Portfolio Optimization

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 Type

Time Period

Start Year

First Month

End Year

Last Month

Optimization Goal

Targeted Annual Return

Targeted Annual Volatility

Targeted Tracking Error

Targeted Monthly CVaR

Robust Optimization

Use Historical Returns

Use Historical Volatility

Use Historical Correlations

Correlation Matrix

Browse…

Asset Constraints

Group Constraints

Compared Allocation

Benchmark

Benchmark Ticker

Portfolio Assets

Allocation

Expected Return

Volatility

Min. Weight

Max. Weight

Group

Select asset 1

Enter percentage allocation for asset 1 %

Expected return for asset 1 %

Expected volatility for asset 1 %

Minimum allocation for asset 1 %

Maximum allocation for asset 1 %

Group assignment for asset 1

Select asset 2

Enter percentage allocation for asset 2 %

Expected return for asset 2 %

Expected volatility for asset 2 %

Minimum allocation for asset 2 %

Maximum allocation for asset 2 %

Group assignment for asset 2

Select asset 3

Enter percentage allocation for asset 3 %

Expected return for asset 3 %

Expected volatility for asset 3 %

Minimum allocation for asset 3 %

Maximum allocation for asset 3 %

Group assignment for asset 3

Select asset 4

Enter percentage allocation for asset 4 %

Expected return for asset 4 %

Expected volatility for asset 4 %

Minimum allocation for asset 4 %

Maximum allocation for asset 4 %

Group assignment for asset 4

Select asset 5

Enter percentage allocation for asset 5 %

Expected return for asset 5 %

Expected volatility for asset 5 %

Minimum allocation for asset 5 %

Maximum allocation for asset 5 %

Group assignment for asset 5

Select asset 6

Enter percentage allocation for asset 6 %

Expected return for asset 6 %

Expected volatility for asset 6 %

Minimum allocation for asset 6 %

Maximum allocation for asset 6 %

Group assignment for asset 6

Select asset 7

Enter percentage allocation for asset 7 %

Expected return for asset 7 %

Expected volatility for asset 7 %

Minimum allocation for asset 7 %

Maximum allocation for asset 7 %

Group assignment for asset 7

Select asset 8

Enter percentage allocation for asset 8 %

Expected return for asset 8 %

Expected volatility for asset 8 %

Minimum allocation for asset 8 %

Maximum allocation for asset 8 %

Group assignment for asset 8

Select asset 9

Enter percentage allocation for asset 9 %

Expected return for asset 9 %

Expected volatility for asset 9 %

Minimum allocation for asset 9 %

Maximum allocation for asset 9 %

Group assignment for asset 9

Select asset 10

Enter percentage allocation for asset 10 %

Expected return for asset 10 %

Expected volatility for asset 10 %

Minimum allocation for asset 10 %

Maximum allocation for asset 10 %

Group assignment for asset 10

Total

Total allocation for portfolio %

Asset Groups

Min. Weight

Max. Weight

Full name for group A at index 1

Minimum allocation for group A at index 1 %

Maximum allocation for group A at index 1 %

Full name for group B at index 2

Minimum allocation for group B at index 2 %

Maximum allocation for group B at index 2 %

Full name for group C at index 3

Minimum allocation for group C at index 3 %

Maximum allocation for group C at index 3 %

Full name for group D at index 4

Minimum allocation for group D at index 4 %

Maximum allocation for group D at index 4 %

Full name for group E at index 5

Minimum allocation for group E at index 5 %

Maximum allocation for group E at index 5 %

Full name for group F at index 6

Minimum allocation for group F at index 6 %

Maximum allocation for group F at index 6 %

Portfolio Optimization Results (Jan 2004 - Apr 2022) Save

Note: The time period was constrained by the available data for iShares MSCI Emerging Markets ETF (EEM) [May 2003 - Apr 2022].

Portfolio optimization results with goal to maximize Sharpe ratio. The possible range of expected annual portfolio returns for the given period taking into account the specified constraints is 6.15% to 9.23%. Refer to the efficient frontier section for additional details.

Portfolio Allocations

Maximum Sharpe Ratio
Ticker	Name	Allocation
SPY	SPDR S&P 500 ETF Trust	28.24%
IJS	iShares S&P Small-Cap 600 Value ETF	5.00%
EFA	iShares MSCI EAFE ETF	5.00%
EEM	iShares MSCI Emerging Markets ETF	5.00%
TLT	iShares 20+ Year Treasury Bond ETF	21.76%
IEF	iShares 7-10 Year Treasury Bond ETF	30.00%
LQD	iShares iBoxx $ Invmt Grade Corp Bd ETF	5.00%
Save portfolio »

Portfolio Performance Summary

Portfolio performance statistics
Metric	Maximum Sharpe Ratio
Start Balance	$10,000
End Balance	$33,223
Annualized Return (CAGR)	6.77%
Expected Return	7.05%
Standard Deviation	7.23%
Best Year	18.72%
Worst Year	-13.30%
Maximum Drawdown	-20.20%
Sharpe Ratio (ex-ante)	0.78
Sharpe Ratio (ex-post)	0.78
Sortino Ratio	1.16
Stock Market Correlation	0.75
Results based on historical returns. Expected return is the annualized monthly arithmetic mean return.

Trailing Returns

Trailing Returns
Name	Total Return			Annualized Return				Annualized Standard Deviation
Name	3 Month	Year To Date	1 year	3 year	5 year	10 year	Full	3 year	5 year
Maximum Sharpe Ratio	-10.10%	-13.30%	-7.61%	5.47%	5.83%	6.30%	6.77%	8.93%	7.76%
Trailing return and volatility are as of last full calendar month ending April 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.
Allocation constraints are only applied to the optimized portfolio, not to compared allocations and benchmarks.
The annual results for 2022 are based on full calendar months from January to April.
The optimization results assume monthly rebalancing of portfolio assets to match the specified allocation.

Efficient Frontier Assets
#	Asset	Group	Expected Return	Standard Deviation	Sharpe Ratio	Min. Weight	Max. Weight
1	SPDR S&P 500 ETF Trust (SPY)	Equity	10.65%	14.41%	0.624	5.00%	40.00%
2	iShares S&P Small-Cap 600 Value ETF (IJS)	Equity	11.36%	19.89%	0.485	5.00%	20.00%
3	iShares MSCI EAFE ETF (EFA)	Equity	6.56%	16.70%	0.311	5.00%	30.00%
4	iShares MSCI Emerging Markets ETF (EEM)	Equity	9.11%	21.38%	0.355	5.00%	15.00%
5	iShares 20+ Year Treasury Bond ETF (TLT)	Fixed Income	6.07%	13.15%	0.360	5.00%	30.00%
6	iShares 7-10 Year Treasury Bond ETF (IEF)	Fixed Income	3.93%	6.21%	0.433	5.00%	30.00%
7	iShares iBoxx $ Invmt Grade Corp Bd ETF (LQD)	Fixed Income	4.50%	7.35%	0.440	5.00%	20.00%
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 Groups
Asset Group	Min. Weight	Max. Weight
Equity	20.00%	80.00%
Fixed Income	20.00%	80.00%

Asset Correlations

Efficient Frontier Asset Correlations
Name	Ticker	SPY	IJS	EFA	EEM	TLT	IEF	LQD
SPDR S&P 500 ETF Trust	SPY	1.00	0.86	0.88	0.76	-0.25	-0.25	0.35
iShares S&P Small-Cap 600 Value ETF	IJS	0.86	1.00	0.77	0.70	-0.34	-0.34	0.25
iShares MSCI EAFE ETF	EFA	0.88	0.77	1.00	0.87	-0.21	-0.19	0.40
iShares MSCI Emerging Markets ETF	EEM	0.76	0.70	0.87	1.00	-0.20	-0.16	0.37
iShares 20+ Year Treasury Bond ETF	TLT	-0.25	-0.34	-0.21	-0.20	1.00	0.91	0.54
iShares 7-10 Year Treasury Bond ETF	IEF	-0.25	-0.34	-0.19	-0.16	0.91	1.00	0.55
iShares iBoxx $ Invmt Grade Corp Bd ETF	LQD	0.35	0.25	0.40	0.37	0.54	0.55	1.00
Based on monthly returns from Jan 2004 to Apr 2022

Note: You can hover over any of the data points on the chart for more information.

