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Portfolio Optimization

Portfolio Optimization Overview

This portfolio optimizer tool supports the following portfolio optimization strategies:

  • Mean Variance Optimization – Find the optimal risk adjusted portfolio that lies on the efficient frontier
  • Conditional Value-at-Risk – Optimize the portfolio to minimize the expected tail loss
  • Risk Parity – Find the portfolio that equalizes the risk contribution of portfolio assets
  • Tracking Error – Find the portfolio that minimizes the tracking error against the selected benchmark
  • Information Ratio – Find the portfolio that maximizes the information ratio against the selected benchmark
  • Kelly Criterion – Finds the portfolio with the maximum expected geometric growth rate
  • Sortino Ratio – Find the portfolio that maximizes the Sortino ratio for the given minimum acceptable return
  • Omega Ratio – Find the portfolio that maximizes the Omega ratio for the given minimum acceptable return
  • Maximum Drawdown – Find the portfolio with the minimum worst case drawdown with optional minimum acceptable return

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.

Portfolio Optimization Configuration
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Portfolio Optimization Results (Jan 2023 - Dec 2024) Save

Portfolio optimization results with the goal to maximize Sharpe ratio. The possible range of expected annual portfolio returns for the given period is 4.84% to 18.51%. Refer to the efficient frontier section for additional details.

Provided Portfolio

Ticker Name Allocation
BNDW Vanguard Total World Bond ETF 40.00%
REET iShares Global REIT ETF 5.00%
VT Vanguard Total World Stock ETF 55.00%

Maximum Sharpe Ratio

Ticker Name Allocation
VT Vanguard Total World Stock ETF 100.00%

Performance Summary

MetricProvided PortfolioMaximum Sharpe Ratio
Start Balance$10,000$10,000
End Balance$12,706$14,215
Annualized Return (CAGR)12.72%19.23%
Expected Return12.51%18.51%
Standard Deviation10.07%13.02%
Best Year15.45%22.02%
Worst Year10.05%16.49%
Maximum Drawdown -7.30% -9.69%
Sharpe Ratio (ex-ante)0.741.03
Sharpe Ratio (ex-post)0.741.03
Sortino Ratio1.291.97
Results based on historical returns. Expected return is the annualized monthly arithmetic mean return.

Portfolio Growth

   

Annual Returns

Trailing Returns

NameTotal ReturnAnnualized Return
3 MonthYear To Date1 yearFull
Provided Portfolio-1.68%10.05%10.05%12.72%
Maximum Sharpe Ratio-1.13%16.49%16.49%19.23%
Trailing returns are as of last calendar month ending December 2024

Efficient Frontier Assets

#AssetExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1Vanguard Total World Bond ETF4.84%6.03%-0.0360.00%100.00%
2iShares Global REIT ETF7.90%18.77%0.1510.00%100.00%
3Vanguard Total World Stock ETF18.51%13.02%1.0340.00%100.00%
Results based on historical returns. Expected return is the annualized monthly arithmetic mean return. Ex-ante Sharpe Ratio calculated using U.S. 3-Month Treasury Bill Rate returns as the risk-free rate.

Asset Correlations

NameTickerBNDWREETVT
Vanguard Total World Bond ETFBNDW1.000.850.80
iShares Global REIT ETFREET0.851.000.90
Vanguard Total World Stock ETFVT0.800.901.00
Based on monthly returns from Jan 2023 to Dec 2024

