Portfolio Optimization

Portfolio Optimization Configuration

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Asset Groups
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Portfolio Optimization Results Save

Portfolio optimization results with the 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 Dec 2022 were used for non-user supplied parameters based on the selected time period and available data for the portfolio assets.

Provided Portfolio

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

Maximum Sharpe Ratio
Ticker Name Allocation
VTI Vanguard Total Stock Market ETF 0.01%
VXUS Vanguard Total International Stock ETF 99.99%
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Portfolio Summary

Performance Summary

Portfolio statistics
PortfolioExpected ReturnStandard DeviationSharpe Ratio
Provided Portfolio4.38%10.35%0.00
Maximum Sharpe Ratio5.70%14.94%0.09
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 and Disclosures
  • 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

Efficient Frontier Assets
#AssetExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1Vanguard Total Stock Market ETF (VTI)5.50%14.79%0.0760.00%100.00%
2Vanguard Total International Stock ETF (VXUS)5.70%14.94%0.0890.00%100.00%
3Vanguard Total Bond Market ETF (BND)1.80%4.16%-0.6180.00%100.00%
4Vanguard Real Estate ETF (VNQ)5.00%16.60%0.0380.00%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 ETFVTI1.000.850.280.71
Vanguard Total International Stock ETFVXUS0.851.000.330.63
Vanguard Total Bond Market ETFBND0.280.331.000.51
Vanguard Real Estate ETFVNQ0.710.630.511.00
Based on monthly returns from Jan 2012 to Dec 2022

