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 - Sep 2022) Save

Note: The time period was constrained by the available data for iShares MSCI Emerging Markets ETF (EEM) [May 2003 - Sep 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 5.27% to 7.97%. Refer to the efficient frontier section for additional details.

Portfolio Allocations

Maximum Sharpe Ratio
Ticker	Name	Allocation
SPY	SPDR S&P 500 ETF Trust	30.16%
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	19.84%
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	$29,995
Annualized Return (CAGR)	6.03%
Expected Return	6.17%
Standard Deviation	7.73%
Best Year	19.03%
Worst Year	-22.66%
Maximum Drawdown	-22.66%
Sharpe Ratio (ex-ante)	0.65
Sharpe Ratio (ex-post)	0.64
Sortino Ratio	0.92
Stock Market Correlation	0.80
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	-7.03%	-22.66%	-19.33%	-0.32%	2.74%	4.83%	6.03%	10.95%	9.42%
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.
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 September.
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	9.29%	14.77%	0.549	5.00%	40.00%
2	iShares S&P Small-Cap 600 Value ETF (IJS)	Equity	9.89%	20.08%	0.434	5.00%	20.00%
3	iShares MSCI EAFE ETF (EFA)	Equity	5.33%	16.91%	0.245	5.00%	30.00%
4	iShares MSCI Emerging Markets ETF (EEM)	Equity	7.61%	21.38%	0.301	5.00%	15.00%
5	iShares 20+ Year Treasury Bond ETF (TLT)	Fixed Income	5.04%	13.24%	0.291	5.00%	30.00%
6	iShares 7-10 Year Treasury Bond ETF (IEF)	Fixed Income	3.46%	6.36%	0.357	5.00%	30.00%
7	iShares iBoxx $ Invmt Grade Corp Bd ETF (LQD)	Fixed Income	3.90%	7.62%	0.356	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	0.87	0.88	0.75	-0.20	-0.17	0.40
iShares S&P Small-Cap 600 Value ETF	IJS	0.87	1.00	0.78	0.70	-0.29	-0.28	0.29
iShares MSCI EAFE ETF	EFA	0.88	0.78	1.00	0.86	-0.17	-0.13	0.44
iShares MSCI Emerging Markets ETF	EEM	0.75	0.70	0.86	1.00	-0.17	-0.12	0.39
iShares 20+ Year Treasury Bond ETF	TLT	-0.20	-0.29	-0.17	-0.17	1.00	0.91	0.56
iShares 7-10 Year Treasury Bond ETF	IEF	-0.17	-0.28	-0.13	-0.12	0.91	1.00	0.59
iShares iBoxx $ Invmt Grade Corp Bd ETF	LQD	0.40	0.29	0.44	0.39	0.56	0.59	1.00
Based on monthly returns from Jan 2004 to Sep 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	13.02%	5.00%	5.00%	5.00%	21.98%	30.00%	20.00%	5.27%	7.05%	0.580
2	13.66%	5.00%	5.00%	5.00%	21.34%	30.00%	20.00%	5.30%	7.05%	0.584
3	14.30%	5.00%	5.00%	5.00%	20.70%	30.00%	20.00%	5.33%	7.06%	0.588
4	14.94%	5.00%	5.00%	5.00%	20.06%	30.00%	20.00%	5.36%	7.06%	0.591
5	15.58%	5.00%	5.00%	5.00%	19.42%	30.00%	20.00%	5.38%	7.07%	0.594
6	16.22%	5.00%	5.00%	5.00%	18.78%	30.00%	20.00%	5.41%	7.08%	0.597
7	16.87%	5.00%	5.00%	5.00%	18.13%	30.00%	20.00%	5.44%	7.10%	0.599
8	17.35%	5.00%	5.00%	5.00%	18.23%	30.00%	19.42%	5.47%	7.12%	0.602
9	17.78%	5.00%	5.00%	5.00%	18.60%	30.00%	18.62%	5.49%	7.13%	0.604
10	18.21%	5.00%	5.00%	5.00%	18.98%	30.00%	17.82%	5.52%	7.15%	0.606
11	18.63%	5.00%	5.00%	5.00%	19.35%	30.00%	17.02%	5.55%	7.17%	0.609
12	19.06%	5.00%	5.00%	5.00%	19.72%	30.00%	16.22%	5.57%	7.19%	0.611
13	19.49%	5.00%	5.00%	5.00%	20.10%	30.00%	15.42%	5.60%	7.21%	0.613
14	19.91%	5.00%	5.00%	5.00%	20.47%	30.00%	14.62%	5.63%	7.23%	0.615
15	20.34%	5.00%	5.00%	5.00%	20.84%	30.00%	13.82%	5.66%	7.25%	0.617
16	20.77%	5.00%	5.00%	5.00%	21.22%	30.00%	13.02%	5.68%	7.27%	0.619
17	21.19%	5.00%	5.00%	5.00%	21.59%	30.00%	12.22%	5.71%	7.28%	0.621
18	21.62%	5.00%	5.00%	5.00%	21.96%	30.00%	11.42%	5.74%	7.31%	0.623
19	22.05%	5.00%	5.00%	5.00%	22.34%	30.00%	10.62%	5.76%	7.33%	0.625
20	22.47%	5.00%	5.00%	5.00%	22.71%	30.00%	9.82%	5.79%	7.35%	0.627
21	22.90%	5.00%	5.00%	5.00%	23.08%	30.00%	9.02%	5.82%	7.37%	0.629
22	23.33%	5.00%	5.00%	5.00%	23.45%	30.00%	8.22%	5.85%	7.39%	0.631