Efficient Frontier Assets
#	SPY	IJS	EFA	EEM	TLT	IEF	LQD	Expected Return^*	Standard Deviation^*	Sharpe Ratio^*
1	13.74%	5.00%	5.00%	5.00%	21.26%	30.00%	20.00%	6.15%	6.70%	0.720
2	14.42%	5.00%	5.00%	5.00%	20.58%	30.00%	20.00%	6.19%	6.70%	0.724
3	15.10%	5.00%	5.00%	5.00%	19.90%	30.00%	20.00%	6.22%	6.70%	0.727
4	15.79%	5.00%	5.00%	5.00%	19.21%	30.00%	20.00%	6.25%	6.71%	0.731
5	16.47%	5.00%	5.00%	5.00%	18.53%	30.00%	20.00%	6.28%	6.72%	0.734
6	17.06%	5.00%	5.00%	5.00%	18.20%	30.00%	19.74%	6.31%	6.74%	0.737
7	17.47%	5.00%	5.00%	5.00%	18.58%	30.00%	18.96%	6.34%	6.75%	0.739
8	17.87%	5.00%	5.00%	5.00%	18.95%	30.00%	18.17%	6.37%	6.77%	0.742
9	18.28%	5.00%	5.00%	5.00%	19.33%	30.00%	17.39%	6.40%	6.78%	0.744
10	18.69%	5.00%	5.00%	5.00%	19.70%	30.00%	16.61%	6.43%	6.80%	0.747
11	19.09%	5.00%	5.00%	5.00%	20.08%	30.00%	15.83%	6.46%	6.82%	0.749
12	19.50%	5.00%	5.00%	5.00%	20.45%	30.00%	15.05%	6.49%	6.83%	0.752
13	19.91%	5.00%	5.00%	5.00%	20.82%	30.00%	14.27%	6.52%	6.85%	0.754
14	20.31%	5.00%	5.00%	5.00%	21.20%	30.00%	13.49%	6.55%	6.87%	0.756
15	20.72%	5.00%	5.00%	5.00%	21.57%	30.00%	12.71%	6.58%	6.89%	0.758
16	21.13%	5.00%	5.00%	5.00%	21.95%	30.00%	11.93%	6.62%	6.91%	0.761
17	21.53%	5.00%	5.00%	5.00%	22.32%	30.00%	11.15%	6.65%	6.92%	0.763
18	21.94%	5.00%	5.00%	5.00%	22.69%	30.00%	10.37%	6.68%	6.94%	0.765
19	22.35%	5.00%	5.00%	5.00%	23.07%	30.00%	9.59%	6.71%	6.96%	0.767
20	22.75%	5.00%	5.00%	5.00%	23.44%	30.00%	8.80%	6.74%	6.98%	0.769
21	23.16%	5.00%	5.00%	5.00%	23.82%	30.00%	8.02%	6.77%	7.00%	0.771
22	23.57%	5.00%	5.00%	5.00%	24.19%	30.00%	7.24%	6.80%	7.02%	0.773
23	23.97%	5.00%	5.00%	5.00%	24.56%	30.00%	6.46%	6.83%	7.04%	0.775
24	24.38%	5.00%	5.00%	5.00%	24.94%	30.00%	5.68%	6.86%	7.06%	0.777
25	24.82%	5.00%	5.00%	5.00%	25.18%	30.00%	5.00%	6.89%	7.08%	0.779
26	25.51%	5.00%	5.00%	5.00%	24.49%	30.00%	5.00%	6.92%	7.11%	0.780
27	26.19%	5.00%	5.00%	5.00%	23.81%	30.00%	5.00%	6.95%	7.13%	0.781
28	26.87%	5.00%	5.00%	5.00%	23.13%	30.00%	5.00%	6.99%	7.16%	0.782
29	27.56%	5.00%	5.00%	5.00%	22.44%	30.00%	5.00%	7.02%	7.19%	0.783
30	28.24%	5.00%	5.00%	5.00%	21.76%	30.00%	5.00%	7.05%	7.23%	0.783
31	28.92%	5.00%	5.00%	5.00%	21.08%	30.00%	5.00%	7.08%	7.26%	0.783
32	29.28%	5.00%	5.00%	5.00%	21.39%	29.33%	5.00%	7.11%	7.30%	0.783
33	29.57%	5.00%	5.00%	5.00%	21.93%	28.50%	5.00%	7.14%	7.34%	0.783
34	29.85%	5.00%	5.00%	5.00%	22.47%	27.68%	5.00%	7.17%	7.38%	0.782
35	30.14%	5.00%	5.00%	5.00%	23.01%	26.85%	5.00%	7.20%	7.42%	0.782
36	30.42%	5.00%	5.00%	5.00%	23.55%	26.03%	5.00%	7.23%	7.46%	0.782
37	30.70%	5.00%	5.00%	5.00%	24.09%	25.20%	5.00%	7.26%	7.50%	0.781
38	30.99%	5.00%	5.00%	5.00%	24.63%	24.38%	5.00%	7.29%	7.54%	0.781
39	31.27%	5.00%	5.00%	5.00%	25.17%	23.55%	5.00%	7.33%	7.58%	0.781
40	31.56%	5.00%	5.00%	5.00%	25.72%	22.73%	5.00%	7.36%	7.62%	0.780
41	31.84%	5.00%	5.00%	5.00%	26.26%	21.90%	5.00%	7.39%	7.66%	0.780
42	32.13%	5.00%	5.00%	5.00%	26.80%	21.08%	5.00%	7.42%	7.70%	0.780
43	32.41%	5.00%	5.00%	5.00%	27.34%	20.25%	5.00%	7.45%	7.75%	0.779
44	32.70%	5.00%	5.00%	5.00%	27.88%	19.43%	5.00%	7.48%	7.79%	0.779
45	32.98%	5.00%	5.00%	5.00%	28.42%	18.60%	5.00%	7.51%	7.83%	0.779
46	33.27%	5.00%	5.00%	5.00%	28.96%	17.78%	5.00%	7.54%	7.87%	0.778
47	33.55%	5.00%	5.00%	5.00%	29.50%	16.95%	5.00%	7.57%	7.91%	0.778
48	33.85%	5.00%	5.00%	5.00%	30.00%	16.15%	5.00%	7.60%	7.95%	0.778
49	34.31%	5.00%	5.00%	5.00%	30.00%	15.69%	5.00%	7.64%	7.99%	0.777
50	34.77%	5.00%	5.00%	5.00%	30.00%	15.23%	5.00%	7.67%	8.03%	0.777
51	35.23%	5.00%	5.00%	5.00%	30.00%	14.77%	5.00%	7.70%	8.08%	0.776
52	35.69%	5.00%	5.00%	5.00%	30.00%	14.31%	5.00%	7.73%	8.12%	0.776
53	36.15%	5.00%	5.00%	5.00%	30.00%	13.85%	5.00%	7.76%	8.16%	0.775
54	36.61%	5.00%	5.00%	5.00%	30.00%	13.39%	5.00%	7.79%	8.21%	0.775
55	37.07%	5.00%	5.00%	5.00%	30.00%	12.93%	5.00%	7.82%	8.25%	0.774
56	37.53%	5.00%	5.00%	5.00%	30.00%	12.47%	5.00%	7.85%	8.30%	0.773
57	37.99%	5.00%	5.00%	5.00%	30.00%	12.01%	5.00%	7.88%	8.34%	0.772
58	38.45%	5.00%	5.00%	5.00%	30.00%	11.55%	5.00%	7.92%	8.39%	0.772
59	38.92%	5.00%	5.00%	5.00%	30.00%	11.08%	5.00%	7.95%	8.43%	0.771
60	39.38%	5.00%	5.00%	5.00%	30.00%	10.62%	5.00%	7.98%	8.48%	0.770
61	39.84%	5.00%	5.00%	5.00%	30.00%	10.16%	5.00%	8.01%	8.53%	0.769
62	40.00%	5.27%	5.00%	5.00%	30.00%	9.73%	5.00%	8.04%	8.58%	0.768
63	40.00%	5.69%	5.00%	5.00%	30.00%	9.31%	5.00%	8.07%	8.63%	0.767
