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 (Jan 2012 - Sep 2022) Save

Portfolio optimization results for risk parity. The possible range of expected annual portfolio returns for the given period is 1.14% to 12.50%. Refer to the efficient frontier section for additional details.

Portfolio Allocations

Risk Parity
Ticker Name Allocation
VTI Vanguard Total Stock Market ETF 13.45%
VXUS Vanguard Total International Stock ETF 13.80%
VNQ Vanguard Real Estate ETF 11.66%
BND Vanguard Total Bond Market ETF 61.09%
Save portfolio »

Portfolio Performance Summary

Portfolio performance statistics
MetricRisk Parity
Start Balance$10,000
End Balance$15,062
Annualized Return (CAGR)3.88%
Expected Return4.04%
Standard Deviation6.72%
Best Year15.83%
Worst Year-19.32%
Maximum Drawdown -19.32%
Sharpe Ratio (ex-ante)0.51
Sharpe Ratio (ex-post)0.51
Sortino Ratio0.71
Stock Market Correlation0.86
Results based on historical returns. Expected return is the annualized monthly arithmetic mean return.
   

Trailing Returns

Trailing Returns
NameTotal ReturnAnnualized ReturnAnnualized Standard Deviation
3 MonthYear To Date1 year3 year5 year10 yearFull3 year5 year
Risk Parity-6.16%-19.32%-16.72%-0.96%1.57%3.40%3.88%10.07%8.49%
Trailing return and volatility are as of last full calendar month ending September 2022
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 annual results for 2022 are based on full calendar months from January to September.
  • The optimization results assume monthly rebalancing of portfolio assets to match the specified allocation.
Efficient Frontier Assets
#AssetExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1Vanguard Total Stock Market ETF (VTI)12.50%14.60%0.8140.00%100.00%
2Vanguard Total International Stock ETF (VXUS)5.02%14.56%0.3020.00%100.00%
3Vanguard Real Estate ETF (VNQ)8.31%16.60%0.4630.00%100.00%
4Vanguard Total Bond Market ETF (BND)1.14%4.04%0.1290.00%100.00%
Results based on historical returns. Expected return is the annualized monthly arithmetic mean return. Ex-ante Sharpe Ratio calculated using 3-month treasury bill returns as the risk-free rate.