23	23.75%	5.00%	5.00%	5.00%	23.83%	30.00%	7.42%	5.87%	7.41%	0.633
24	24.18%	5.00%	5.00%	5.00%	24.20%	30.00%	6.62%	5.90%	7.43%	0.635
25	24.61%	5.00%	5.00%	5.00%	24.57%	30.00%	5.82%	5.93%	7.45%	0.637
26	25.03%	5.00%	5.00%	5.00%	24.95%	30.00%	5.02%	5.96%	7.48%	0.638
27	25.67%	5.00%	5.00%	5.00%	24.33%	30.00%	5.00%	5.98%	7.50%	0.640
28	26.31%	5.00%	5.00%	5.00%	23.69%	30.00%	5.00%	6.01%	7.53%	0.641
29	26.95%	5.00%	5.00%	5.00%	23.05%	30.00%	5.00%	6.04%	7.55%	0.643
30	27.59%	5.00%	5.00%	5.00%	22.41%	30.00%	5.00%	6.06%	7.59%	0.643
31	28.23%	5.00%	5.00%	5.00%	21.77%	30.00%	5.00%	6.09%	7.62%	0.644
32	28.88%	5.00%	5.00%	5.00%	21.12%	30.00%	5.00%	6.12%	7.66%	0.645
33	29.52%	5.00%	5.00%	5.00%	20.48%	30.00%	5.00%	6.15%	7.69%	0.645
34	30.16%	5.00%	5.00%	5.00%	19.84%	30.00%	5.00%	6.17%	7.73%	0.645
35	30.76%	5.00%	5.00%	5.00%	19.34%	29.90%	5.00%	6.20%	7.78%	0.645
36	31.08%	5.00%	5.00%	5.00%	19.89%	29.03%	5.00%	6.23%	7.82%	0.645
37	31.40%	5.00%	5.00%	5.00%	20.45%	28.15%	5.00%	6.26%	7.86%	0.645
38	31.71%	5.00%	5.00%	5.00%	21.01%	27.28%	5.00%	6.28%	7.91%	0.645
39	32.03%	5.00%	5.00%	5.00%	21.57%	26.40%	5.00%	6.31%	7.95%	0.645
40	32.35%	5.00%	5.00%	5.00%	22.12%	25.53%	5.00%	6.34%	8.00%	0.644
41	32.66%	5.00%	5.00%	5.00%	22.68%	24.66%	5.00%	6.36%	8.04%	0.644
42	32.98%	5.00%	5.00%	5.00%	23.24%	23.78%	5.00%	6.39%	8.09%	0.644
43	33.29%	5.00%	5.00%	5.00%	23.80%	22.91%	5.00%	6.42%	8.13%	0.644
44	33.61%	5.00%	5.00%	5.00%	24.35%	22.04%	5.00%	6.45%	8.18%	0.644
45	33.93%	5.00%	5.00%	5.00%	24.91%	21.16%	5.00%	6.47%	8.22%	0.644
46	34.24%	5.00%	5.00%	5.00%	25.47%	20.29%	5.00%	6.50%	8.26%	0.643
47	34.56%	5.00%	5.00%	5.00%	26.03%	19.41%	5.00%	6.53%	8.31%	0.643
48	34.88%	5.00%	5.00%	5.00%	26.58%	18.54%	5.00%	6.56%	8.35%	0.643
49	35.19%	5.00%	5.00%	5.00%	27.14%	17.67%	5.00%	6.58%	8.40%	0.643
50	35.51%	5.00%	5.00%	5.00%	27.70%	16.79%	5.00%	6.61%	8.44%	0.643
51	35.82%	5.00%	5.00%	5.00%	28.26%	15.92%	5.00%	6.64%	8.49%	0.642
52	36.14%	5.00%	5.00%	5.00%	28.81%	15.05%	5.00%	6.66%	8.54%	0.642
53	36.46%	5.00%	5.00%	5.00%	29.37%	14.17%	5.00%	6.69%	8.58%	0.642
54	36.77%	5.00%	5.00%	5.00%	29.93%	13.30%	5.00%	6.72%	8.63%	0.642
55	37.22%	5.00%	5.00%	5.00%	30.00%	12.78%	5.00%	6.75%	8.67%	0.641
56	37.69%	5.00%	5.00%	5.00%	30.00%	12.31%	5.00%	6.77%	8.72%	0.641
57	38.16%	5.00%	5.00%	5.00%	30.00%	11.84%	5.00%	6.80%	8.77%	0.641
58	38.62%	5.00%	5.00%	5.00%	30.00%	11.38%	5.00%	6.83%	8.81%	0.641
59	39.09%	5.00%	5.00%	5.00%	30.00%	10.91%	5.00%	6.86%	8.86%	0.640
60	39.56%	5.00%	5.00%	5.00%	30.00%	10.44%	5.00%	6.88%	8.91%	0.640
61	40.00%	5.02%	5.00%	5.00%	30.00%	9.98%	5.00%	6.91%	8.96%	0.639
62	40.00%	5.45%	5.00%	5.00%	30.00%	9.55%	5.00%	6.94%	9.01%	0.639
63	40.00%	5.87%	5.00%	5.00%	30.00%	9.13%	5.00%	6.96%	9.06%	0.638
64	40.00%	6.30%	5.00%	5.00%	30.00%	8.70%	5.00%	6.99%	9.11%	0.637
65	40.00%	6.72%	5.00%	5.00%	30.00%	8.28%	5.00%	7.02%	9.17%	0.637
66	40.00%	7.14%	5.00%	5.00%	30.00%	7.86%	5.00%	7.05%	9.22%	0.636
67	40.00%	7.57%	5.00%	5.00%	30.00%	7.43%	5.00%	7.07%	9.28%	0.635
68	40.00%	7.99%	5.00%	5.00%	30.00%	7.01%	5.00%	7.10%	9.33%	0.634
69	40.00%	8.41%	5.00%	5.00%	30.00%	6.59%	5.00%	7.13%	9.39%	0.633
70	40.00%	8.84%	5.00%	5.00%	30.00%	6.16%	5.00%	7.15%	9.45%	0.632
71	40.00%	9.26%	5.00%	5.00%	30.00%	5.74%	5.00%	7.18%	9.50%	0.631
72	40.00%	9.68%	5.00%	5.00%	30.00%	5.32%	5.00%	7.21%	9.56%	0.630
73	40.00%	10.14%	5.00%	5.00%	29.86%	5.00%	5.00%	7.24%	9.62%	0.629
74	40.00%	10.70%	5.00%	5.00%	29.30%	5.00%	5.00%	7.26%	9.69%	0.627
75	40.00%	11.26%	5.00%	5.00%	28.74%	5.00%	5.00%	7.29%	9.76%	0.626
76	40.00%	11.83%	5.00%	5.00%	28.17%	5.00%	5.00%	7.32%	9.84%	0.624
77	40.00%	12.39%	5.00%	5.00%	27.61%	5.00%	5.00%	7.35%	9.91%	0.622
78	40.00%	12.95%	5.00%	5.00%	27.05%	5.00%	5.00%	7.37%	9.99%	0.620
79	40.00%	13.51%	5.00%	5.00%	26.49%	5.00%	5.00%	7.40%	10.07%	0.617