Efficient Frontiers

Efficient Frontier Portfolios

Efficient Frontier Assets
#VTIVXUSBNDVNQExpected Return *Standard Deviation *Sharpe Ratio *
10.11%0.00%99.89%0.00%1.80%4.16%-0.617
21.18%0.00%98.82%0.00%1.84%4.17%-0.607
32.24%0.00%97.76%0.00%1.88%4.18%-0.596
43.31%0.00%96.69%0.00%1.92%4.19%-0.585
54.37%0.00%95.63%0.00%1.96%4.21%-0.573
65.43%0.00%94.57%0.00%2.00%4.23%-0.560
76.50%0.00%93.50%0.00%2.04%4.26%-0.547
87.34%0.21%92.45%0.00%2.08%4.30%-0.533
97.68%0.89%91.43%0.00%2.12%4.34%-0.520
108.03%1.57%90.40%0.00%2.16%4.38%-0.505
118.38%2.25%89.37%0.00%2.20%4.43%-0.491
128.73%2.93%88.34%0.00%2.24%4.48%-0.477
139.07%3.61%87.32%0.00%2.28%4.53%-0.462
149.42%4.29%86.29%0.00%2.32%4.59%-0.448
159.77%4.97%85.26%0.00%2.36%4.65%-0.433
1610.12%5.64%84.24%0.00%2.39%4.72%-0.419
1710.47%6.32%83.21%0.00%2.43%4.79%-0.405
1810.81%7.00%82.18%0.00%2.47%4.86%-0.391
1911.16%7.68%81.16%0.00%2.51%4.93%-0.377
2011.51%8.36%80.13%0.00%2.55%5.01%-0.363
2111.86%9.04%79.10%0.00%2.59%5.09%-0.350
2212.20%9.72%78.08%0.00%2.63%5.17%-0.337
2312.55%10.40%77.05%0.00%2.67%5.26%-0.324
2412.90%11.08%76.02%0.00%2.71%5.34%-0.311
2513.25%11.76%75.00%0.00%2.75%5.43%-0.299
2613.60%12.44%73.97%0.00%2.79%5.52%-0.287
2713.94%13.11%72.94%0.00%2.83%5.62%-0.275
2814.29%13.79%71.92%0.00%2.87%5.71%-0.263
2914.64%14.47%70.89%0.00%2.91%5.81%-0.252
3014.99%15.15%69.86%0.00%2.95%5.91%-0.241
3115.33%15.83%68.83%0.00%2.98%6.01%-0.231
3215.68%16.51%67.81%0.00%3.02%6.11%-0.220
3316.03%17.19%66.78%0.00%3.06%6.22%-0.210
3416.38%17.87%65.75%0.00%3.10%6.32%-0.201
3516.73%18.55%64.73%0.00%3.14%6.43%-0.191
3617.07%19.23%63.70%0.00%3.18%6.53%-0.182
3717.42%19.91%62.67%0.00%3.22%6.64%-0.173
3817.77%20.58%61.65%0.00%3.26%6.75%-0.165
3918.12%21.26%60.62%0.00%3.30%6.86%-0.156
4018.46%21.94%59.59%0.00%3.34%6.98%-0.148
4118.81%22.62%58.57%0.00%3.38%7.09%-0.140
4219.16%23.30%57.54%0.00%3.42%7.20%-0.132
4319.51%23.98%56.51%0.00%3.46%7.32%-0.125
4419.86%24.66%55.49%0.00%3.50%7.43%-0.118
4520.20%25.34%54.46%0.00%3.54%7.55%-0.111
4620.55%26.02%53.43%0.00%3.58%7.67%-0.104
4720.90%26.70%52.41%0.00%3.61%7.79%-0.097
4821.25%27.37%51.38%0.00%3.65%7.90%-0.091
4921.59%28.05%50.35%0.00%3.69%8.02%-0.085
5021.94%28.73%49.32%0.00%3.73%8.14%-0.078
5122.29%29.41%48.30%0.00%3.77%8.26%-0.073
5222.64%30.09%47.27%0.00%3.81%8.39%-0.067
5322.99%30.77%46.24%0.00%3.85%8.51%-0.061
5423.33%31.45%45.22%0.00%3.89%8.63%-0.056
5523.68%32.13%44.19%0.00%3.93%8.75%-0.051
5624.03%32.81%43.16%0.00%3.97%8.88%-0.045
5724.38%33.49%42.14%0.00%4.01%9.00%-0.040
5824.72%34.17%41.11%0.00%4.05%9.12%-0.036
5924.94%34.82%40.06%0.18%4.09%9.25%-0.031
6025.12%35.47%39.00%0.42%4.13%9.37%-0.026
6125.30%36.11%37.94%0.65%4.17%9.50%-0.022
6225.47%36.76%36.88%0.89%4.20%9.63%-0.017
6325.65%37.41%35.82%1.12%4.24%9.75%-0.013
6425.83%38.05%34.76%1.36%4.28%9.88%-0.009
6526.01%38.70%33.69%1.60%4.32%10.01%-0.005
6626.18%39.35%32.63%1.83%4.36%10.13%-0.001
6726.36%39.99%31.57%2.07%4.40%10.26%0.003
6826.54%40.64%30.51%2.30%4.44%10.39%0.007
6926.72%41.29%29.45%2.54%4.48%10.51%0.010
7026.90%41.94%28.39%2.78%4.52%10.64%0.014
7127.07%42.58%27.33%3.01%4.56%10.77%0.017
7227.25%43.23%26.27%3.25%4.60%10.90%0.021
7327.43%43.88%25.21%3.48%4.64%11.03%0.024
7427.61%44.52%24.15%3.72%4.68%11.16%0.027
7527.78%45.17%23.09%3.96%4.72%11.29%0.031
7627.96%45.82%22.03%4.19%4.76%11.42%0.034
7728.14%46.46%20.97%4.43%4.79%11.54%0.037
7828.32%47.11%19.91%4.66%4.83%11.67%0.040
7928.49%47.76%18.85%4.90%4.87%11.80%0.043
8028.67%48.40%17.79%5.14%4.91%11.93%0.045
8128.85%49.05%16.73%5.37%4.95%12.06%0.048
8229.03%49.70%15.67%5.61%4.99%12.19%0.051
8329.20%50.35%14.61%5.84%5.03%12.32%0.053
8429.38%50.99%13.55%6.08%5.07%12.46%0.056
8529.56%51.64%12.49%6.32%5.11%12.59%0.059
8629.74%52.29%11.43%6.55%5.15%12.72%0.061
8729.92%52.93%10.36%6.79%5.19%12.85%0.064
8830.09%53.58%9.30%7.02%5.23%12.98%0.066
8930.27%54.23%8.24%7.26%5.27%13.11%0.068
9030.45%54.87%7.18%7.49%5.31%13.24%0.071
9130.63%55.52%6.12%7.73%5.35%13.37%0.073
9230.80%56.17%5.06%7.97%5.39%13.50%0.075
9330.98%56.81%4.00%8.20%5.42%13.64%0.077
9431.16%57.46%2.94%8.44%5.46%13.77%0.079
9531.34%58.11%1.88%8.67%5.50%13.90%0.081
9631.51%58.75%0.82%8.91%5.54%14.03%0.083
9731.67%60.51%0.00%7.82%5.58%14.17%0.085
9831.74%66.09%0.00%2.18%5.62%14.33%0.087
9919.68%80.32%0.00%0.00%5.66%14.55%0.089
1000.01%99.99%0.00%0.00%5.70%14.94%0.089
*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.