64	40.00%	6.10%	5.00%	5.00%	30.00%	8.90%	5.00%	8.10%	8.68%	0.766
65	40.00%	6.52%	5.00%	5.00%	30.00%	8.48%	5.00%	8.13%	8.73%	0.764
66	40.00%	6.94%	5.00%	5.00%	30.00%	8.06%	5.00%	8.16%	8.79%	0.763
67	40.00%	7.36%	5.00%	5.00%	30.00%	7.64%	5.00%	8.20%	8.84%	0.762
68	40.00%	7.77%	5.00%	5.00%	30.00%	7.23%	5.00%	8.23%	8.90%	0.760
69	40.00%	8.19%	5.00%	5.00%	30.00%	6.81%	5.00%	8.26%	8.95%	0.759
70	40.00%	8.61%	5.00%	5.00%	30.00%	6.39%	5.00%	8.29%	9.01%	0.757
71	40.00%	9.03%	5.00%	5.00%	30.00%	5.97%	5.00%	8.32%	9.06%	0.756
72	40.00%	9.44%	5.00%	5.00%	30.00%	5.56%	5.00%	8.35%	9.12%	0.754
73	40.00%	9.86%	5.00%	5.00%	30.00%	5.14%	5.00%	8.38%	9.18%	0.752
74	40.00%	10.40%	5.00%	5.00%	29.60%	5.00%	5.00%	8.41%	9.25%	0.750
75	40.00%	10.99%	5.00%	5.00%	29.01%	5.00%	5.00%	8.45%	9.33%	0.747
76	40.00%	11.58%	5.00%	5.00%	28.42%	5.00%	5.00%	8.48%	9.40%	0.744
77	40.00%	12.17%	5.00%	5.00%	27.83%	5.00%	5.00%	8.51%	9.48%	0.741
78	40.00%	12.77%	5.00%	5.00%	27.23%	5.00%	5.00%	8.54%	9.57%	0.737
79	40.00%	13.36%	5.00%	5.00%	26.64%	5.00%	5.00%	8.57%	9.65%	0.734
80	40.00%	13.95%	5.00%	5.00%	26.05%	5.00%	5.00%	8.60%	9.74%	0.730
81	40.00%	14.54%	5.00%	5.00%	25.46%	5.00%	5.00%	8.63%	9.83%	0.727
82	40.00%	15.14%	5.00%	5.00%	24.86%	5.00%	5.00%	8.66%	9.92%	0.723
83	40.00%	15.73%	5.00%	5.00%	24.27%	5.00%	5.00%	8.70%	10.01%	0.719
84	40.00%	16.32%	5.00%	5.00%	23.68%	5.00%	5.00%	8.73%	10.10%	0.715
85	40.00%	16.91%	5.00%	5.00%	23.09%	5.00%	5.00%	8.76%	10.20%	0.712
86	40.00%	17.51%	5.00%	5.00%	22.49%	5.00%	5.00%	8.79%	10.29%	0.708
87	40.00%	18.10%	5.00%	5.00%	21.90%	5.00%	5.00%	8.82%	10.39%	0.704
88	40.00%	18.69%	5.00%	5.00%	21.31%	5.00%	5.00%	8.85%	10.49%	0.700
89	40.00%	19.28%	5.00%	5.00%	20.72%	5.00%	5.00%	8.88%	10.59%	0.696
90	40.00%	19.88%	5.00%	5.00%	20.12%	5.00%	5.00%	8.92%	10.70%	0.692
91	40.00%	20.00%	5.00%	5.81%	19.19%	5.00%	5.00%	8.95%	10.86%	0.684
92	40.00%	20.00%	5.00%	6.83%	18.17%	5.00%	5.00%	8.98%	11.04%	0.676
93	40.00%	20.00%	5.00%	7.85%	17.15%	5.00%	5.00%	9.01%	11.22%	0.667
94	40.00%	20.00%	5.00%	8.87%	16.13%	5.00%	5.00%	9.04%	11.41%	0.659
95	40.00%	20.00%	5.00%	9.89%	15.11%	5.00%	5.00%	9.07%	11.60%	0.651
96	40.00%	20.00%	5.00%	10.91%	14.09%	5.00%	5.00%	9.10%	11.79%	0.642
97	40.00%	20.00%	5.00%	11.94%	13.06%	5.00%	5.00%	9.14%	11.99%	0.634
98	40.00%	20.00%	5.00%	12.96%	12.04%	5.00%	5.00%	9.17%	12.19%	0.626
99	40.00%	20.00%	5.00%	13.98%	11.02%	5.00%	5.00%	9.20%	12.39%	0.618
100	40.00%	20.00%	5.00%	15.00%	10.00%	5.00%	5.00%	9.23%	12.60%	0.611
^*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
Year	Inflation	Maximum Sharpe Ratio Return	Maximum Sharpe Ratio Balance	SPDR S&P 500 ETF Trust (SPY)	iShares S&P Small-Cap 600 Value ETF (IJS)	iShares MSCI EAFE ETF (EFA)	iShares MSCI Emerging Markets ETF (EEM)	iShares 20+ Year Treasury Bond ETF (TLT)	iShares 7-10 Year Treasury Bond ETF (IEF)	iShares iBoxx $ Invmt Grade Corp Bd ETF (LQD)
2004	3.26%	9.81%	$10,981	10.70%	22.60%	18.95%	24.63%	8.71%	4.12%	5.72%
2005	3.42%	6.81%	$11,728	4.83%	6.00%	13.32%	32.62%	8.61%	2.64%	1.16%
2006	2.54%	9.30%	$12,819	15.85%	19.37%	25.81%	31.19%	0.71%	2.52%	4.22%
2007	4.08%	9.02%	$13,975	5.14%	-5.56%	9.94%	33.31%	10.29%	10.37%	3.73%
2008	0.09%	-7.43%	$12,937	-36.81%	-29.39%	-41.04%	-48.88%	33.93%	17.91%	2.40%
2009	2.72%	5.56%	$13,657	26.36%	22.36%	26.95%	68.93%	-21.80%	-6.59%	8.46%
2010	1.50%	13.02%	$15,436	15.06%	24.69%	8.15%	16.51%	9.05%	9.37%	9.33%
2011	2.96%	11.57%	$17,221	1.89%	-1.65%	-12.25%	-18.82%	33.96%	15.64%	9.73%
2012	1.74%	9.87%	$18,921	15.99%	18.24%	18.82%	19.10%	2.63%	3.66%	10.58%
2013	1.50%	5.69%	$19,998	32.31%	39.34%	21.40%	-3.69%	-13.37%	-6.09%	-2.00%
2014	0.76%	12.61%	$22,519	13.46%	7.56%	-6.20%	-3.93%	27.30%	9.07%	8.21%
2015	0.73%	-0.45%	$22,418	1.25%	-6.90%	-1.00%	-16.18%	-1.79%	1.51%	-1.25%
2016	2.07%	6.65%	$23,907	12.00%	31.25%	1.37%	10.87%	1.18%	1.00%	6.21%
2017	2.11%	12.65%	$26,931	21.70%	11.35%	25.10%	37.28%	9.18%	2.55%	7.06%
2018	1.91%	-3.31%	$26,040	-4.56%	-12.84%	-13.81%	-15.31%	-1.61%	0.99%	-3.79%
2019	2.29%	18.72%	$30,915	31.22%	24.12%	22.03%	18.20%	14.12%	8.03%	17.37%
2020	1.36%	15.50%	$35,708	18.37%	2.63%	7.59%	17.03%	18.15%	10.01%	10.97%
2021	7.04%	7.32%	$38,320	28.74%	30.53%	11.46%	-3.61%	-4.60%	-3.33%	-1.85%
2022	3.70%	-13.30%	$33,223	-12.99%	-8.00%	-12.76%	-13.24%	-19.05%	-10.33%	-14.52%
Annual return for 2022 is from 01/01/2022 to 04/30/2022