80	40.00%	14.07%	5.00%	5.00%	25.93%	5.00%	5.00%	7.43%	10.15%	0.615
81	40.00%	14.63%	5.00%	5.00%	25.37%	5.00%	5.00%	7.45%	10.23%	0.613
82	40.00%	15.19%	5.00%	5.00%	24.81%	5.00%	5.00%	7.48%	10.31%	0.611
83	40.00%	15.76%	5.00%	5.00%	24.24%	5.00%	5.00%	7.51%	10.40%	0.608
84	40.00%	16.32%	5.00%	5.00%	23.68%	5.00%	5.00%	7.54%	10.49%	0.606
85	40.00%	16.88%	5.00%	5.00%	23.12%	5.00%	5.00%	7.56%	10.57%	0.603
86	40.00%	17.44%	5.00%	5.00%	22.56%	5.00%	5.00%	7.59%	10.66%	0.601
87	40.00%	18.00%	5.00%	5.00%	22.00%	5.00%	5.00%	7.62%	10.75%	0.598
88	40.00%	18.56%	5.00%	5.00%	21.44%	5.00%	5.00%	7.65%	10.85%	0.596
89	40.00%	19.12%	5.00%	5.00%	20.88%	5.00%	5.00%	7.67%	10.94%	0.593
90	40.00%	19.69%	5.00%	5.00%	20.31%	5.00%	5.00%	7.70%	11.04%	0.591
91	40.00%	20.00%	5.00%	5.47%	19.53%	5.00%	5.00%	7.73%	11.17%	0.586
92	40.00%	20.00%	5.00%	6.53%	18.47%	5.00%	5.00%	7.75%	11.34%	0.579
93	40.00%	20.00%	5.00%	7.59%	17.41%	5.00%	5.00%	7.78%	11.52%	0.573
94	40.00%	20.00%	5.00%	8.64%	16.36%	5.00%	5.00%	7.81%	11.71%	0.566
95	40.00%	20.00%	5.00%	9.70%	15.30%	5.00%	5.00%	7.84%	11.90%	0.559
96	40.00%	20.00%	5.00%	10.76%	14.24%	5.00%	5.00%	7.86%	12.09%	0.553
97	40.00%	20.00%	5.00%	11.82%	13.18%	5.00%	5.00%	7.89%	12.28%	0.546
98	40.00%	20.00%	5.00%	12.88%	12.12%	5.00%	5.00%	7.92%	12.48%	0.540
99	40.00%	20.00%	5.00%	13.94%	11.06%	5.00%	5.00%	7.95%	12.69%	0.533
100	40.00%	20.00%	5.00%	15.00%	10.00%	5.00%	5.00%	7.97%	12.89%	0.527
^*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%	9.85%	$10,985	10.70%	22.60%	18.95%	24.63%	8.71%	4.12%	5.72%
2005	3.42%	6.73%	$11,724	4.83%	6.00%	13.32%	32.62%	8.61%	2.64%	1.16%
2006	2.54%	9.59%	$12,848	15.85%	19.37%	25.81%	31.19%	0.71%	2.52%	4.22%
2007	4.08%	8.92%	$13,994	5.14%	-5.56%	9.94%	33.31%	10.29%	10.37%	3.73%
2008	0.09%	-8.76%	$12,769	-36.81%	-29.39%	-41.04%	-48.88%	33.93%	17.91%	2.40%
2009	2.72%	6.53%	$13,603	26.36%	22.36%	26.95%	68.93%	-21.80%	-6.59%	8.46%
2010	1.50%	13.13%	$15,389	15.06%	24.69%	8.15%	16.51%	9.05%	9.37%	9.33%
2011	2.96%	10.96%	$17,076	1.89%	-1.65%	-12.25%	-18.82%	33.96%	15.64%	9.73%
2012	1.74%	10.12%	$18,804	15.99%	18.24%	18.82%	19.10%	2.63%	3.66%	10.58%
2013	1.50%	6.55%	$20,036	32.31%	39.34%	21.40%	-3.69%	-13.37%	-6.09%	-2.00%
2014	0.76%	12.36%	$22,511	13.46%	7.56%	-6.20%	-3.93%	27.30%	9.07%	8.21%
2015	0.73%	-0.39%	$22,423	1.25%	-6.90%	-1.00%	-16.18%	-1.79%	1.51%	-1.25%
2016	2.07%	6.85%	$23,958	12.00%	31.25%	1.37%	10.87%	1.18%	1.00%	6.21%
2017	2.11%	12.88%	$27,045	21.70%	11.35%	25.10%	37.28%	9.18%	2.55%	7.06%
2018	1.91%	-3.36%	$26,135	-4.56%	-12.84%	-13.81%	-15.31%	-1.61%	0.99%	-3.79%
2019	2.29%	19.03%	$31,109	31.22%	24.12%	22.03%	18.20%	14.12%	8.03%	17.37%
2020	1.36%	15.50%	$35,931	18.37%	2.63%	7.59%	17.03%	18.15%	10.01%	10.97%
2021	7.04%	7.93%	$38,782	28.74%	30.53%	11.46%	-3.61%	-4.60%	-3.33%	-1.85%
2022	6.23%	-22.66%	$29,995	-23.93%	-20.15%	-27.20%	-27.98%	-29.92%	-15.68%	-21.24%
Annual return for 2022 is from 01/01/2022 to 09/30/2022

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	1.62%	$10,162	1.98%	2.17%	1.13%	2.42%	1.86%	1.02%	1.22%
2004	2	1.86%	$10,351	1.36%	2.50%	2.30%	3.95%	2.28%	1.61%	1.51%
2004	3	0.44%	$10,396	-1.32%	1.82%	0.07%	0.55%	1.41%	1.30%	0.99%
2004	4	-4.16%	$9,964	-1.89%	-3.93%	-3.39%	-9.80%	-6.23%	-4.35%	-3.89%
2004	5	0.47%	$10,011	1.71%	1.58%	1.14%	1.17%	-0.26%	-0.53%	-0.52%
2004	6	1.45%	$10,156	1.85%	5.35%	3.35%	0.92%	1.06%	0.65%	0.13%
2004	7	-0.86%	$10,069	-3.22%	-4.75%	-4.27%	-3.64%	1.53%	1.21%	1.56%
2004	8	2.15%	$10,286	0.24%	0.24%	1.19%	3.53%	4.17%	2.83%	3.08%
2004	9	1.29%	$10,418	1.00%	4.69%	2.07%	6.98%	0.95%	0.32%	0.31%
2004	10	1.46%	$10,570	1.29%	0.95%	3.50%	2.85%	1.77%	0.99%	1.18%
2004	11	1.47%	$10,726	4.45%	9.11%	6.08%	9.95%	-2.39%	-1.98%	-1.22%