Asset Correlations

Efficient Frontier Asset Correlations
NameTickerVTIVXUSVNQBND
Vanguard Total Stock Market ETFVTI1.000.860.710.28
Vanguard Total International Stock ETFVXUS0.861.000.620.28
Vanguard Real Estate ETFVNQ0.710.621.000.51
Vanguard Total Bond Market ETFBND0.280.280.511.00
Based on monthly returns from Jan 2012 to Sep 2022
Efficient Frontier Assets
#VTIVXUSVNQBNDExpected Return*Standard Deviation*Sharpe Ratio*
10.00%0.00%0.00%100.00%1.14%4.04%0.129
21.01%0.00%0.00%98.99%1.26%4.04%0.157
32.02%0.00%0.00%97.98%1.37%4.05%0.185
43.03%0.00%0.00%96.97%1.49%4.06%0.213
54.04%0.00%0.00%95.96%1.60%4.08%0.240
65.05%0.00%0.00%94.95%1.72%4.10%0.267
76.06%0.00%0.00%93.94%1.83%4.13%0.293
87.07%0.00%0.00%92.93%1.95%4.16%0.318
98.08%0.00%0.00%91.92%2.06%4.20%0.343
109.09%0.00%0.00%90.91%2.18%4.24%0.366
1110.10%0.00%0.00%89.90%2.29%4.28%0.389
1211.11%0.00%0.00%88.89%2.41%4.33%0.411
1312.12%0.00%0.00%87.88%2.52%4.39%0.433
1413.13%0.00%0.00%86.87%2.64%4.44%0.453
1514.14%0.00%0.00%85.86%2.75%4.50%0.472
1615.15%0.00%0.00%84.85%2.86%4.57%0.491
1716.16%0.00%0.00%83.84%2.98%4.64%0.508
1817.17%0.00%0.00%82.83%3.09%4.71%0.525
1918.18%0.00%0.00%81.82%3.21%4.78%0.541
2019.19%0.00%0.00%80.81%3.32%4.86%0.556
2120.20%0.00%0.00%79.80%3.44%4.94%0.570
2221.21%0.00%0.00%78.79%3.55%5.02%0.584
2322.22%0.00%0.00%77.78%3.67%5.11%0.596
2423.23%0.00%0.00%76.77%3.78%5.19%0.608
2524.24%0.00%0.00%75.76%3.90%5.28%0.620
2625.25%0.00%0.00%74.75%4.01%5.38%0.630
2726.26%0.00%0.00%73.74%4.13%5.47%0.640
2827.27%0.00%0.00%72.73%4.24%5.57%0.650
2928.28%0.00%0.00%71.72%4.36%5.67%0.659
3029.29%0.00%0.00%70.71%4.47%5.77%0.667
3130.30%0.00%0.00%69.70%4.59%5.87%0.675
3231.31%0.00%0.00%68.69%4.70%5.97%0.683
3332.32%0.00%0.00%67.68%4.82%6.08%0.690
3433.33%0.00%0.00%66.67%4.93%6.18%0.697
3534.34%0.00%0.00%65.66%5.05%6.29%0.703
3635.35%0.00%0.00%64.65%5.16%6.40%0.709
3736.36%0.00%0.00%63.64%5.27%6.51%0.714
3837.37%0.00%0.00%62.63%5.39%6.62%0.720
3938.38%0.00%0.00%61.62%5.50%6.73%0.725
4039.39%0.00%0.00%60.61%5.62%6.85%0.729
4140.40%0.00%0.00%59.60%5.73%6.96%0.734
4241.41%0.00%0.00%58.59%5.85%7.08%0.738
4342.42%0.00%0.00%57.58%5.96%7.20%0.742
4443.43%0.00%0.00%56.57%6.08%7.31%0.746
4544.44%0.00%0.00%55.56%6.19%7.43%0.749
4645.45%0.00%0.00%54.55%6.31%7.55%0.753
4746.46%0.00%0.00%53.54%6.42%7.67%0.756
4847.47%0.00%0.00%52.53%6.54%7.79%0.759
4948.48%0.00%0.00%51.52%6.65%7.91%0.762
5049.49%0.00%0.00%50.51%6.77%8.04%0.764
5150.51%0.00%0.00%49.49%6.88%8.16%0.767
5251.52%0.00%0.00%48.48%7.00%8.28%0.769
5352.53%0.00%0.00%47.47%7.11%8.41%0.772
5453.54%0.00%0.00%46.46%7.23%8.53%0.774
5554.55%0.00%0.00%45.45%7.34%8.65%0.776
5655.56%0.00%0.00%44.44%7.46%8.78%0.778
5756.57%0.00%0.00%43.43%7.57%8.91%0.780
5857.58%0.00%0.00%42.42%7.68%9.03%0.782
5958.59%0.00%0.00%41.41%7.80%9.16%0.783
6059.60%0.00%0.00%40.40%7.91%9.29%0.785
6160.61%0.00%0.00%39.39%8.03%9.41%0.787
6261.62%0.00%0.00%38.38%8.14%9.54%0.788
6362.63%0.00%0.00%37.37%8.26%9.67%0.789
6463.64%0.00%0.00%36.36%8.37%9.80%0.791
