio*
12.48%0.92%96.59%0.00%1.93%3.66%0.383
22.93%1.29%95.70%0.08%1.96%3.66%0.391
33.27%1.64%94.88%0.21%1.99%3.68%0.397
43.54%2.01%94.08%0.37%2.02%3.69%0.403
53.74%2.39%93.31%0.56%2.05%3.71%0.408
63.95%2.78%92.50%0.77%2.07%3.74%0.413
74.17%3.17%91.68%0.98%2.10%3.76%0.418
84.39%3.57%90.83%1.21%2.14%3.79%0.423
94.60%3.97%89.98%1.45%2.17%3.83%0.427
104.81%4.37%89.12%1.70%2.20%3.87%0.431
115.02%4.76%88.26%1.96%2.23%3.91%0.434
125.22%5.16%87.39%2.23%2.26%3.95%0.437
135.43%5.55%86.52%2.50%2.29%4.00%0.440
145.62%5.94%85.66%2.78%2.32%4.04%0.442
155.83%6.32%84.78%3.07%2.35%4.10%0.444
166.03%6.70%83.90%3.37%2.38%4.15%0.445
176.23%7.08%83.02%3.67%2.42%4.21%0.447
186.43%7.46%82.14%3.97%2.45%4.26%0.448
196.65%7.82%81.25%4.27%2.48%4.33%0.449
206.87%8.19%80.37%4.58%2.51%4.39%0.449
217.08%8.55%79.48%4.89%2.54%4.45%0.450
227.29%8.91%78.60%5.20%2.57%4.52%0.450
237.50%9.27%77.71%5.52%2.61%4.59%0.450
247.71%9.62%76.83%5.84%2.64%4.66%0.450
257.91%9.98%75.94%6.17%2.67%4.73%0.449
268.12%10.34%75.05%6.49%2.70%4.80%0.449
278.32%10.69%74.17%6.82%2.73%4.88%0.449
288.53%11.05%73.28%7.15%2.76%4.95%0.448
298.73%11.41%72.39%7.47%2.80%5.03%0.447
308.94%11.76%71.50%7.80%2.83%5.11%0.446
319.15%12.12%70.61%8.13%2.86%5.19%0.445
329.36%12.47%69.72%8.45%2.89%5.27%0.444
339.56%12.82%68.83%8.79%2.92%5.35%0.443
349.77%13.17%67.94%9.12%2.95%5.44%0.442
359.97%13.52%67.05%9.46%2.99%5.52%0.441
3610.18%13.87%66.16%9.80%3.02%5.61%0.440
3710.38%14.21%65.26%10.14%3.05%5.69%0.439
3810.59%14.56%64.37%10.48%3.08%5.78%0.437
3910.80%14.90%63.48%10.82%3.11%5.87%0.436
4011.00%15.25%62.59%11.16%3.15%5.96%0.435
4111.21%15.59%61.69%11.50%3.18%6.05%0.434
4211.42%15.94%60.80%11.84%3.21%6.14%0.432
4311.63%16.28%59.91%12.19%3.24%6.23%0.431
4411.84%16.62%59.01%12.53%3.27%6.32%0.430
4512.05%16.97%58.11%12.87%3.31%6.41%0.428
4612.26%17.31%57.22%13.21%3.34%6.50%0.427
4712.47%17.65%56.32%13.56%3.37%6.60%0.426
4812.68%18.00%55.42%13.90%3.40%6.69%0.424
4912.89%18.34%54.53%14.25%3.43%6.79%0.423
5013.10%18.68%53.63%14.59%3.47%6.88%0.422
5113.31%19.03%52.73%14.93%3.50%6.98%0.420
5213.52%19.37%51.83%15.28%3.53%7.08%0.419
5313.73%19.71%50.94%15.63%3.56%7.17%0.418
5413.93%20.05%50.04%15.97%3.59%7.27%0.416
5514.14%20.39%49.14%16.32%3.63%7.37%0.415
5614.35%20.74%48.24%16.67%3.66%7.47%0.414
5714.56%21.08%47.34%17.02%3.69%7.56%0.412
5814.77%21.42%46.44%17.37%3.72%7.66%0.411
5914.98%21.76%45.55%17.71%3.76%7.76%0.410
6015.19%22.10%44.65%18.06%3.79%7.86%0.409
6115.40%22.44%43.75%18.41%3.82%7.96%0.407
6215.61%22.79%42.85%18.76%3.85%8.06%0.406
6315.82%23.13%41.95%19.10%3.88%8.16%0.405
6416.03%23.47%41.05%19.45%3.92%8.26%0.404
6516.24%23.81%40.15%19.80%3.95%8.36%0.403
6616.45%24.15%39.25%20.15%3.98%8.47%0.402
6716.66%24.50%38.35%20.49%4.01%8.57%0.400
6816.86%24.84%37.46%20.84%4.05%8.67%0.399
6917.07%25.18%36.56%21.19%4.08%8.77%0.398
7017.28%25.52%35.66%21.54%4.11%8.87%0.397
7117.49%25.86%34.76%21.88%4.14%8.98%0.396
7217.70%26.20%33.86%22.23%4.18%9.08%0.395
7317.91%26.54%32.96%22.58%4.21%9.18%0.394
7418.12%26.89%32.06%22.93%4.24%9.28%0.393
7518.33%27.23%31.16%23.28%4.27%9.39%0.392
7618.54%27.57%30.26%23.62%4.30%9.49%0.391
7718.76%27.91%29.36%23.97%4.34%9.60%0.390
7818.97%28.25%28.47%24.32%4.37%9.70%0.389
7919.18%28.59%27.57%24.67%4.40%9.80%0.388
8019.39%28.92%26.67%25.02%4.43%9.91%0.387
8119.60%29.26%25.77%25.37%4.47%10.01%0.386
8219.81%29.60%24.87%25.71%4.50%10.12%0.385
8320.02%29.94%23.98%26.06%4.53%10.22%0.384
8420.23%30.28%23.08%26.41%4.56%10.33%0.384
8520.44%30.61%22.18%26.76%4.60%10.43%0.383
8620.65%30.95%21.28%27.11%4.63%10.54%0.382
8720.87%31.29%20.38%27.46%4.66%10.64%0.381
8821.06%31.62%19.49%27.82%4.69%10.75%0.380
8921.25%31.93%18.61%28.21%4.73%10.85%0.379
9021.43%32.22%17.74%28.61%4.76%10.95%0.378
9121.57%32.49%16.89%29.05%4.79%11.05%0.378
9221.69%32.73%16.05%29.52%4.82%11.15%0.377
9321.82%32.92%15.23%30.03%4.84%11.25%0.376
9421.94%33.08%14.42%30.57%4.87%11.35%0.375
9522.00%33.13%13.63%31.25%4.90%11.45%0.374
9621.84%33.16%12.88%32.12%4.92%11.54%0.373
9721.61%33.19%12.19%33.01%4.94%11.63%0.372
9821.48%33.07%11.56%33.89%4.96%11.71%0.371
9921.70%32.80%11.00%34.50%4.98%11.78%0.370
10022.00%32.50%10.50%35.00%5.00%11.85%0.369
*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.