2004	12	2.41%	$10,985	3.02%	1.57%	4.80%	4.74%	2.66%	1.17%	1.39%
2005	1	0.07%	$10,992	-2.24%	-3.25%	-1.90%	-0.53%	3.57%	0.87%	1.23%
2005	2	0.70%	$11,069	2.09%	2.90%	3.78%	9.68%	-1.47%	-1.37%	-0.94%
2005	3	-1.47%	$10,906	-1.83%	-2.36%	-2.62%	-7.91%	-0.45%	-0.40%	-1.26%
2005	4	0.64%	$10,976	-1.87%	-5.12%	-1.62%	-1.25%	3.86%	2.52%	1.62%
2005	5	2.60%	$11,261	3.22%	6.16%	-0.86%	3.16%	3.14%	1.84%	0.62%
2005	6	1.14%	$11,390	0.15%	3.92%	1.43%	3.97%	2.16%	0.48%	1.22%
2005	7	0.61%	$11,460	3.83%	5.84%	3.00%	7.68%	-3.38%	-2.18%	-0.82%
2005	8	1.25%	$11,603	-0.94%	-1.87%	3.84%	1.32%	3.48%	2.00%	1.50%
2005	9	-0.47%	$11,548	0.80%	0.05%	3.69%	8.65%	-3.61%	-1.75%	-1.86%
2005	10	-2.25%	$11,288	-2.37%	-3.41%	-3.18%	-6.34%	-2.24%	-1.24%	-1.58%
2005	11	2.33%	$11,551	4.40%	4.91%	2.31%	5.79%	0.69%	0.63%	0.66%
2005	12	1.50%	$11,724	-0.19%	-1.06%	5.18%	6.10%	2.98%	1.37%	0.86%
2006	1	1.66%	$11,919	2.40%	8.75%	5.77%	14.20%	-1.34%	-0.70%	-0.44%
2006	2	0.18%	$11,941	0.57%	0.27%	-0.70%	-3.85%	1.11%	-0.10%	0.68%
2006	3	-0.35%	$11,899	1.65%	4.86%	4.01%	2.17%	-4.57%	-1.36%	-1.68%
2006	4	0.21%	$11,924	1.26%	0.18%	4.79%	6.52%	-2.75%	-0.63%	-0.20%
2006	5	-1.96%	$11,690	-3.01%	-4.55%	-3.82%	-11.14%	-0.19%	-0.10%	-0.19%
2006	6	0.39%	$11,736	0.26%	0.04%	-0.06%	0.21%	1.18%	0.23%	-0.09%
2006	7	1.14%	$11,870	0.45%	-3.10%	0.81%	2.34%	2.16%	1.68%	1.46%
2006	8	2.25%	$12,136	2.18%	2.70%	2.55%	1.58%	3.06%	1.76%	2.22%
2006	9	1.63%	$12,334	2.70%	1.19%	0.22%	-0.87%	1.91%	1.21%	0.87%
2006	10	2.15%	$12,598	3.15%	5.52%	3.75%	7.06%	0.85%	0.54%	1.00%
2006	11	2.10%	$12,862	1.99%	2.38%	3.07%	5.98%	2.31%	1.31%	1.46%
2006	12	-0.11%	$12,848	1.34%	0.32%	3.20%	5.44%	-2.69%	-1.28%	-0.90%
2007	1	0.32%	$12,890	1.50%	2.14%	1.39%	0.11%	-1.00%	-0.40%	0.09%
2007	2	0.58%	$12,965	-1.96%	-0.92%	-0.12%	-3.24%	3.39%	2.06%	2.00%
2007	3	0.39%	$13,016	1.16%	0.91%	2.90%	5.33%	-1.70%	-0.14%	-0.68%
2007	4	2.21%	$13,303	4.43%	1.84%	3.75%	3.73%	0.90%	0.61%	0.89%
2007	5	0.69%	$13,395	3.39%	4.63%	2.36%	5.06%	-2.31%	-1.39%	-1.23%
2007	6	-0.77%	$13,292	-1.46%	-2.24%	-0.32%	3.68%	-1.01%	-0.47%	-0.81%
2007	7	-0.04%	$13,286	-3.13%	-6.26%	-2.29%	0.71%	3.32%	2.26%	-0.82%
2007	8	1.63%	$13,503	1.28%	1.33%	-0.63%	1.04%	1.79%	2.26%	2.38%
2007	9	2.14%	$13,791	3.87%	0.31%	5.32%	11.57%	0.23%	0.09%	0.73%
2007	10	2.00%	$14,067	1.36%	1.06%	4.25%	11.87%	1.81%	1.08%	0.97%
2007	11	0.24%	$14,100	-3.87%	-7.15%	-3.62%	-7.65%	5.35%	4.04%	1.02%
2007	12	-0.75%	$13,994	-1.13%	-0.71%	-2.99%	-1.43%	-0.64%	0.05%	-0.81%
2008	1	-1.31%	$13,811	-6.05%	-4.00%	-7.85%	-8.92%	2.10%	3.36%	2.57%
2008	2	-0.65%	$13,720	-2.58%	-3.36%	-1.02%	1.99%	-0.46%	1.24%	-0.71%
2008	3	0.40%	$13,775	-0.90%	0.83%	0.42%	-3.75%	2.14%	1.34%	-0.60%
2008	4	1.14%	$13,933	4.77%	2.64%	5.44%	9.14%	-2.48%	-2.41%	1.25%
2008	5	-0.31%	$13,890	1.51%	3.92%	1.19%	3.16%	-2.69%	-1.78%	-2.21%
2008	6	-3.04%	$13,468	-8.35%	-8.41%	-8.80%	-9.29%	2.65%	1.14%	-1.29%
2008	7	-0.41%	$13,413	-0.90%	2.87%	-3.32%	-5.50%	-0.37%	0.72%	0.39%
2008	8	1.18%	$13,572	1.55%	4.76%	-4.25%	-6.32%	2.74%	1.53%	0.15%
2008	9	-4.68%	$12,937	-9.44%	-4.82%	-11.44%	-14.68%	1.47%	-0.14%	-10.73%
2008	10	-9.02%	$11,770	-16.52%	-19.86%	-20.83%	-25.58%	-1.86%	-0.87%	-1.95%
2008	11	1.84%	$11,986	-6.96%	-11.80%	-6.37%	-9.75%	14.34%	7.75%	3.35%
2008	12	6.53%	$12,769	0.98%	6.57%	8.88%	10.35%	13.64%	5.15%	13.80%
2009	1	-8.17%	$11,725	-8.21%	-13.94%	-13.73%	-9.29%	-13.07%	-3.89%	-1.80%
2009	2	-5.51%	$11,079	-10.74%	-13.03%	-10.39%	-6.27%	-1.54%	-0.74%	-5.20%
2009	3	5.98%	$11,741	8.35%	7.58%	8.39%	16.86%	4.04%	3.31%	0.47%
2009	4	3.23%	$12,121	9.93%	18.89%	11.52%	15.56%	-6.95%	-2.75%	2.78%
2009	5	2.01%	$12,365	5.85%	0.67%	13.19%	15.94%	-3.69%	-2.08%	2.32%
2009	6	0.00%	$12,365	-0.07%	1.52%	-1.43%	-2.25%	0.76%	-0.55%	2.89%
2009	7	4.45%	$12,915	7.46%	11.00%	10.04%	11.01%	0.58%	0.83%	4.63%