Efficient Frontier

Efficient Frontier Portfolios

#Vanguard Total World Bond ETFiShares Global REIT ETFVanguard Total World Stock ETFExpected Return *Standard Deviation *Sharpe Ratio *
1100.00%0.00%0.00%4.84%6.03%-0.036
298.99%0.00%1.01%4.98%6.07%-0.013
397.98%0.00%2.02%5.12%6.12%0.010
496.97%0.00%3.03%5.26%6.16%0.032
595.96%0.00%4.04%5.39%6.21%0.054
694.95%0.00%5.05%5.53%6.26%0.076
793.94%0.00%6.06%5.67%6.31%0.097
892.93%0.00%7.07%5.81%6.36%0.118
991.92%0.00%8.08%5.95%6.41%0.138
1090.91%0.00%9.09%6.08%6.46%0.159
1189.90%0.00%10.10%6.22%6.51%0.179
1288.89%0.00%11.11%6.36%6.57%0.198
1387.88%0.00%12.12%6.50%6.62%0.217
1486.87%0.00%13.13%6.64%6.68%0.236
1585.86%0.00%14.14%6.78%6.73%0.255
1684.85%0.00%15.15%6.91%6.79%0.273
1783.84%0.00%16.16%7.05%6.85%0.291
1882.83%0.00%17.17%7.19%6.91%0.308
1981.82%0.00%18.18%7.33%6.97%0.326
2080.81%0.00%19.19%7.47%7.03%0.343
2179.80%0.00%20.20%7.60%7.09%0.359
2278.79%0.00%21.21%7.74%7.15%0.375
2377.78%0.00%22.22%7.88%7.21%0.391
2476.77%0.00%23.23%8.02%7.27%0.407
2575.76%0.00%24.24%8.16%7.33%0.422
2674.75%0.00%25.25%8.29%7.40%0.437
2773.74%0.00%26.26%8.43%7.46%0.452
2872.73%0.00%27.27%8.57%7.52%0.467
2971.72%0.00%28.28%8.71%7.59%0.481
3070.71%0.00%29.29%8.85%7.66%0.495
3169.70%0.00%30.30%8.98%7.72%0.508
3268.69%0.00%31.31%9.12%7.79%0.522
3367.68%0.00%32.32%9.26%7.85%0.535
3466.67%0.00%33.33%9.40%7.92%0.548
3565.66%0.00%34.34%9.54%7.99%0.560
3664.65%0.00%35.35%9.68%8.06%0.573
3763.64%0.00%36.36%9.81%8.13%0.585
3862.63%0.00%37.37%9.95%8.20%0.597
3961.62%0.00%38.38%10.09%8.27%0.608
4060.61%0.00%39.39%10.23%8.34%0.620
4159.60%0.00%40.40%10.37%8.41%0.631
4258.59%0.00%41.41%10.50%8.48%0.642
4357.58%0.00%42.42%10.64%8.55%0.653
4456.57%0.00%43.43%10.78%8.62%0.664
4555.56%0.00%44.44%10.92%8.69%0.674
4654.55%0.00%45.45%11.06%8.77%0.684
4753.54%0.00%46.46%11.19%8.84%0.694
4852.53%0.00%47.47%11.33%8.91%0.704
4951.52%0.00%48.48%11.47%8.98%0.714
5050.51%0.00%49.49%11.61%9.06%0.723
5149.49%0.00%50.51%11.75%9.13%0.732
5248.48%0.00%51.52%11.88%9.21%0.741
5347.47%0.00%52.53%12.02%9.28%0.750
5446.46%0.00%53.54%12.16%9.36%0.759
5545.45%0.00%54.55%12.30%9.43%0.768
5644.44%0.00%55.56%12.44%9.51%0.776
5743.43%0.00%56.57%12.58%9.58%0.784
5842.42%0.00%57.58%12.71%9.66%0.793
5941.41%0.00%58.59%12.85%9.73%0.801
6040.40%0.00%59.60%12.99%9.81%0.808
6139.39%0.00%60.61%13.13%9.89%0.816
6238.38%0.00%61.62%13.27%9.96%0.824
6337.37%0.00%62.63%13.40%10.04%0.831
6436.36%0.00%63.64%13.54%10.12%0.838
6535.35%0.00%64.65%13.68%10.20%0.846
6634.34%0.00%65.66%13.82%10.27%0.853
6733.33%0.00%66.67%13.96%10.35%0.859
6832.32%0.00%67.68%14.09%10.43%0.866
6931.31%0.00%68.69%14.23%10.51%0.873
7030.30%0.00%69.70%14.37%10.59%0.880
7129.29%0.00%70.71%14.51%10.67%0.886
7228.28%0.00%71.72%14.65%10.74%0.892
7327.27%0.00%72.73%14.78%10.82%0.899
7426.26%0.00%73.74%14.92%10.90%0.905
7525.25%0.00%74.75%15.06%10.98%0.911
7624.24%0.00%75.76%15.20%11.06%0.917
7723.23%0.00%76.77%15.34%11.14%0.922
7822.22%0.00%77.78%15.47%11.22%0.928
7921.21%0.00%78.79%15.61%11.30%0.934
8020.20%0.00%79.80%15.75%11.38%0.939
8119.19%0.00%80.81%15.89%11.46%0.945
8218.18%0.00%81.82%16.03%11.54%0.950
8317.17%0.00%82.83%16.17%11.62%0.955
8416.16%0.00%83.84%16.30%11.70%0.961
8515.15%0.00%84.85%16.44%11.79%0.966
8614.14%0.00%85.86%16.58%11.87%0.971
8713.13%0.00%86.87%16.72%11.95%0.976
8812.12%0.00%87.88%16.86%12.03%0.981
8911.11%0.00%88.89%16.99%12.11%0.985
9010.10%0.00%89.90%17.13%12.19%0.990
919.09%0.00%90.91%17.27%12.28%0.995
928.08%0.00%91.92%17.41%12.36%0.999
937.07%0.00%92.93%17.55%12.44%1.004
946.06%0.00%93.94%17.68%12.52%1.008
955.05%0.00%94.95%17.82%12.60%1.013
964.04%0.00%95.96%17.96%12.69%1.017
973.03%0.00%96.97%18.10%12.77%1.021
982.02%0.00%97.98%18.24%12.85%1.025
991.01%0.00%98.99%18.37%12.93%1.029
1000.00%0.00%100.00%18.51%13.02%1.034
*Annualized ex-ante values shown for portfolio return and volatility. Ex-ante Sharpe Ratio calculated using historical U.S. 3-Month Treasury Bill Rate returns as the risk-free rate.