6564.65%0.00%0.00%35.35%8.49%9.93%0.792
6665.66%0.00%0.00%34.34%8.60%10.06%0.793
6766.67%0.00%0.00%33.33%8.72%10.19%0.794
6867.68%0.00%0.00%32.32%8.83%10.32%0.795
6968.69%0.00%0.00%31.31%8.95%10.45%0.796
7069.70%0.00%0.00%30.30%9.06%10.58%0.797
7170.71%0.00%0.00%29.29%9.18%10.71%0.798
7271.72%0.00%0.00%28.28%9.29%10.84%0.799
7372.73%0.00%0.00%27.27%9.41%10.97%0.800
7473.74%0.00%0.00%26.26%9.52%11.11%0.801
7574.75%0.00%0.00%25.25%9.64%11.24%0.802
7675.76%0.00%0.00%24.24%9.75%11.37%0.803
7776.77%0.00%0.00%23.23%9.86%11.50%0.803
7877.78%0.00%0.00%22.22%9.98%11.64%0.804
7978.79%0.00%0.00%21.21%10.09%11.77%0.805
8079.80%0.00%0.00%20.20%10.21%11.90%0.805
8180.81%0.00%0.00%19.19%10.32%12.04%0.806
8281.82%0.00%0.00%18.18%10.44%12.17%0.807
8382.83%0.00%0.00%17.17%10.55%12.30%0.807
8483.84%0.00%0.00%16.16%10.67%12.44%0.808
8584.85%0.00%0.00%15.15%10.78%12.57%0.808
8685.86%0.00%0.00%14.14%10.90%12.71%0.809
8786.87%0.00%0.00%13.13%11.01%12.84%0.809
8887.88%0.00%0.00%12.12%11.13%12.97%0.810
8988.89%0.00%0.00%11.11%11.24%13.11%0.810
9089.90%0.00%0.00%10.10%11.36%13.24%0.810
9190.91%0.00%0.00%9.09%11.47%13.38%0.811
9291.92%0.00%0.00%8.08%11.59%13.51%0.811
9392.93%0.00%0.00%7.07%11.70%13.65%0.812
9493.94%0.00%0.00%6.06%11.82%13.78%0.812
9594.95%0.00%0.00%5.05%11.93%13.92%0.812
9695.96%0.00%0.00%4.04%12.05%14.06%0.813
9796.97%0.00%0.00%3.03%12.16%14.19%0.813
9897.98%0.00%0.00%2.02%12.27%14.33%0.813
9998.99%0.00%0.00%1.01%12.39%14.46%0.814
100100.00%0.00%0.00%0.00%12.50%14.60%0.814
*Annualized ex-ante values shown for portfolio return and volatility. Ex-ante Sharpe Ratio calculated using historical 3-month treasury bill returns as the risk-free rate.
Annual returns for the configured portfolios
YearInflationRisk Parity ReturnRisk Parity BalanceVanguard Total Stock Market ETF (VTI)Vanguard Total International Stock ETF (VXUS)Vanguard Real Estate ETF (VNQ)Vanguard Total Bond Market ETF (BND)
20121.74%8.83%$10,88316.45%18.61%17.63%3.16%
20131.50%5.04%$11,43233.45%14.61%2.31%-2.10%
20140.76%7.94%$12,33912.54%-4.74%30.36%5.82%
20150.73%0.37%$12,3840.36%-4.19%2.42%0.56%
20162.07%5.11%$13,01812.83%4.81%8.60%2.52%
20172.11%9.09%$14,20021.21%27.45%4.91%3.57%
20181.91%-3.29%$13,733-5.21%-14.43%-6.02%-0.12%
20192.29%15.83%$15,90830.67%21.75%28.87%8.83%
20201.36%9.08%$17,35221.03%10.69%-4.68%7.71%
20217.04%7.58%$18,66825.67%9.00%40.52%-1.86%
20226.23%-19.32%$15,062-24.81%-26.65%-29.31%-14.51%
Annual return for 2022 is from 01/01/2022 to 09/30/2022
Monthly returns for the configured portfolios
YearMonthRisk Parity ReturnRisk Parity BalanceVanguard Total Stock Market ETF (VTI)Vanguard Total International Stock ETF (VXUS)Vanguard Real Estate ETF (VNQ)Vanguard Total Bond Market ETF (BND)
201212.83%$10,2835.07%7.33%6.38%0.63%
201221.09%$10,3944.22%4.56%-1.15%0.04%
201230.63%$10,4603.06%-0.54%5.19%-0.51%
201240.63%$10,526-0.64%-2.08%2.86%1.10%
20125-2.29%$10,286-6.23%-10.83%-4.51%0.93%
201262.05%$10,4974.05%5.97%5.52%0.07%