2009	8	2.19%	$13,197	3.69%	3.48%	4.50%	-1.31%	2.24%	0.77%	1.31%
2009	9	2.89%	$13,579	3.55%	4.21%	3.80%	10.20%	2.46%	1.12%	1.76%
2009	10	-1.77%	$13,339	-1.92%	-6.07%	-2.52%	-3.44%	-2.62%	-0.14%	-0.49%
2009	11	3.54%	$13,811	6.16%	2.90%	3.92%	7.85%	1.21%	2.02%	1.95%
2009	12	-1.50%	$13,603	1.91%	8.10%	0.70%	3.27%	-6.34%	-4.40%	-2.07%
2010	1	-0.56%	$13,527	-3.63%	-2.54%	-5.07%	-7.76%	2.69%	2.37%	1.25%
2010	2	1.34%	$13,708	3.12%	4.76%	0.27%	1.78%	-0.34%	0.33%	0.51%
2010	3	2.26%	$14,018	6.09%	7.80%	6.39%	8.11%	-2.06%	-1.06%	0.65%
2010	4	1.90%	$14,284	1.55%	6.63%	-2.80%	-0.17%	3.32%	1.65%	1.91%
2010	5	-2.02%	$13,995	-7.95%	-8.54%	-11.19%	-9.39%	5.11%	2.93%	-1.31%
2010	6	0.08%	$14,006	-5.17%	-8.27%	-2.07%	-1.40%	5.80%	3.05%	3.28%
2010	7	3.71%	$14,526	6.83%	6.71%	11.61%	10.93%	-0.95%	0.91%	2.11%
2010	8	0.71%	$14,630	-4.50%	-7.91%	-3.80%	-3.24%	8.40%	3.36%	2.86%
2010	9	3.86%	$15,194	8.96%	10.93%	9.97%	11.76%	-2.51%	-0.00%	0.46%
2010	10	0.79%	$15,315	3.82%	4.04%	3.81%	3.02%	-4.47%	-0.01%	-0.26%
2010	11	-0.95%	$15,170	0.00%	2.47%	-4.82%	-2.91%	-1.69%	-0.90%	-1.62%
2010	12	1.45%	$15,389	6.68%	8.97%	8.30%	7.27%	-3.68%	-3.43%	-0.75%
2011	1	-0.01%	$15,387	2.33%	-0.24%	2.10%	-3.84%	-3.08%	-0.02%	0.04%
2011	2	1.75%	$15,657	3.47%	4.21%	3.55%	-0.04%	1.65%	-0.21%	1.08%
2011	3	0.24%	$15,695	0.01%	2.21%	-2.39%	6.29%	0.03%	-0.15%	-0.54%
2011	4	2.49%	$16,085	2.90%	1.06%	5.63%	2.73%	2.34%	1.84%	2.50%
2011	5	0.81%	$16,215	-1.12%	-1.77%	-2.21%	-2.94%	3.42%	2.51%	1.27%
2011	6	-1.35%	$15,996	-1.69%	-1.59%	-1.19%	-0.93%	-2.33%	-0.51%	-0.80%
2011	7	1.04%	$16,162	-2.00%	-2.77%	-2.38%	-1.03%	4.42%	3.17%	2.43%
2011	8	0.37%	$16,222	-5.50%	-7.98%	-8.75%	-9.25%	9.66%	4.65%	0.34%
2011	9	-0.75%	$16,100	-6.94%	-10.57%	-10.81%	-17.89%	13.20%	2.24%	0.35%
2011	10	4.33%	$16,798	10.91%	15.34%	9.63%	16.27%	-3.84%	-1.29%	2.51%
2011	11	0.11%	$16,816	-0.41%	0.63%	-2.18%	-1.96%	1.98%	0.58%	-3.16%
2011	12	1.54%	$17,076	1.04%	2.02%	-2.21%	-4.30%	3.44%	1.99%	3.49%
2012	1	2.91%	$17,572	4.64%	7.90%	5.27%	10.99%	-0.33%	0.86%	2.14%
2012	2	1.14%	$17,772	4.34%	1.71%	4.83%	5.27%	-2.59%	-1.10%	1.63%
2012	3	-0.41%	$17,699	3.22%	2.89%	0.42%	-3.11%	-4.23%	-1.59%	-1.42%
2012	4	1.28%	$17,926	-0.67%	-1.91%	-2.08%	-1.70%	4.83%	2.51%	1.08%
2012	5	-0.57%	$17,823	-6.01%	-7.18%	-11.14%	-10.71%	9.03%	2.87%	0.76%
2012	6	1.64%	$18,116	4.05%	4.54%	7.11%	5.08%	-1.68%	-0.42%	0.87%
2012	7	1.68%	$18,420	1.18%	-0.69%	0.08%	-0.03%	3.82%	1.40%	3.48%
2012	8	0.84%	$18,575	2.51%	4.08%	3.20%	0.41%	-1.32%	-0.12%	-0.05%
2012	9	0.77%	$18,717	2.54%	3.14%	2.71%	5.22%	-2.53%	-0.35%	1.10%
2012	10	-0.76%	$18,575	-1.82%	-1.96%	1.09%	-0.44%	-0.48%	-0.40%	1.35%
2012	11	1.02%	$18,763	0.57%	1.65%	2.78%	1.56%	1.38%	0.98%	-0.42%
2012	12	0.21%	$18,804	0.90%	3.55%	4.37%	6.80%	-2.49%	-0.94%	-0.33%
2013	1	0.90%	$18,973	5.12%	5.35%	3.73%	-0.29%	-3.19%	-1.29%	-1.30%
2013	2	0.93%	$19,149	1.28%	1.63%	-1.29%	-2.28%	1.24%	1.13%	1.08%
2013	3	1.37%	$19,410	3.80%	4.11%	1.31%	-1.02%	-0.42%	0.29%	-0.05%
2013	4	2.39%	$19,875	1.92%	0.12%	5.02%	1.22%	4.68%	1.52%	2.17%
2013	5	-1.90%	$19,497	2.36%	4.29%	-3.02%	-4.83%	-6.76%	-3.11%	-3.22%
2013	6	-2.39%	$19,031	-1.34%	-0.14%	-2.70%	-5.35%	-3.27%	-2.55%	-3.27%
2013	7	1.72%	$19,359	5.17%	6.56%	5.32%	1.32%	-2.26%	-0.35%	1.11%
2013	8	-2.04%	$18,963	-3.00%	-3.41%	-1.96%	-2.54%	-1.34%	-1.42%	-1.00%
2013	9	2.76%	$19,487	3.17%	6.59%	7.82%	7.21%	0.66%	1.85%	0.74%
2013	10	2.55%	$19,983	4.63%	3.48%	3.26%	4.17%	1.43%	0.78%	1.81%
2013	11	0.32%	$20,047	2.96%	4.25%	0.55%	-0.26%	-2.70%	-0.88%	-0.14%
2013	12	-0.05%	$20,036	2.59%	1.29%	2.16%	-0.42%	-1.87%	-2.09%	0.22%
2014	1	0.33%	$20,102	-3.52%	-3.51%	-5.20%	-8.64%	6.30%	3.06%	1.88%
2014	2	2.35%	$20,574	4.55%	4.63%	6.13%	3.38%	0.52%	0.36%	1.14%