Risk and Return Metrics

MetricProvided PortfolioMaximum Sharpe Ratio
Arithmetic Mean (monthly)1.04%1.54%
Arithmetic Mean (annualized)13.26%20.17%
Geometric Mean (monthly)1.00%1.48%
Geometric Mean (annualized)12.72%19.23%
Standard Deviation (monthly)2.91%3.76%
Standard Deviation (annualized)10.07%13.02%
Downside Deviation (monthly)1.44%1.74%
Maximum Drawdown-7.30%-9.69%
Benchmark Correlation0.950.98
Beta(*)0.720.96
Alpha (annualized)-4.18%-3.59%
R290.74%95.19%
Sharpe Ratio0.741.03
Sortino Ratio1.291.97
Treynor Ratio (%)10.3414.09
Modigliani–Modigliani Measure14.91%18.80%
Active Return-12.02%-5.51%
Tracking Error4.81%2.92%
Information Ratio-2.50-1.89
Skewness0.090.08
Excess Kurtosis-0.70-0.89
Historical Value-at-Risk (5%)3.03%3.52%
Analytical Value-at-Risk (5%)3.64%4.64%
Conditional Value-at-Risk (5%)3.28%3.92%
Upside Capture Ratio (%)60.0886.69
Downside Capture Ratio (%)90.55108.64
Safe Withdrawal Rate57.74%62.69%
Perpetual Withdrawal Rate8.52%13.51%
Positive Periods15 out of 24 (62.50%)15 out of 24 (62.50%)
Gain/Loss Ratio1.371.39
* U.S. Stock Market is used as the benchmark for calculations. Value-at-risk metrics are monthly values.

Annual Returns

YearInflationProvided PortfolioMaximum Sharpe RatioVanguard Total World Bond ETF (BNDW)iShares Global REIT ETF (REET)Vanguard Total World Stock ETF (VT)
ReturnBalanceReturnBalance
20242.89%10.05%$12,70616.49%$14,2152.41%2.65%16.49%
20233.35%15.45%$11,54522.02%$12,2027.18%10.31%22.02%

Monthly Returns

YearMonthProvided PortfolioMaximum Sharpe RatioVanguard Total World Bond ETF (BNDW)iShares Global REIT ETF (REET)Vanguard Total World Stock ETF (VT)
ReturnBalanceReturnBalance
202412-2.47%$12,706-2.94%$14,215-1.21%-7.36%-2.94%
2024112.98%$13,0284.14%$14,6451.36%3.14%4.14%
202410-2.10%$12,651-2.18%$14,063-1.70%-4.42%-2.18%
202491.90%$12,9222.20%$14,3761.32%3.31%2.20%
202481.98%$12,6812.33%$14,0671.05%5.54%2.33%
202472.28%$12,4351.98%$13,7462.20%6.28%1.98%
202461.24%$12,1571.59%$13,4800.79%1.01%1.59%
202453.15%$12,0094.60%$13,2690.99%4.39%4.60%
20244-3.06%$11,643-3.58%$12,686-1.90%-6.59%-3.58%
202432.28%$12,0103.19%$13,1570.98%2.65%3.19%
202422.12%$11,7434.49%$12,750-0.90%0.22%4.49%
20241-0.40%$11,4990.00%$12,202-0.48%-4.26%0.00%
2023124.69%$11,5455.15%$12,2023.46%9.38%5.15%
2023117.06%$11,0289.01%$11,6043.93%10.60%9.01%
202310-2.18%$10,301-2.92%$10,645-0.86%-4.63%-2.92%
20239-3.49%$10,531-4.25%$10,965-2.08%-6.38%-4.25%
20238-1.81%$10,912-2.84%$11,452-0.16%-3.54%-2.84%
202372.15%$11,1133.72%$11,788-0.17%3.35%3.72%
202363.29%$10,8795.82%$11,365-0.16%3.22%5.82%
20235-1.05%$10,532-1.21%$10,740-0.48%-3.91%-1.21%
202341.03%$10,6441.42%$10,8720.43%1.57%1.42%
202332.49%$10,5362.85%$10,7192.62%-2.52%2.85%
20232-2.84%$10,280-3.18%$10,422-2.14%-4.71%-3.18%
202315.81%$10,5817.65%$10,7652.82%9.47%7.65%