201271.15%$10,6170.88%0.31%2.00%1.23%
201280.82%$10,7042.70%2.60%-0.01%0.16%
201290.70%$10,7792.49%3.41%-1.86%0.18%
201210-0.30%$10,747-1.81%0.81%-0.91%-0.10%
2012110.52%$10,8030.77%2.06%-0.26%0.27%
2012120.74%$10,8831.29%4.88%3.72%-0.88%
201311.07%$11,0005.42%2.40%3.74%-0.69%
201320.48%$11,0541.28%-1.14%1.22%0.54%
201331.04%$11,1693.95%0.93%2.87%0.08%
201342.10%$11,4041.61%3.50%6.73%1.01%
20135-2.00%$11,1762.44%-3.30%-5.98%-1.93%
20136-1.92%$10,961-1.43%-3.57%-1.98%-1.65%
201371.75%$11,1525.75%4.62%0.90%0.38%
20138-2.01%$10,928-3.03%-1.95%-6.98%-0.86%
201392.65%$11,2173.90%7.51%3.49%1.11%
2013102.13%$11,4564.27%3.67%4.52%0.86%
201311-0.41%$11,4092.70%0.13%-5.25%-0.29%
2013120.20%$11,4322.73%1.52%0.10%-0.64%
201410.27%$11,463-3.17%-5.40%4.28%1.55%
201422.30%$11,7274.87%5.59%5.07%0.47%
201430.09%$11,7380.51%0.49%0.49%-0.17%
201441.06%$11,8620.06%1.26%3.29%0.80%
201451.47%$12,0362.10%1.93%2.40%1.05%
201460.80%$12,1322.62%1.89%1.13%0.08%
20147-0.67%$12,051-1.99%-1.73%0.08%-0.28%
201481.77%$12,2654.15%1.16%3.04%1.14%
20149-2.03%$12,016-2.10%-5.01%-6.04%-0.57%
2014101.96%$12,2512.75%-0.08%9.94%0.72%
2014111.00%$12,3752.48%-0.51%2.00%0.83%
201412-0.28%$12,339-0.04%-3.87%1.88%0.06%
201511.94%$12,578-2.74%0.27%6.85%2.40%
201520.34%$12,6215.74%5.78%-3.67%-1.31%
201530.18%$12,644-1.16%-1.49%1.74%0.55%
20154-0.13%$12,6270.62%4.81%-5.85%-0.32%
20155-0.29%$12,5901.30%-0.91%-0.30%-0.50%
20156-1.83%$12,360-1.67%-2.73%-4.68%-1.11%
201571.36%$12,5291.70%-0.56%5.77%0.88%
20158-2.73%$12,187-6.09%-7.43%-6.29%-0.25%
20159-0.07%$12,178-2.92%-3.85%3.05%0.81%
2015102.62%$12,4967.91%6.25%5.76%0.03%
201511-0.41%$12,4440.60%-1.32%-0.63%-0.39%
201512-0.48%$12,384-2.13%-2.17%1.82%-0.18%
20161-1.19%$12,237-5.72%-5.45%-3.44%1.20%
201620.14%$12,254-0.01%-2.46%-0.36%0.85%
201633.87%$12,7287.11%8.33%10.48%0.88%
201640.36%$12,7730.66%2.16%-2.35%0.40%
201650.36%$12,8191.73%-0.98%2.25%-0.01%
201661.95%$13,0690.27%-0.90%6.92%2.02%
201672.02%$13,3333.98%4.52%4.26%0.60%
20168-0.54%$13,2610.21%0.45%-3.76%-0.31%
201690.12%$13,2770.21%1.70%-1.82%0.11%
201610-1.80%$13,038-2.19%-1.91%-5.74%-0.94%
201611-1.44%$12,8504.49%-2.01%-1.68%-2.57%
2016121.30%$13,0181.98%1.96%4.82%0.33%
201710.90%$13,1351.86%4.08%-0.19%0.19%
201721.47%$13,3283.69%1.34%3.51%0.62%
201730.11%$13,3430.06%3.00%-2.42%-0.04%
201740.94%$13,4691.06%2.05%0.24%0.80%
201750.89%$13,5891.01%2.96%-0.72%0.71%
201760.51%$13,6580.95%0.63%2.23%0.05%
201771.11%$13,8091.88%3.37%1.24%0.40%
201780.59%$13,8900.15%0.54%-0.26%0.86%
201790.29%$13,9312.44%1.88%-0.11%-0.47%
2017100.43%$13,9912.17%2.03%-1.07%-0.03%
2017110.74%$14,0943.03%0.63%2.66%-0.11%
2017120.76%$14,2001.16%2.07%-0.14%0.54%
201810.24%$14,2355.23%5.72%-4.25%-1.24%
20182-2.76%$13,842-3.76%-5.24%-7.68%-1.04%
201830.56%$13,919-1.95%-0.38%3.88%0.69%
20184-0.30%$13,8770.45%0.46%0.82%-0.85%
201850.99%$14,0142.72%-1.64%3.68%0.68%
201860.26%$14,0510.70%-2.14%4.20%-0.04%
201870.85%$14,1703.32%2.55%0.60%-0.04%
201880.84%$14,2893.43%-2.40%2.58%0.67%