2014	3	0.46%	$20,670	0.83%	1.34%	-0.46%	3.88%	0.73%	-0.56%	-0.03%
2014	4	0.93%	$20,861	0.70%	-2.29%	1.67%	0.78%	2.10%	0.76%	1.33%
2014	5	2.17%	$21,313	2.32%	0.62%	1.60%	2.95%	2.95%	1.82%	1.51%
2014	6	0.87%	$21,498	2.06%	3.85%	0.92%	2.40%	-0.25%	-0.22%	0.01%
2014	7	-0.67%	$21,354	-1.34%	-5.07%	-2.60%	1.36%	0.67%	-0.22%	-0.32%
2014	8	3.16%	$22,030	3.95%	4.46%	0.18%	2.83%	4.72%	1.88%	2.00%
2014	9	-2.11%	$21,564	-1.38%	-5.94%	-3.88%	-7.77%	-2.11%	-1.05%	-1.68%
2014	10	2.20%	$22,040	2.36%	7.13%	-0.27%	1.42%	2.81%	1.53%	1.23%
2014	11	1.80%	$22,436	2.75%	0.48%	0.06%	-1.54%	2.97%	1.29%	0.91%
2014	12	0.33%	$22,511	-0.26%	2.56%	-4.00%	-3.99%	3.25%	0.13%	-0.02%
2015	1	2.26%	$23,021	-2.96%	-5.32%	0.62%	-0.69%	9.82%	4.30%	3.75%
2015	2	0.50%	$23,135	5.62%	5.86%	6.34%	4.41%	-6.14%	-2.47%	-1.42%
2015	3	-0.09%	$23,115	-1.57%	1.03%	-1.43%	-1.50%	1.10%	0.86%	0.20%
2015	4	-0.20%	$23,069	0.98%	-1.82%	3.65%	6.85%	-3.43%	-0.63%	-1.19%
2015	5	-0.42%	$22,972	1.29%	0.75%	0.20%	-4.10%	-2.37%	-0.42%	-1.12%
2015	6	-2.28%	$22,447	-2.03%	0.42%	-3.12%	-2.93%	-4.07%	-1.63%	-1.88%
2015	7	1.73%	$22,836	2.26%	-2.70%	2.03%	-6.31%	4.55%	1.52%	0.83%
2015	8	-3.04%	$22,143	-6.10%	-4.62%	-7.43%	-8.84%	-0.69%	0.08%	-0.83%
2015	9	-0.41%	$22,052	-2.54%	-3.77%	-4.42%	-3.13%	1.97%	1.58%	1.19%
2015	10	3.30%	$22,779	8.51%	6.57%	6.61%	6.38%	-0.41%	-0.64%	0.57%
2015	11	-0.24%	$22,725	0.37%	2.47%	-0.75%	-2.52%	-0.87%	-0.43%	-0.15%
2015	12	-1.33%	$22,423	-1.72%	-5.08%	-2.34%	-3.83%	-0.30%	-0.45%	-1.08%
2016	1	-0.21%	$22,376	-4.98%	-5.85%	-5.52%	-5.03%	5.57%	3.33%	0.12%
2016	2	0.98%	$22,595	-0.08%	2.08%	-3.33%	-0.82%	3.09%	1.49%	1.05%
2016	3	3.62%	$23,413	6.72%	9.41%	6.58%	12.96%	-0.09%	-0.06%	3.62%
2016	4	0.24%	$23,470	0.39%	2.13%	2.22%	0.41%	-0.74%	-0.16%	1.55%
2016	5	0.45%	$23,576	1.70%	0.44%	-0.09%	-3.69%	0.81%	-0.10%	-0.51%
2016	6	2.71%	$24,215	0.35%	0.83%	-2.42%	4.56%	6.93%	3.09%	3.09%
2016	7	2.38%	$24,790	3.65%	5.06%	3.98%	5.38%	2.10%	0.25%	1.29%
2016	8	-0.33%	$24,708	0.12%	1.13%	0.53%	0.88%	-1.01%	-1.01%	0.18%
2016	9	-0.01%	$24,707	0.01%	0.87%	1.34%	2.52%	-1.51%	0.24%	-0.32%
2016	10	-2.26%	$24,149	-1.73%	-3.74%	-2.22%	-0.83%	-4.38%	-1.49%	-1.53%
2016	11	-1.59%	$23,766	3.68%	13.34%	-1.78%	-4.42%	-8.21%	-4.23%	-3.17%
2016	12	0.81%	$23,958	2.03%	3.20%	2.71%	-0.25%	-0.46%	-0.12%	0.84%
2017	1	1.21%	$24,249	1.79%	-1.21%	3.29%	6.66%	0.81%	0.22%	0.15%
2017	2	2.00%	$24,733	3.93%	1.35%	1.19%	1.74%	1.59%	0.72%	1.32%
2017	3	0.23%	$24,790	0.13%	-0.65%	3.23%	3.69%	-0.65%	0.08%	-0.29%
2017	4	1.23%	$25,096	0.99%	0.51%	2.42%	1.70%	1.57%	1.11%	1.19%
2017	5	1.32%	$25,428	1.41%	-2.26%	3.54%	2.85%	1.89%	0.83%	1.33%
2017	6	0.43%	$25,537	0.64%	2.96%	0.31%	0.93%	0.79%	-0.51%	0.48%
2017	7	1.10%	$25,819	2.06%	0.75%	2.65%	5.82%	-0.66%	0.38%	0.77%
2017	8	1.21%	$26,132	0.29%	-2.72%	-0.04%	2.35%	3.41%	1.46%	0.68%
2017	9	0.26%	$26,199	2.01%	8.58%	2.36%	-0.04%	-2.32%	-1.44%	-0.05%
2017	10	0.93%	$26,444	2.36%	0.59%	1.68%	3.28%	-0.04%	-0.19%	0.19%
2017	11	1.18%	$26,757	3.06%	3.76%	0.69%	-0.39%	0.74%	-0.28%	-0.12%
2017	12	1.08%	$27,045	1.21%	-0.37%	1.35%	3.77%	1.81%	0.18%	1.22%
2018	1	1.08%	$27,337	5.64%	1.33%	5.02%	8.30%	-3.26%	-2.15%	-1.23%
2018	2	-2.83%	$26,563	-3.64%	-4.04%	-4.83%	-5.90%	-3.04%	-0.93%	-2.24%
2018	3	0.17%	$26,608	-2.74%	1.37%	-0.84%	0.54%	2.86%	1.16%	0.56%
2018	4	-0.70%	$26,423	0.52%	1.76%	1.52%	-2.82%	-2.09%	-1.28%	-1.57%
2018	5	1.52%	$26,825	2.43%	5.87%	-1.89%	-2.62%	2.01%	0.99%	0.52%
2018	6	0.07%	$26,844	0.58%	0.80%	-1.57%	-4.54%	0.65%	0.20%	-0.49%
2018	7	1.19%	$27,164	3.70%	2.62%	2.85%	3.53%	-1.44%	-0.53%	1.34%
2018	8	1.39%	$27,540	3.19%	3.14%	-2.24%	-3.77%	1.31%	1.01%	0.02%
2018	9	-0.89%	$27,295	0.59%	-3.05%	0.97%	-0.58%	-2.86%	-1.20%	-0.14%
2018	10	-4.20%	$26,148	-6.91%	-9.94%	-8.13%	-8.76%	-2.93%	-0.30%	-2.05%