Monthly returns for the configured portfolios
Year	Month	Maximum Sharpe Ratio Return	Maximum Sharpe Ratio Balance	SPDR S&P 500 ETF Trust (SPY)	iShares S&P Small-Cap 600 Value ETF (IJS)	iShares MSCI EAFE ETF (EFA)	iShares MSCI Emerging Markets ETF (EEM)	iShares 20+ Year Treasury Bond ETF (TLT)	iShares 7-10 Year Treasury Bond ETF (IEF)	iShares iBoxx $ Invmt Grade Corp Bd ETF (LQD)
2004	1	1.61%	$10,161	1.98%	2.17%	1.13%	2.42%	1.86%	1.02%	1.22%
2004	2	1.88%	$10,352	1.36%	2.50%	2.30%	3.95%	2.28%	1.61%	1.51%
2004	3	0.50%	$10,403	-1.32%	1.82%	0.07%	0.55%	1.41%	1.30%	0.99%
2004	4	-4.25%	$9,962	-1.89%	-3.93%	-3.39%	-9.80%	-6.23%	-4.35%	-3.89%
2004	5	0.44%	$10,005	1.71%	1.58%	1.14%	1.17%	-0.26%	-0.53%	-0.52%
2004	6	1.44%	$10,149	1.85%	5.35%	3.35%	0.92%	1.06%	0.65%	0.13%
2004	7	-0.77%	$10,071	-3.22%	-4.75%	-4.27%	-3.64%	1.53%	1.21%	1.56%
2004	8	2.23%	$10,295	0.24%	0.24%	1.19%	3.53%	4.17%	2.83%	3.08%
2004	9	1.29%	$10,428	1.00%	4.69%	2.07%	6.98%	0.95%	0.32%	0.31%
2004	10	1.47%	$10,581	1.29%	0.95%	3.50%	2.85%	1.77%	0.99%	1.18%
2004	11	1.34%	$10,723	4.45%	9.11%	6.08%	9.95%	-2.39%	-1.98%	-1.22%
2004	12	2.40%	$10,981	3.02%	1.57%	4.80%	4.74%	2.66%	1.17%	1.39%
2005	1	0.18%	$11,001	-2.24%	-3.25%	-1.90%	-0.53%	3.57%	0.87%	1.23%
2005	2	0.63%	$11,070	2.09%	2.90%	3.78%	9.68%	-1.47%	-1.37%	-0.94%
2005	3	-1.44%	$10,910	-1.83%	-2.36%	-2.62%	-7.91%	-0.45%	-0.40%	-1.26%
2005	4	0.75%	$10,992	-1.87%	-5.12%	-1.62%	-1.25%	3.86%	2.52%	1.62%
2005	5	2.60%	$11,277	3.22%	6.16%	-0.86%	3.16%	3.14%	1.84%	0.62%
2005	6	1.18%	$11,411	0.15%	3.92%	1.43%	3.97%	2.16%	0.48%	1.22%
2005	7	0.48%	$11,465	3.83%	5.84%	3.00%	7.68%	-3.38%	-2.18%	-0.82%
2005	8	1.33%	$11,618	-0.94%	-1.87%	3.84%	1.32%	3.48%	2.00%	1.50%
2005	9	-0.56%	$11,553	0.80%	0.05%	3.69%	8.65%	-3.61%	-1.75%	-1.86%
2005	10	-2.25%	$11,293	-2.37%	-3.41%	-3.18%	-6.34%	-2.24%	-1.24%	-1.58%
2005	11	2.26%	$11,548	4.40%	4.91%	2.31%	5.79%	0.69%	0.63%	0.66%
2005	12	1.56%	$11,728	-0.19%	-1.06%	5.18%	6.10%	2.98%	1.37%	0.86%
2006	1	1.59%	$11,915	2.40%	8.75%	5.77%	14.20%	-1.34%	-0.70%	-0.44%
2006	2	0.19%	$11,938	0.57%	0.27%	-0.70%	-3.85%	1.11%	-0.10%	0.68%
2006	3	-0.47%	$11,882	1.65%	4.86%	4.01%	2.17%	-4.57%	-1.36%	-1.68%
2006	4	0.13%	$11,898	1.26%	0.18%	4.79%	6.52%	-2.75%	-0.63%	-0.20%
2006	5	-1.91%	$11,671	-3.01%	-4.55%	-3.82%	-11.14%	-0.19%	-0.10%	-0.19%
2006	6	0.40%	$11,718	0.26%	0.04%	-0.06%	0.21%	1.18%	0.23%	-0.09%
2006	7	1.18%	$11,856	0.45%	-3.10%	0.81%	2.34%	2.16%	1.68%	1.46%
2006	8	2.26%	$12,124	2.18%	2.70%	2.55%	1.58%	3.06%	1.76%	2.22%
2006	9	1.61%	$12,320	2.70%	1.19%	0.22%	-0.87%	1.91%	1.21%	0.87%
2006	10	2.10%	$12,579	3.15%	5.52%	3.75%	7.06%	0.85%	0.54%	1.00%
2006	11	2.10%	$12,843	1.99%	2.38%	3.07%	5.98%	2.31%	1.31%	1.46%
2006	12	-0.19%	$12,819	1.34%	0.32%	3.20%	5.44%	-2.69%	-1.28%	-0.90%
2007	1	0.27%	$12,854	1.50%	2.14%	1.39%	0.11%	-1.00%	-0.40%	0.09%
2007	2	0.69%	$12,942	-1.96%	-0.92%	-0.12%	-3.24%	3.39%	2.06%	2.00%
2007	3	0.34%	$12,986	1.16%	0.91%	2.90%	5.33%	-1.70%	-0.14%	-0.68%
2007	4	2.14%	$13,264	4.43%	1.84%	3.75%	3.73%	0.90%	0.61%	0.89%
2007	5	0.58%	$13,341	3.39%	4.63%	2.36%	5.06%	-2.31%	-1.39%	-1.23%
2007	6	-0.76%	$13,239	-1.46%	-2.24%	-0.32%	3.68%	-1.01%	-0.47%	-0.81%
2007	7	0.08%	$13,250	-3.13%	-6.26%	-2.29%	0.71%	3.32%	2.26%	-0.82%
2007	8	1.64%	$13,467	1.28%	1.33%	-0.63%	1.04%	1.79%	2.26%	2.38%
2007	9	2.07%	$13,745	3.87%	0.31%	5.32%	11.57%	0.23%	0.09%	0.73%
2007	10	2.01%	$14,021	1.36%	1.06%	4.25%	11.87%	1.81%	1.08%	0.97%
2007	11	0.41%	$14,079	-3.87%	-7.15%	-3.62%	-7.65%	5.35%	4.04%	1.02%
2007	12	-0.74%	$13,975	-1.13%	-0.71%	-2.99%	-1.43%	-0.64%	0.05%	-0.81%
2008	1	-1.15%	$13,814	-6.05%	-4.00%	-7.85%	-8.92%	2.10%	3.36%	2.57%
2008	2	-0.61%	$13,729	-2.58%	-3.36%	-1.02%	1.99%	-0.46%	1.24%	-0.71%
2008	3	0.46%	$13,792	-0.90%	0.83%	0.42%	-3.75%	2.14%	1.34%	-0.60%
2008	4	1.01%	$13,930	4.77%	2.64%	5.44%	9.14%	-2.48%	-2.41%	1.25%
2008	5	-0.39%	$13,876	1.51%	3.92%	1.19%	3.16%	-2.69%	-1.78%	-2.21%
2008	6	-2.83%	$13,484	-8.35%	-8.41%	-8.80%	-9.29%	2.65%	1.14%	-1.29%
2008	7	-0.40%	$13,430	-0.90%	2.87%	-3.32%	-5.50%	-0.37%	0.72%	0.39%
2008	8	1.21%	$13,593	1.55%	4.76%	-4.25%	-6.32%	2.74%	1.53%	0.15%
2008	9	-4.47%	$12,985	-9.44%	-4.82%	-11.44%	-14.68%	1.47%	-0.14%	-10.73%
2008	10	-8.74%	$11,850	-16.52%	-19.86%	-20.83%	-25.58%	-1.86%	-0.87%	-1.95%
2008	11	2.25%	$12,117	-6.96%	-11.80%	-6.37%	-9.75%	14.34%	7.75%	3.35%
2008	12	6.77%	$12,937	0.98%	6.57%	8.88%	10.35%	13.64%	5.15%	13.80%
2009	1	-8.27%	$11,868	-8.21%	-13.94%	-13.73%	-9.29%	-13.07%	-3.89%	-1.80%
2009	2	-5.33%	$11,235	-10.74%	-13.03%	-10.39%	-6.27%	-1.54%	-0.74%	-5.20%
2009	3	5.90%	$11,897	8.35%	7.58%	8.39%	16.86%	4.04%	3.31%	0.47%
2009	4	2.91%	$12,243	9.93%	18.89%	11.52%	15.56%	-6.95%	-2.75%	2.78%
2009	5	1.83%	$12,467	5.85%	0.67%	13.19%	15.94%	-3.69%	-2.08%	2.32%
2009	6	0.02%	$12,469	-0.07%	1.52%	-1.43%	-2.25%	0.76%	-0.55%	2.89%
2009	7	4.32%	$13,007	7.46%	11.00%	10.04%	11.01%	0.58%	0.83%	4.63%
2009	8	2.16%	$13,288	3.69%	3.48%	4.50%	-1.31%	2.24%	0.77%	1.31%
2009	9	2.87%	$13,669	3.55%	4.21%	3.80%	10.20%	2.46%	1.12%	1.76%
2009	10	-1.78%	$13,426	-1.92%	-6.07%	-2.52%	-3.44%	-2.62%	-0.14%	-0.49%