20189-0.59%$14,2050.20%0.21%-2.64%-0.55%
201810-3.04%$13,773-7.41%-8.56%-2.93%-0.86%
2018111.44%$13,9702.01%1.68%4.67%0.64%
201812-1.70%$13,733-9.16%-4.93%-7.96%1.87%
201914.27%$14,3198.54%7.67%11.85%1.11%
201920.73%$14,4243.56%1.63%0.70%-0.09%
201931.97%$14,7091.42%0.77%4.21%1.94%
201940.88%$14,8383.93%2.77%-0.16%-0.02%
20195-0.48%$14,766-6.45%-5.42%0.14%1.83%
201962.69%$15,1637.08%5.77%1.54%1.25%
201970.21%$15,1941.41%-1.99%1.70%0.15%
201981.55%$15,430-2.08%-2.17%3.75%2.77%
201990.49%$15,5061.78%2.73%1.93%-0.57%
2019101.08%$15,6732.11%3.43%1.13%0.31%
2019110.47%$15,7463.79%0.99%-1.30%-0.04%
2019121.02%$15,9082.80%4.38%0.76%-0.07%
202010.88%$16,047-0.06%-3.39%1.23%1.98%
20202-1.79%$15,760-8.00%-6.60%-7.03%1.67%
20203-7.25%$14,617-13.91%-16.26%-19.42%-1.43%
202045.55%$15,42813.13%7.60%8.96%2.76%
202052.03%$15,7415.40%5.01%1.73%0.67%
202061.58%$15,9902.29%4.24%2.41%0.67%
202072.66%$16,4155.74%4.15%3.64%1.45%
202081.04%$16,5867.10%4.43%0.44%-0.94%
20209-1.10%$16,404-3.54%-1.82%-2.68%-0.10%
202010-1.27%$16,196-1.95%-2.30%-3.00%-0.56%
2020115.20%$17,03711.80%12.62%9.67%1.21%
2020121.85%$17,3524.68%5.86%2.72%0.15%
20211-0.53%$17,260-0.33%0.25%0.04%-0.86%
202120.19%$17,2933.14%2.30%3.43%-1.55%
202130.57%$17,3923.65%1.87%5.15%-1.27%
202142.51%$17,8285.04%2.78%7.86%0.87%
202150.67%$17,9480.46%3.07%0.81%0.15%
202161.14%$18,1532.48%-0.34%2.64%0.90%
202171.31%$18,3901.74%-1.13%4.42%1.17%
202180.72%$18,5232.86%1.46%2.15%-0.19%
20219-2.36%$18,086-4.46%-3.45%-5.68%-1.01%
2021102.17%$18,4796.69%2.88%7.13%0.07%
202111-0.90%$18,312-1.46%-4.26%-2.11%0.20%
2021121.94%$18,6683.79%3.58%9.69%-0.31%
20221-3.45%$18,024-6.06%-2.83%-8.42%-2.06%
20222-1.83%$17,694-2.49%-2.85%-3.48%-1.14%
20223-0.55%$17,5973.26%-0.28%6.27%-2.75%
20224-5.03%$16,712-9.13%-6.49%-4.09%-3.97%
202250.14%$16,735-0.25%1.52%-4.69%0.83%
20226-4.09%$16,051-8.23%-7.96%-7.46%-1.66%
202274.22%$16,7289.35%3.64%8.62%2.38%
20228-3.53%$16,137-3.73%-4.49%-6.01%-2.80%
20229-6.66%$15,062-9.22%-9.91%-12.86%-4.18%
Portfolio return and risk metrics
MetricRisk Parity
Arithmetic Mean (monthly)0.34%
Arithmetic Mean (annualized)4.12%
Geometric Mean (monthly)0.32%
Geometric Mean (annualized)3.88%
Standard Deviation (monthly)1.94%
Standard Deviation (annualized)6.72%
Downside Deviation (monthly)1.36%
Maximum Drawdown-19.32%
Stock Market Correlation0.86
Beta(*)0.39
Alpha (annualized)-0.83%
R273.12%
Sharpe Ratio0.51
Sortino Ratio0.71
Treynor Ratio (%)8.69
Calmar Ratio-0.05
Active Return-8.04%
Tracking Error9.53%
Information Ratio-0.84
Skewness-0.88
Excess Kurtosis2.86
Historical Value-at-Risk (5%)-2.93%
Analytical Value-at-Risk (5%)-2.84%
Conditional Value-at-Risk (5%)-4.72%
Upside Capture Ratio (%)33.91
Downside Capture Ratio (%)40.95
Safe Withdrawal Rate12.55%
Perpetual Withdrawal Rate1.37%
Positive Periods89 out of 129 (68.99%)
Gain/Loss Ratio0.72
* US stock market is used as the benchmark for calculations. Value-at-risk metrics are based on monthly values.