2018	11	1.59%	$26,565	1.85%	0.57%	0.50%	4.90%	1.79%	1.33%	-0.36%
2018	12	-1.62%	$26,135	-8.79%	-12.38%	-5.35%	-3.50%	5.85%	2.80%	1.86%
2019	1	4.32%	$27,263	8.01%	12.26%	6.63%	10.34%	0.38%	0.65%	3.37%
2019	2	0.79%	$27,479	3.24%	4.13%	2.54%	-1.53%	-1.38%	-0.52%	-0.20%
2019	3	2.50%	$28,167	1.81%	-3.91%	0.92%	1.13%	5.57%	2.66%	2.93%
2019	4	1.18%	$28,500	4.09%	4.32%	2.93%	2.35%	-1.99%	-0.52%	0.44%
2019	5	-0.69%	$28,305	-6.38%	-9.98%	-5.03%	-7.33%	6.84%	3.05%	1.65%
2019	6	3.80%	$29,381	6.96%	7.66%	5.91%	6.20%	0.95%	1.22%	3.25%
2019	7	0.37%	$29,489	1.51%	1.30%	-1.95%	-2.66%	0.26%	0.04%	0.25%
2019	8	2.52%	$30,233	-1.67%	-5.14%	-1.92%	-3.78%	11.04%	3.95%	3.88%
2019	9	0.18%	$30,288	1.95%	5.57%	3.16%	1.69%	-2.68%	-1.19%	-0.76%
2019	10	1.00%	$30,592	2.21%	2.00%	3.39%	4.18%	-1.11%	0.19%	0.44%
2019	11	1.02%	$30,903	3.62%	2.71%	1.13%	-0.09%	-0.41%	-0.69%	0.47%
2019	12	0.67%	$31,109	2.90%	2.84%	2.98%	7.71%	-3.20%	-0.93%	0.53%
2020	1	1.91%	$31,703	-0.04%	-6.31%	-2.82%	-6.15%	7.69%	3.47%	2.45%
2020	2	-1.21%	$31,318	-7.92%	-10.15%	-7.77%	-3.78%	6.63%	2.96%	1.09%
2020	3	-4.47%	$29,917	-12.46%	-25.76%	-14.11%	-15.77%	6.38%	3.72%	-6.31%
2020	4	5.75%	$31,637	12.70%	13.89%	5.82%	7.35%	1.22%	0.27%	4.85%
2020	5	1.86%	$32,224	4.76%	2.55%	5.43%	2.97%	-1.76%	0.33%	2.46%
2020	6	1.41%	$32,677	1.78%	3.58%	3.51%	6.61%	0.34%	0.04%	2.13%
2020	7	3.71%	$33,888	5.89%	2.58%	1.94%	8.25%	4.44%	0.85%	3.10%
2020	8	1.36%	$34,349	6.98%	5.07%	4.72%	2.89%	-5.05%	-0.97%	-1.78%
2020	9	-1.31%	$33,899	-3.74%	-5.18%	-2.05%	-1.01%	0.77%	0.33%	-0.44%
2020	10	-1.79%	$33,293	-2.49%	3.66%	-3.55%	1.41%	-3.39%	-1.38%	-0.51%
2020	11	6.02%	$35,298	10.88%	19.21%	14.27%	8.99%	1.66%	0.34%	3.77%
2020	12	1.79%	$35,931	3.71%	7.50%	5.01%	7.14%	-1.23%	-0.24%	0.15%
2021	1	-1.02%	$35,566	-1.02%	6.25%	-0.78%	3.17%	-3.63%	-1.09%	-1.83%
2021	2	-0.43%	$35,413	2.78%	10.80%	2.24%	0.79%	-5.73%	-2.36%	-2.26%
2021	3	-0.09%	$35,381	4.54%	5.61%	2.51%	-0.73%	-5.24%	-2.39%	-1.48%
2021	4	2.73%	$36,349	5.29%	1.69%	2.95%	1.20%	2.49%	1.00%	1.04%
2021	5	0.81%	$36,643	0.66%	3.89%	3.48%	1.65%	0.00%	0.42%	0.62%
2021	6	1.93%	$37,350	2.25%	-0.71%	-1.08%	0.95%	4.42%	1.02%	2.21%
2021	7	1.64%	$37,962	2.44%	-4.36%	0.77%	-6.44%	3.72%	1.99%	1.42%
2021	8	0.94%	$38,318	2.98%	1.82%	1.45%	1.57%	-0.34%	-0.39%	-0.34%
2021	9	-2.97%	$37,182	-4.66%	-1.46%	-3.26%	-3.87%	-2.91%	-1.60%	-1.51%
2021	10	2.85%	$38,243	7.02%	2.86%	3.18%	1.07%	2.46%	-0.44%	0.53%
2021	11	0.07%	$38,269	-0.80%	-2.62%	-4.53%	-4.08%	2.77%	1.09%	-0.12%
2021	12	1.34%	$38,782	4.63%	4.12%	4.41%	1.53%	-2.01%	-0.52%	-0.03%
2022	1	-3.58%	$37,392	-5.27%	-4.40%	-3.63%	-0.02%	-3.91%	-2.11%	-3.59%
2022	2	-1.69%	$36,762	-2.95%	2.28%	-3.43%	-4.32%	-1.63%	-0.30%	-2.13%
2022	3	-1.43%	$36,236	3.76%	0.50%	0.52%	-3.38%	-5.45%	-4.06%	-2.89%
2022	4	-7.08%	$33,670	-8.78%	-6.38%	-6.74%	-6.14%	-9.42%	-4.23%	-6.70%
2022	5	0.15%	$33,719	0.23%	2.32%	2.00%	0.61%	-2.25%	0.62%	1.87%
2022	6	-4.32%	$32,262	-8.25%	-8.96%	-8.72%	-5.14%	-1.27%	-0.86%	-3.62%
2022	7	5.04%	$33,887	9.21%	8.53%	5.17%	-0.35%	2.43%	2.96%	4.44%
2022	8	-4.10%	$32,496	-4.08%	-4.16%	-6.12%	-1.33%	-4.56%	-3.89%	-4.43%
2022	9	-7.70%	$29,995	-9.24%	-10.41%	-9.22%	-11.54%	-8.23%	-4.73%	-5.98%

Portfolio return and risk metrics
Metric	Maximum Sharpe Ratio
Arithmetic Mean (monthly)	0.51%
Arithmetic Mean (annualized)	6.35%
Geometric Mean (monthly)	0.49%
Geometric Mean (annualized)	6.03%
Standard Deviation (monthly)	2.23%
Standard Deviation (annualized)	7.73%
Downside Deviation (monthly)	1.53%
Maximum Drawdown	-22.66%
Stock Market Correlation	0.80
Beta^(*)	0.40
Alpha (annualized)	2.37%
R²	63.43%
Sharpe Ratio	0.64
Sortino Ratio	0.92
Treynor Ratio (%)	12.39
Calmar Ratio	-0.01
Active Return	-2.54%
Tracking Error	10.26%
Information Ratio	-0.25
Skewness	-1.01
Excess Kurtosis	3.29