2009	11	3.44%	$13,888	6.16%	2.90%	3.92%	7.85%	1.21%	2.02%	1.95%
2009	12	-1.66%	$13,657	1.91%	8.10%	0.70%	3.27%	-6.34%	-4.40%	-2.07%
2010	1	-0.43%	$13,598	-3.63%	-2.54%	-5.07%	-7.76%	2.69%	2.37%	1.25%
2010	2	1.27%	$13,771	3.12%	4.76%	0.27%	1.78%	-0.34%	0.33%	0.51%
2010	3	2.10%	$14,060	6.09%	7.80%	6.39%	8.11%	-2.06%	-1.06%	0.65%
2010	4	1.93%	$14,332	1.55%	6.63%	-2.80%	-0.17%	3.32%	1.65%	1.91%
2010	5	-1.77%	$14,078	-7.95%	-8.54%	-11.19%	-9.39%	5.11%	2.93%	-1.31%
2010	6	0.29%	$14,119	-5.17%	-8.27%	-2.07%	-1.40%	5.80%	3.05%	3.28%
2010	7	3.56%	$14,622	6.83%	6.71%	11.61%	10.93%	-0.95%	0.91%	2.11%
2010	8	0.96%	$14,762	-4.50%	-7.91%	-3.80%	-3.24%	8.40%	3.36%	2.86%
2010	9	3.64%	$15,299	8.96%	10.93%	9.97%	11.76%	-2.51%	-0.00%	0.46%
2010	10	0.63%	$15,396	3.82%	4.04%	3.81%	3.02%	-4.47%	-0.01%	-0.26%
2010	11	-0.98%	$15,245	0.00%	2.47%	-4.82%	-2.91%	-1.69%	-0.90%	-1.62%
2010	12	1.25%	$15,436	6.68%	8.97%	8.30%	7.27%	-3.68%	-3.43%	-0.75%
2011	1	-0.12%	$15,418	2.33%	-0.24%	2.10%	-3.84%	-3.08%	-0.02%	0.04%
2011	2	1.72%	$15,683	3.47%	4.21%	3.55%	-0.04%	1.65%	-0.21%	1.08%
2011	3	0.24%	$15,720	0.01%	2.21%	-2.39%	6.29%	0.03%	-0.15%	-0.54%
2011	4	2.47%	$16,109	2.90%	1.06%	5.63%	2.73%	2.34%	1.84%	2.50%
2011	5	0.90%	$16,254	-1.12%	-1.77%	-2.21%	-2.94%	3.42%	2.51%	1.27%
2011	6	-1.36%	$16,033	-1.69%	-1.59%	-1.19%	-0.93%	-2.33%	-0.51%	-0.80%
2011	7	1.16%	$16,219	-2.00%	-2.77%	-2.38%	-1.03%	4.42%	3.17%	2.43%
2011	8	0.66%	$16,326	-5.50%	-7.98%	-8.75%	-9.25%	9.66%	4.65%	0.34%
2011	9	-0.36%	$16,267	-6.94%	-10.57%	-10.81%	-17.89%	13.20%	2.24%	0.35%
2011	10	4.05%	$16,925	10.91%	15.34%	9.63%	16.27%	-3.84%	-1.29%	2.51%
2011	11	0.16%	$16,952	-0.41%	0.63%	-2.18%	-1.96%	1.98%	0.58%	-3.16%
2011	12	1.59%	$17,221	1.04%	2.02%	-2.21%	-4.30%	3.44%	1.99%	3.49%
2012	1	2.81%	$17,705	4.64%	7.90%	5.27%	10.99%	-0.33%	0.86%	2.14%
2012	2	1.00%	$17,883	4.34%	1.71%	4.83%	5.27%	-2.59%	-1.10%	1.63%
2012	3	-0.55%	$17,784	3.22%	2.89%	0.42%	-3.11%	-4.23%	-1.59%	-1.42%
2012	4	1.39%	$18,031	-0.67%	-1.91%	-2.08%	-1.70%	4.83%	2.51%	1.08%
2012	5	-0.28%	$17,980	-6.01%	-7.18%	-11.14%	-10.71%	9.03%	2.87%	0.76%
2012	6	1.53%	$18,255	4.05%	4.54%	7.11%	5.08%	-1.68%	-0.42%	0.87%
2012	7	1.73%	$18,571	1.18%	-0.69%	0.08%	-0.03%	3.82%	1.40%	3.48%
2012	8	0.77%	$18,713	2.51%	4.08%	3.20%	0.41%	-1.32%	-0.12%	-0.05%
2012	9	0.67%	$18,838	2.54%	3.14%	2.71%	5.22%	-2.53%	-0.35%	1.10%
2012	10	-0.74%	$18,700	-1.82%	-1.96%	1.09%	-0.44%	-0.48%	-0.40%	1.35%
2012	11	1.03%	$18,893	0.57%	1.65%	2.78%	1.56%	1.38%	0.98%	-0.42%
2012	12	0.15%	$18,921	0.90%	3.55%	4.37%	6.80%	-2.49%	-0.94%	-0.33%
2013	1	0.74%	$19,061	5.12%	5.35%	3.73%	-0.29%	-3.19%	-1.29%	-1.30%
2013	2	0.93%	$19,238	1.28%	1.63%	-1.29%	-2.28%	1.24%	1.13%	1.08%
2013	3	1.28%	$19,485	3.80%	4.11%	1.31%	-1.02%	-0.42%	0.29%	-0.05%
2013	4	2.45%	$19,961	1.92%	0.12%	5.02%	1.22%	4.68%	1.52%	2.17%
2013	5	-2.08%	$19,547	2.36%	4.29%	-3.02%	-4.83%	-6.76%	-3.11%	-3.22%
2013	6	-2.43%	$19,073	-1.34%	-0.14%	-2.70%	-5.35%	-3.27%	-2.55%	-3.27%
2013	7	1.58%	$19,374	5.17%	6.56%	5.32%	1.32%	-2.26%	-0.35%	1.11%
2013	8	-2.01%	$18,984	-3.00%	-3.41%	-1.96%	-2.54%	-1.34%	-1.42%	-1.00%
2013	9	2.71%	$19,499	3.17%	6.59%	7.82%	7.21%	0.66%	1.85%	0.74%
2013	10	2.49%	$19,984	4.63%	3.48%	3.26%	4.17%	1.43%	0.78%	1.81%
2013	11	0.21%	$20,025	2.96%	4.25%	0.55%	-0.26%	-2.70%	-0.88%	-0.14%
2013	12	-0.14%	$19,998	2.59%	1.29%	2.16%	-0.42%	-1.87%	-2.09%	0.22%
2014	1	0.52%	$20,102	-3.52%	-3.51%	-5.20%	-8.64%	6.30%	3.06%	1.88%
2014	2	2.27%	$20,558	4.55%	4.63%	6.13%	3.38%	0.52%	0.36%	1.14%
2014	3	0.46%	$20,653	0.83%	1.34%	-0.46%	3.88%	0.73%	-0.56%	-0.03%
2014	4	0.95%	$20,850	0.70%	-2.29%	1.67%	0.78%	2.10%	0.76%	1.33%
2014	5	2.18%	$21,304	2.32%	0.62%	1.60%	2.95%	2.95%	1.82%	1.51%
2014	6	0.82%	$21,480	2.06%	3.85%	0.92%	2.40%	-0.25%	-0.22%	0.01%
2014	7	-0.63%	$21,344	-1.34%	-5.07%	-2.60%	1.36%	0.67%	-0.22%	-0.32%
2014	8	3.18%	$22,022	3.95%	4.46%	0.18%	2.83%	4.72%	1.88%	2.00%
2014	9	-2.13%	$21,554	-1.38%	-5.94%	-3.88%	-7.77%	-2.11%	-1.05%	-1.68%
2014	10	2.21%	$22,031	2.36%	7.13%	-0.27%	1.42%	2.81%	1.53%	1.23%
2014	11	1.80%	$22,429	2.75%	0.48%	0.06%	-1.54%	2.97%	1.29%	0.91%
2014	12	0.40%	$22,519	-0.26%	2.56%	-4.00%	-3.99%	3.25%	0.13%	-0.02%
2015	1	2.51%	$23,084	-2.96%	-5.32%	0.62%	-0.69%	9.82%	4.30%	3.75%
2015	2	0.27%	$23,146	5.62%	5.86%	6.34%	4.41%	-6.14%	-2.47%	-1.42%
2015	3	-0.03%	$23,138	-1.57%	1.03%	-1.43%	-1.50%	1.10%	0.86%	0.20%
2015	4	-0.28%	$23,072	0.98%	-1.82%	3.65%	6.85%	-3.43%	-0.63%	-1.19%
2015	5	-0.49%	$22,959	1.29%	0.75%	0.20%	-4.10%	-2.37%	-0.42%	-1.12%
2015	6	-2.32%	$22,426	-2.03%	0.42%	-3.12%	-2.93%	-4.07%	-1.63%	-1.88%
2015	7	1.78%	$22,824	2.26%	-2.70%	2.03%	-6.31%	4.55%	1.52%	0.83%
2015	8	-2.93%	$22,154	-6.10%	-4.62%	-7.43%	-8.84%	-0.69%	0.08%	-0.83%
2015	9	-0.32%	$22,083	-2.54%	-3.77%	-4.42%	-3.13%	1.97%	1.58%	1.19%
2015	10	3.13%	$22,773	8.51%	6.57%	6.61%	6.38%	-0.41%	-0.64%	0.57%
2015	11	-0.26%	$22,714	0.37%	2.47%	-0.75%	-2.52%	-0.87%	-0.43%	-0.15%
2015	12	-1.30%	$22,418	-1.72%	-5.08%	-2.34%	-3.83%	-0.30%	-0.45%	-1.08%
2016	1	-0.01%	$22,416	-4.98%	-5.85%	-5.52%	-5.03%	5.57%	3.33%	0.12%