Drawdowns

Historical Market Stress Periods

Drawdowns for Provided Portfolio

RankStartEndLengthRecovery ByRecovery TimeUnderwater PeriodDrawdown
1Aug 2023Oct 20233 monthsDec 20232 months5 months-7.30%
2Apr 2024Apr 20241 monthJun 20242 months3 months-3.06%
3Feb 2023Feb 20231 monthApr 20232 months3 months-2.84%
4Dec 2024Dec 20241 month-2.47%
5Oct 2024Oct 20241 monthNov 20241 month2 months-2.10%
6May 2023May 20231 monthJun 20231 month2 months-1.05%
7Jan 2024Jan 20241 monthFeb 20241 month2 months-0.40%

Drawdowns for Maximum Sharpe Ratio

RankStartEndLengthRecovery ByRecovery TimeUnderwater PeriodDrawdown
1Aug 2023Oct 20233 monthsDec 20232 months5 months-9.69%
2Apr 2024Apr 20241 monthMay 20241 month2 months-3.58%
3Feb 2023Feb 20231 monthApr 20232 months3 months-3.18%
4Dec 2024Dec 20241 month-2.94%
5Oct 2024Oct 20241 monthNov 20241 month2 months-2.18%
6May 2023May 20231 monthJun 20231 month2 months-1.21%

Portfolio Assets

TickerNameCAGRStdevBest YearWorst YearMax DrawdownSharpe RatioSortino Ratio
BNDWVanguard Total World Bond ETF4.77%6.03%7.18%2.41%-3.87%-0.04-0.05
REETiShares Global REIT ETF6.41%18.77%10.31%2.65%-16.70%0.150.23
VTVanguard Total World Stock ETF19.23%13.02%22.02%16.49%-9.69%1.031.97

Portfolio Asset Performance

NameTotal ReturnExpense Ratio
3 MonthYear To Date1 yearNetGross
Vanguard Total World Bond ETF-1.57%2.41%2.41%0.05%0.05%
iShares Global REIT ETF-8.68%2.65%2.65%0.14%0.14%
Vanguard Total World Stock ETF-1.13%16.49%16.49%0.06%0.06%
Trailing returns as of last calendar month ending December 2024

Monthly Correlations

TickerNameBNDWREETVTProvided PortfolioMaximum Sharpe Ratio
BNDWVanguard Total World Bond ETF1.000.850.800.890.80
REETiShares Global REIT ETF0.851.000.900.930.90
VTVanguard Total World Stock ETF0.800.901.000.991.00

Portfolio Return Decomposition

TickerNameProvided PortfolioMaximum Sharpe Ratio
BNDWVanguard Total World Bond ETF$412
REETiShares Global REIT ETF$80.79
VTVanguard Total World Stock ETF$2,213$4,215
Return attribution decomposes portfolio gains into its constituent parts and identifies the contribution to returns by each of the assets.

Portfolio Risk Decomposition

TickerNameProvided PortfolioMaximum Sharpe Ratio
BNDWVanguard Total World Bond ETF21.20%
REETiShares Global REIT ETF8.71%
VTVanguard Total World Stock ETF70.09%100.00%
Risk attribution decomposes portfolio risk into its constituent parts and identifies the contribution to overall volatility by each of the assets.

Annual Asset Returns

  • 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. Other investments not considered may have characteristics similar or superior to those being analyzed.
  • 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.
  • 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.
  • Risk-free returns are calculated based on U.S. 3-Month Treasury Bill Rate.
  • Inflation is calculated based on U.S. Consumer Price Index.
  • 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. For example, if the 95% confidence one-month VaR is 3%, there is 95% confidence that over the next month the portfolio will not lose more than 3%. 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.
  • Invesco QQQ is a paid sponsor of the SRL Analytics Tool, Portfolio Visualizer. The model portfolios are for illustrative purposes only and do not constitute a recommendation or suitability for any investor. Inveso is not affiliated with SRL Global.
  • The optimization results assume monthly rebalancing of portfolio assets to match the specified allocation.