Historical Value-at-Risk (5%)	-3.47%
Analytical Value-at-Risk (5%)	-3.15%
Conditional Value-at-Risk (5%)	-5.58%
Upside Capture Ratio (%)	43.12
Downside Capture Ratio (%)	35.48
Safe Withdrawal Rate	8.34%
Perpetual Withdrawal Rate	3.41%
Positive Periods	154 out of 225 (68.44%)
Gain/Loss Ratio	0.86
^* 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	-21.43%
COVID-19 Start	Jan 2020	Mar 2020	-5.63%

Drawdowns for Maximum Sharpe Ratio

Drawdowns for Maximum Sharpe Ratio (worst 10)
Rank	Start	End	Length	Recovery By	Recovery Time	Underwater Period	Drawdown
1	Jan 2022	Sep 2022	9 months				-22.66%
2	Dec 2007	Feb 2009	1 year 3 months	Apr 2010	1 year 2 months	2 years 5 months	-21.43%
3	Feb 2020	Mar 2020	2 months	May 2020	2 months	4 months	-5.63%
4	Sep 2018	Dec 2018	4 months	Mar 2019	3 months	7 months	-5.10%
5	Mar 2015	Sep 2015	7 months	Mar 2016	6 months	1 year 1 month	-4.68%
6	May 2013	Aug 2013	4 months	Oct 2013	2 months	6 months	-4.58%
7	Apr 2004	Apr 2004	1 month	Sep 2004	5 months	6 months	-4.16%
8	Aug 2016	Nov 2016	4 months	Mar 2017	4 months	8 months	-4.13%
9	Feb 2018	Apr 2018	3 months	Aug 2018	4 months	7 months	-3.34%
10	Sep 2020	Oct 2020	2 months	Nov 2020	1 month	3 months	-3.07%
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	8.50%	14.77%	32.31%	-36.81%	-50.80%	0.55	0.80	1.00
IJS	iShares S&P Small-Cap 600 Value ETF	8.13%	20.08%	39.34%	-29.39%	-54.13%	0.43	0.63	0.90
EFA	iShares MSCI EAFE ETF	3.94%	16.91%	26.95%	-41.04%	-57.38%	0.25	0.34	0.88
EEM	iShares MSCI Emerging Markets ETF	5.44%	21.38%	68.93%	-48.88%	-60.44%	0.30	0.44	0.76
TLT	iShares 20+ Year Treasury Bond ETF	4.26%	13.24%	33.96%	-29.92%	-37.93%	0.29	0.47	-0.20
IEF	iShares 7-10 Year Treasury Bond ETF	3.31%	6.36%	17.91%	-15.68%	-20.05%	0.36	0.56	-0.18
LQD	iShares iBoxx $ Invmt Grade Corp Bd ETF	3.67%	7.62%	17.37%	-21.24%	-22.69%	0.35	0.52	0.39

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	-4.93%	-23.93%	-15.51%	8.11%	9.16%	11.60%	0.09%	0.09%
iShares S&P Small-Cap 600 Value ETF	-6.82%	-20.15%	-16.72%	4.84%	3.77%	9.31%	0.18%	0.18%
iShares MSCI EAFE ETF	-10.37%	-27.20%	-25.14%	-2.04%	-0.96%	3.59%	0.32%	0.32%
iShares MSCI Emerging Markets ETF	-13.02%	-27.98%	-29.11%	-3.06%	-2.79%	0.36%	0.68%	0.68%
iShares 20+ Year Treasury Bond ETF	-10.29%	-29.92%	-27.69%	-9.02%	-1.88%	0.43%	0.15%	0.15%
iShares 7-10 Year Treasury Bond ETF	-5.73%	-15.68%	-15.58%	-4.03%	-0.50%	0.49%	0.15%	0.15%
iShares iBoxx $ Invmt Grade Corp Bd ETF	-6.15%	-21.24%	-20.94%	-4.52%	-0.38%	1.50%	0.14%	0.14%
Trailing returns as of last calendar month ending September 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	0.87	0.88	0.75	-0.20	-0.17	0.40	0.80
IJS	iShares S&P Small-Cap 600 Value ETF	0.87	1.00	0.78	0.70	-0.29	-0.28	0.29	0.66
EFA	iShares MSCI EAFE ETF	0.88	0.78	1.00	0.86	-0.17	-0.13	0.44	0.77
EEM	iShares MSCI Emerging Markets ETF	0.75	0.70	0.86	1.00	-0.17	-0.12	0.39	0.69
TLT	iShares 20+ Year Treasury Bond ETF	-0.20	-0.29	-0.17	-0.17	1.00	0.91	0.56	0.40
IEF	iShares 7-10 Year Treasury Bond ETF	-0.17	-0.28	-0.13	-0.12	0.91	1.00	0.59	0.42
LQD	iShares iBoxx $ Invmt Grade Corp Bd ETF	0.40	0.29	0.44	0.39	0.56	0.59	1.00	0.75

Portfolio Risk Decomposition

Portfolio risk decomposition
Ticker	Name	Maximum Sharpe Ratio
SPY	SPDR S&P 500 ETF Trust	45.98%
IJS	iShares S&P Small-Cap 600 Value ETF	8.55%
EFA	iShares MSCI EAFE ETF	8.40%
EEM	iShares MSCI Emerging Markets ETF	9.50%
TLT	iShares 20+ Year Treasury Bond ETF	13.58%
IEF	iShares 7-10 Year Treasury Bond ETF	10.30%
LQD	iShares iBoxx $ Invmt Grade Corp Bd ETF	3.69%
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	7.41%	23.73%	-19.33%
3 years	7.41%	17.06%	-2.47%
5 years	7.24%	13.18%	1.37%
7 years	7.52%	10.72%	4.49%
10 years	7.61%	9.51%	4.83%
15 years	7.23%	8.06%	5.32%