2016	2	1.04%	$22,650	-0.08%	2.08%	-3.33%	-0.82%	3.09%	1.49%	1.05%
2016	3	3.49%	$23,440	6.72%	9.41%	6.58%	12.96%	-0.09%	-0.06%	3.62%
2016	4	0.22%	$23,492	0.39%	2.13%	2.22%	0.41%	-0.74%	-0.16%	1.55%
2016	5	0.43%	$23,594	1.70%	0.44%	-0.09%	-3.69%	0.81%	-0.10%	-0.51%
2016	6	2.84%	$24,263	0.35%	0.83%	-2.42%	4.56%	6.93%	3.09%	3.09%
2016	7	2.35%	$24,832	3.65%	5.06%	3.98%	5.38%	2.10%	0.25%	1.29%
2016	8	-0.35%	$24,745	0.12%	1.13%	0.53%	0.88%	-1.01%	-1.01%	0.18%
2016	9	-0.03%	$24,736	0.01%	0.87%	1.34%	2.52%	-1.51%	0.24%	-0.32%
2016	10	-2.31%	$24,166	-1.73%	-3.74%	-2.22%	-0.83%	-4.38%	-1.49%	-1.53%
2016	11	-1.82%	$23,727	3.68%	13.34%	-1.78%	-4.42%	-8.21%	-4.23%	-3.17%
2016	12	0.76%	$23,907	2.03%	3.20%	2.71%	-0.25%	-0.46%	-0.12%	0.84%
2017	1	1.19%	$24,193	1.79%	-1.21%	3.29%	6.66%	0.81%	0.22%	0.15%
2017	2	1.95%	$24,665	3.93%	1.35%	1.19%	1.74%	1.59%	0.72%	1.32%
2017	3	0.22%	$24,718	0.13%	-0.65%	3.23%	3.69%	-0.65%	0.08%	-0.29%
2017	4	1.25%	$25,026	0.99%	0.51%	2.42%	1.70%	1.57%	1.11%	1.19%
2017	5	1.33%	$25,359	1.41%	-2.26%	3.54%	2.85%	1.89%	0.83%	1.33%
2017	6	0.43%	$25,469	0.64%	2.96%	0.31%	0.93%	0.79%	-0.51%	0.48%
2017	7	1.05%	$25,737	2.06%	0.75%	2.65%	5.82%	-0.66%	0.38%	0.77%
2017	8	1.27%	$26,065	0.29%	-2.72%	-0.04%	2.35%	3.41%	1.46%	0.68%
2017	9	0.17%	$26,110	2.01%	8.58%	2.36%	-0.04%	-2.32%	-1.44%	-0.05%
2017	10	0.89%	$26,342	2.36%	0.59%	1.68%	3.28%	-0.04%	-0.19%	0.19%
2017	11	1.14%	$26,641	3.06%	3.76%	0.69%	-0.39%	0.74%	-0.28%	-0.12%
2017	12	1.09%	$26,931	1.21%	-0.37%	1.35%	3.77%	1.81%	0.18%	1.22%
2018	1	0.91%	$27,176	5.64%	1.33%	5.02%	8.30%	-3.26%	-2.15%	-1.23%
2018	2	-2.82%	$26,410	-3.64%	-4.04%	-4.83%	-5.90%	-3.04%	-0.93%	-2.24%
2018	3	0.28%	$26,483	-2.74%	1.37%	-0.84%	0.54%	2.86%	1.16%	0.56%
2018	4	-0.75%	$26,286	0.52%	1.76%	1.52%	-2.82%	-2.09%	-1.28%	-1.57%
2018	5	1.51%	$26,683	2.43%	5.87%	-1.89%	-2.62%	2.01%	0.99%	0.52%
2018	6	0.07%	$26,703	0.58%	0.80%	-1.57%	-4.54%	0.65%	0.20%	-0.49%
2018	7	1.09%	$26,994	3.70%	2.62%	2.85%	3.53%	-1.44%	-0.53%	1.34%
2018	8	1.35%	$27,359	3.19%	3.14%	-2.24%	-3.77%	1.31%	1.01%	0.02%
2018	9	-0.96%	$27,097	0.59%	-3.05%	0.97%	-0.58%	-2.86%	-1.20%	-0.14%
2018	10	-4.12%	$25,980	-6.91%	-9.94%	-8.13%	-8.76%	-2.93%	-0.30%	-2.05%
2018	11	1.59%	$26,393	1.85%	0.57%	0.50%	4.90%	1.79%	1.33%	-0.36%
2018	12	-1.34%	$26,040	-8.79%	-12.38%	-5.35%	-3.50%	5.85%	2.80%	1.86%
2019	1	4.17%	$27,126	8.01%	12.26%	6.63%	10.34%	0.38%	0.65%	3.37%
2019	2	0.71%	$27,317	3.24%	4.13%	2.54%	-1.53%	-1.38%	-0.52%	-0.20%
2019	3	2.57%	$28,020	1.81%	-3.91%	0.92%	1.13%	5.57%	2.66%	2.93%
2019	4	1.07%	$28,319	4.09%	4.32%	2.93%	2.35%	-1.99%	-0.52%	0.44%
2019	5	-0.43%	$28,197	-6.38%	-9.98%	-5.03%	-7.33%	6.84%	3.05%	1.65%
2019	6	3.69%	$29,237	6.96%	7.66%	5.91%	6.20%	0.95%	1.22%	3.25%
2019	7	0.34%	$29,337	1.51%	1.30%	-1.95%	-2.66%	0.26%	0.04%	0.25%
2019	8	2.77%	$30,148	-1.67%	-5.14%	-1.92%	-3.78%	11.04%	3.95%	3.88%
2019	9	0.09%	$30,177	1.95%	5.57%	3.16%	1.69%	-2.68%	-1.19%	-0.76%
2019	10	0.94%	$30,460	2.21%	2.00%	3.39%	4.18%	-1.11%	0.19%	0.44%
2019	11	0.94%	$30,746	3.62%	2.71%	1.13%	-0.09%	-0.41%	-0.69%	0.47%
2019	12	0.55%	$30,915	2.90%	2.84%	2.98%	7.71%	-3.20%	-0.93%	0.53%
2020	1	2.06%	$31,552	-0.04%	-6.31%	-2.82%	-6.15%	7.69%	3.47%	2.45%
2020	2	-0.94%	$31,257	-7.92%	-10.15%	-7.77%	-3.78%	6.63%	2.96%	1.09%
2020	3	-4.11%	$29,971	-12.46%	-25.76%	-14.11%	-15.77%	6.38%	3.72%	-6.31%
2020	4	5.53%	$31,628	12.70%	13.89%	5.82%	7.35%	1.22%	0.27%	4.85%
2020	5	1.73%	$32,176	4.76%	2.55%	5.43%	2.97%	-1.76%	0.33%	2.46%
2020	6	1.38%	$32,620	1.78%	3.58%	3.51%	6.61%	0.34%	0.04%	2.13%
2020	7	3.68%	$33,819	5.89%	2.58%	1.94%	8.25%	4.44%	0.85%	3.10%
2020	8	1.13%	$34,200	6.98%	5.07%	4.72%	2.89%	-5.05%	-0.97%	-1.78%
2020	9	-1.22%	$33,782	-3.74%	-5.18%	-2.05%	-1.01%	0.77%	0.33%	-0.44%
2020	10	-1.80%	$33,172	-2.49%	3.66%	-3.55%	1.41%	-3.39%	-1.38%	-0.51%
2020	11	5.85%	$35,112	10.88%	19.21%	14.27%	8.99%	1.66%	0.34%	3.77%
2020	12	1.70%	$35,708	3.71%	7.50%	5.01%	7.14%	-1.23%	-0.24%	0.15%
2021	1	-1.07%	$35,328	-1.02%	6.25%	-0.78%	3.17%	-3.63%	-1.09%	-1.83%
2021	2	-0.59%	$35,118	2.78%	10.80%	2.24%	0.79%	-5.73%	-2.36%	-2.26%
2021	3	-0.28%	$35,020	4.54%	5.61%	2.51%	-0.73%	-5.24%	-2.39%	-1.48%
2021	4	2.68%	$35,959	5.29%	1.69%	2.95%	1.20%	2.49%	1.00%	1.04%
2021	5	0.80%	$36,245	0.66%	3.89%	3.48%	1.65%	0.00%	0.42%	0.62%
2021	6	1.97%	$36,960	2.25%	-0.71%	-1.08%	0.95%	4.42%	1.02%	2.21%
2021	7	1.66%	$37,575	2.44%	-4.36%	0.77%	-6.44%	3.72%	1.99%	1.42%
2021	8	0.87%	$37,903	2.98%	1.82%	1.45%	1.57%	-0.34%	-0.39%	-0.34%
2021	9	-2.93%	$36,792	-4.66%	-1.46%	-3.26%	-3.87%	-2.91%	-1.60%	-1.51%
2021	10	2.77%	$37,810	7.02%	2.86%	3.18%	1.07%	2.46%	-0.44%	0.53%
2021	11	0.14%	$37,861	-0.80%	-2.62%	-4.53%	-4.08%	2.77%	1.09%	-0.12%
2021	12	1.21%	$38,320	4.63%	4.12%	4.41%	1.53%	-2.01%	-0.52%	-0.03%
2022	1	-3.56%	$36,957	-5.27%	-4.40%	-3.63%	-0.02%	-3.91%	-2.11%	-3.59%
2022	2	-1.66%	$36,344	-2.95%	2.28%	-3.43%	-4.32%	-1.63%	-0.30%	-2.13%
2022	3	-1.61%	$35,760	3.76%	0.50%	0.52%	-3.38%	-5.45%	-4.06%	-2.89%
2022	4	-7.10%	$33,223	-8.78%	-6.38%	-6.74%	-6.14%	-9.42%	-4.23%	-6.70%