Drawdowns for Historical Market Stress Periods

Drawdowns for Historical Market Stress Periods
Stress PeriodStartEndRisk Parity
COVID-19 StartJan 2020Mar 2020-8.91%

Drawdowns for Risk Parity

Drawdowns for Risk Parity (worst 10)
RankStartEndLengthRecovery ByRecovery TimeUnderwater PeriodDrawdown
1Jan 2022Sep 20229 months-19.32%
2Feb 2020Mar 20202 monthsJul 20204 months6 months-8.91%
3May 2013Aug 20134 monthsOct 20132 months6 months-4.17%
4Sep 2018Dec 20184 monthsJan 20191 month5 months-3.89%
5Apr 2015Sep 20156 monthsMar 20166 months1 year-3.69%
6Aug 2016Nov 20164 monthsMar 20174 months8 months-3.62%
7Feb 2018Feb 20181 monthAug 20186 months7 months-2.76%
8Sep 2021Sep 20211 monthDec 20213 months4 months-2.36%
9Sep 2020Oct 20202 monthsNov 20201 month3 months-2.36%
10May 2012May 20121 monthJul 20122 months3 months-2.29%
Worst 10 drawdowns included above

Portfolio Assets

Performance statistics for portfolio components
TickerNameCAGRStdevBest YearWorst YearMax DrawdownSharpe RatioSortino RatioMarket Correlation
VTIVanguard Total Stock Market ETF12.06%14.60%33.45%-24.81%-24.81%0.811.241.00
VXUSVanguard Total International Stock ETF4.02%14.56%27.45%-26.65%-27.76%0.300.420.86
VNQVanguard Real Estate ETF7.14%16.60%40.52%-29.31%-29.31%0.460.670.71
BNDVanguard Total Bond Market ETF1.07%4.04%8.83%-14.51%-16.31%0.130.170.28

Portfolio Asset Performance

Performance of portfolio assets
NameTotal ReturnAnnualized ReturnExpense Ratio
3 MonthYear To Date1 year3 year5 year10 yearNetGross
Vanguard Total Stock Market ETF-4.44%-24.81%-17.96%7.60%8.57%11.34%0.03%0.03%
Vanguard Total International Stock ETF-10.82%-26.65%-25.16%-1.18%-0.69%3.35%0.07%0.07%
Vanguard Real Estate ETF-11.04%-29.31%-18.68%-1.62%3.07%6.23%0.12%0.12%
Vanguard Total Bond Market ETF-4.65%-14.51%-14.55%-3.26%-0.27%0.76%0.03%0.03%
Trailing returns as of last calendar month ending September 2022

Monthly Correlations

Correlations for the portfolio assets
TickerNameVTIVXUSVNQBNDRisk Parity
VTIVanguard Total Stock Market ETF1.000.860.710.280.86
VXUSVanguard Total International Stock ETF0.861.000.620.280.84
VNQVanguard Real Estate ETF0.710.621.000.510.87
BNDVanguard Total Bond Market ETF0.280.280.511.000.68

Portfolio Risk Decomposition

Portfolio risk decomposition
TickerNameRisk Parity
VTIVanguard Total Stock Market ETF25.00%
VXUSVanguard Total International Stock ETF25.00%
VNQVanguard Real Estate ETF25.00%
BNDVanguard Total Bond Market ETF25.00%
Risk attribution decomposes portfolio risk into its constituent parts and identifies the contribution to overall volatility by each of the assets.

Annual Asset Returns

Rolling returns summary
Roll PeriodAverageHighLow
1 year5.26%18.98%-16.72%
3 years5.39%10.77%-0.96%
5 years5.22%7.48%1.57%
7 years5.25%6.22%3.08%
10 years4.93%6.44%3.40%