Portfolio return and risk metrics
Metric	Maximum Sharpe Ratio
Arithmetic Mean (monthly)	0.57%
Arithmetic Mean (annualized)	7.05%
Geometric Mean (monthly)	0.55%
Geometric Mean (annualized)	6.77%
Standard Deviation (monthly)	2.09%
Standard Deviation (annualized)	7.23%
Downside Deviation (monthly)	1.38%
Maximum Drawdown	-20.20%
Stock Market Correlation	0.75
Beta^(*)	0.36
Alpha (annualized)	3.10%
R²	56.08%
Sharpe Ratio	0.78
Sortino Ratio	1.16
Treynor Ratio (%)	15.64
Calmar Ratio	0.41
Active Return	-2.82%
Tracking Error	10.68%
Information Ratio	-0.26
Skewness	-0.98
Excess Kurtosis	3.72
Historical Value-at-Risk (5%)	-2.83%
Analytical Value-at-Risk (5%)	-2.85%
Conditional Value-at-Risk (5%)	-5.07%
Upside Capture Ratio (%)	41.02
Downside Capture Ratio (%)	29.48
Safe Withdrawal Rate	8.35%
Perpetual Withdrawal Rate	4.08%
Positive Periods	153 out of 220 (69.55%)
Gain/Loss Ratio	0.92
^* 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 Period	Start	End	Maximum Sharpe Ratio
Subprime Crisis	Nov 2007	Mar 2009	-20.20%
COVID-19 Start	Jan 2020	Mar 2020	-5.01%

Drawdowns for Maximum Sharpe Ratio

Drawdowns for Maximum Sharpe Ratio (worst 10)
Rank	Start	End	Length	Recovery By	Recovery Time	Underwater Period	Drawdown
1	Dec 2007	Feb 2009	1 year 3 months	Apr 2010	1 year 2 months	2 years 5 months	-20.20%
2	Jan 2022	Apr 2022	4 months				-13.30%
3	Sep 2018	Oct 2018	2 months	Mar 2019	5 months	7 months	-5.04%
4	Feb 2020	Mar 2020	2 months	Apr 2020	1 month	3 months	-5.01%
5	May 2013	Aug 2013	4 months	Oct 2013	2 months	6 months	-4.89%
6	Mar 2015	Sep 2015	7 months	Mar 2016	6 months	1 year 1 month	-4.59%
7	Aug 2016	Nov 2016	4 months	Apr 2017	5 months	9 months	-4.45%
8	Apr 2004	Apr 2004	1 month	Sep 2004	5 months	6 months	-4.25%
9	Feb 2018	Apr 2018	3 months	Aug 2018	4 months	7 months	-3.28%
10	Sep 2020	Oct 2020	2 months	Nov 2020	1 month	3 months	-3.01%
Worst 10 drawdowns included above

Portfolio Assets

Performance statistics for portfolio components
Ticker	Name	CAGR	Stdev	Best Year	Worst Year	Max Drawdown	Sharpe Ratio	Sortino Ratio	Market Correlation
SPY	SPDR S&P 500 ETF Trust	9.50%	14.41%	32.31%	-36.81%	-50.80%	0.62	0.92	1.00
IJS	iShares S&P Small-Cap 600 Value ETF	9.16%	19.89%	39.34%	-29.39%	-54.13%	0.48	0.71	0.89
EFA	iShares MSCI EAFE ETF	5.07%	16.70%	26.95%	-41.04%	-57.38%	0.31	0.44	0.88
EEM	iShares MSCI Emerging Markets ETF	6.64%	21.38%	68.93%	-48.88%	-60.44%	0.36	0.53	0.77
TLT	iShares 20+ Year Treasury Bond ETF	5.18%	13.15%	33.96%	-21.80%	-28.31%	0.36	0.59	-0.25
IEF	iShares 7-10 Year Treasury Bond ETF	3.73%	6.21%	17.91%	-10.33%	-14.98%	0.43	0.70	-0.26
LQD	iShares iBoxx $ Invmt Grade Corp Bd ETF	4.22%	7.35%	17.37%	-14.52%	-16.09%	0.44	0.67	0.35

Portfolio Asset Performance

Performance of portfolio assets
Name	Total Return			Annualized Return			Expense Ratio
Name	3 Month	Year To Date	1 year	3 year	5 year	10 year	Net	Gross
SPDR S&P 500 ETF Trust	-8.14%	-12.99%	0.04%	13.77%	13.57%	13.56%	0.09%	0.09%
iShares S&P Small-Cap 600 Value ETF	-3.77%	-8.00%	-5.01%	9.29%	8.23%	11.24%	0.18%	0.18%
iShares MSCI EAFE ETF	-9.47%	-12.76%	-9.17%	3.97%	4.49%	5.59%	0.32%	0.32%
iShares MSCI Emerging Markets ETF	-13.23%	-13.24%	-19.96%	0.94%	3.28%	2.15%	0.68%	0.68%
iShares 20+ Year Treasury Bond ETF	-15.76%	-19.05%	-12.47%	0.55%	1.60%	2.58%	0.15%	0.15%
iShares 7-10 Year Treasury Bond ETF	-8.40%	-10.33%	-8.96%	0.25%	0.87%	1.44%	0.15%	0.15%
iShares iBoxx $ Invmt Grade Corp Bd ETF	-11.33%	-14.52%	-12.15%	0.82%	1.92%	2.96%	0.14%	0.14%
Trailing returns as of last calendar month ending April 2022

Monthly Correlations

Correlations for the portfolio assets
Ticker	Name	SPY	IJS	EFA	EEM	TLT	IEF	LQD	Maximum Sharpe Ratio
SPY	SPDR S&P 500 ETF Trust	1.00	0.86	0.88	0.76	-0.25	-0.25	0.35	0.75
IJS	iShares S&P Small-Cap 600 Value ETF	0.86	1.00	0.77	0.70	-0.34	-0.34	0.25	0.61
EFA	iShares MSCI EAFE ETF	0.88	0.77	1.00	0.87	-0.21	-0.19	0.40	0.73
EEM	iShares MSCI Emerging Markets ETF	0.76	0.70	0.87	1.00	-0.20	-0.16	0.37	0.67
TLT	iShares 20+ Year Treasury Bond ETF	-0.25	-0.34	-0.21	-0.20	1.00	0.91	0.54	0.42
IEF	iShares 7-10 Year Treasury Bond ETF	-0.25	-0.34	-0.19	-0.16	0.91	1.00	0.55	0.41
LQD	iShares iBoxx $ Invmt Grade Corp Bd ETF	0.35	0.25	0.40	0.37	0.54	0.55	1.00	0.74

Portfolio Risk Decomposition

Portfolio risk decomposition
Ticker	Name	Maximum Sharpe Ratio
SPY	SPDR S&P 500 ETF Trust	42.24%
IJS	iShares S&P Small-Cap 600 Value ETF	8.37%
EFA	iShares MSCI EAFE ETF	8.44%
EEM	iShares MSCI Emerging Markets ETF	9.90%
TLT	iShares 20+ Year Treasury Bond ETF	16.62%
IEF	iShares 7-10 Year Treasury Bond ETF	10.66%
LQD	iShares iBoxx $ Invmt Grade Corp Bd ETF	3.77%
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 Period	Average	High	Low
1 year	7.82%	22.57%	-18.17%
3 years	7.48%	16.76%	-2.00%
5 years	7.27%	12.85%	1.65%
7 years	7.54%	10.54%	5.35%
10 years	7.63%	9.29%	6.30%
15 years	7.33%	7.99%	6.31%