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 2006 - Dec 2021) Save

Portfolio optimization results with goal to maximize return subject to 10.00% targeted annual volatility. The possible range of expected annual portfolio returns for the given period is 6.94% to 12.32%. Refer to the efficient frontier section for additional details.

Portfolio Allocations

Maximum Return at 10.00% Volatility
Ticker	Name	Allocation
VTI	Vanguard Total Stock Market ETF	63.37%
TLT	iShares 20+ Year Treasury Bond ETF	23.13%
GLD	SPDR Gold Shares	13.50%
Save portfolio »

Equal Weighted
Ticker	Name	Allocation
VTI	Vanguard Total Stock Market ETF	12.50%
IJS	iShares S&P Small-Cap 600 Value ETF	12.50%
EFA	iShares MSCI EAFE ETF	12.50%
EEM	iShares MSCI Emerging Markets ETF	12.50%
VNQ	Vanguard Real Estate ETF	12.50%
TLT	iShares 20+ Year Treasury Bond ETF	12.50%
LQD	iShares iBoxx $ Invmt Grade Corp Bd ETF	12.50%
GLD	SPDR Gold Shares	12.50%
Save portfolio »

Portfolio Performance Summary

Portfolio performance statistics
Metric	Maximum Return at 10.00% Volatility	Equal Weighted
Start Balance	$10,000	$10,000
End Balance	$47,200	$35,502
Annualized Return (CAGR)	10.18%	8.24%
Expected Return	10.72%	8.99%
Standard Deviation	9.87%	11.75%
Best Year	25.64%	23.38%
Worst Year	-18.28%	-21.23%
Maximum Drawdown	-30.57%	-36.98%
Sharpe Ratio (ex-ante)	0.93	0.65
Sharpe Ratio (ex-post)	0.93	0.64
Sortino Ratio	1.46	0.97
Stock Market Correlation	0.91	0.88
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 Return at 10.00% Volatility	7.10%	14.09%	14.09%	20.60%	14.70%	11.93%	10.18%	11.52%	10.11%
Equal Weighted	4.67%	11.08%	11.08%	15.47%	10.62%	8.61%	8.24%	12.03%	10.28%
Trailing return and volatility are as of last full calendar month ending December 2021

Notes on results:

IMPORTANT: The projections or other information generated by Portfolio Visualizer regarding the likelihood of various investment outcomes are hypothetical in nature, do not reflect actual investment results and are not guarantees of future results. Results may vary with each use and over time.
The results do not constitute investment advice or recommendation, are provided solely for informational purposes, and are not an offer to buy or sell any securities. All use is subject to terms of service.
Investing involves risk, including possible loss of principal. Past performance is not a guarantee of future results.
Asset allocation and diversification strategies do not guarantee a profit or protect against a loss.
Hypothetical returns do not reflect trading costs, transaction fees, commissions, or actual taxes due on investment returns.
The results are based on information from a variety of sources we consider reliable, but we do not represent that the information is accurate or complete.
Refer to the related documentation sections for more details on terms and definitions, methodology, and data sources.
Portfolio optimization is a process of choosing the proportions of various assets to be held in a portfolio in such a way as to make the portfolio better than any other combination according to the selected objective function such as maximizing risk-adjusted return. Portfolio optimization determines target weights for portfolio assets based on mathematical models that can use either historical or forecasted data as inputs. Optimization results are not guarantees of future performance.
The results are based on the total return of assets and assume that all received dividends and distributions are reinvested.
Compound annualized growth rate (CAGR) is the annualized geometric mean return of the portfolio. It is calculated from the portfolio start and end balance and is thus impacted by any cashflows.
The time-weighted rate of return (TWRR) is a measure of the compound rate of growth in a portfolio. This is calculated from the holding period returns (e.g. monthly returns), and TWRR will thus not be impacted by cashflows. If there are no external cashflows, TWRR will equal CAGR.
The money-weighted rate of return (MWRR) is the internal rate of return (IRR) taking into account cashflows. This is the discount rate at which the present value of cash inflows equals the present value of cash outflows.
Standard deviation (Stdev) is used to measure the dispersion of returns around the mean and is often used as a measure of risk. A higher standard deviation implies greater the dispersion of data points around the mean.
Sharpe Ratio is a measure of risk-adjusted performance of the portfolio, and it is calculated by dividing the mean monthly excess return of the portfolio over the risk-free rate by the standard deviation of excess return, and the displayed value is annualized.
Sortino Ratio is a measure of risk-adjusted return which is a modification of the Sharpe Ratio. While the latter is the ratio of average returns in excess of a risk-free rate divided by the standard deviation of those excess returns, the Sortino Ratio has the same denominator divided by the standard deviation of returns below the risk-free rate.
Treynor Ratio is a measure of risk-adjusted performance of the portfolio. It is similar to the Sharpe Ratio, but it uses portfolio beta (systematic risk) as the risk metric in the denominator.
Calmar Ratio is a measure of risk-adjusted performance of the portfolio. It is calculated as the annualized return over the past 36 months divided by the maximum drawdown over the past 36 months based on monthly returns.
Risk-free returns are calculated based on the Federal Reserve 3-Month Treasury Bill (secondary market) rates.
Downside deviation measures the downside volatility of the portfolio returns unlike standard deviation, which includes both upside and downside deviations. Downside deviation is calculated based on negative returns that hurt the portfolio performance.
Correlation measures to what degree the returns of the two assets move in relation to each other. Correlation coefficient is a numerical value between -1 and +1. If one variable goes up by a certain amount, the correlation coefficient indicates which way the other variable moves and by how much. Asset correlations are calculated based on monthly returns.
Skewness is a measure of the asymmetry of the probability distribution or returns from a normal Gaussian distribution shape about its mean. Negative skewness is associated with the left (typically negative returns) tail of the distribution extending further than the right tail; and positive skewness is associated with the right (typically positive returns) tail of the distribution extending further than the left tail.
Excess kurtosis is a measure of whether a data distribution is peaked or flat relative to a normal distribution. Distributions with high kurtosis tend to have a distinct peak near the mean, decline rather rapidly, and have heavy or fat tails.
A drawdown refers to the decline in value of a single investment or an investment portfolio from a relative peak value to a relative trough. A maximum drawdown (Max Drawdown) is the maximum observed loss from a peak to a trough of a portfolio before a new peak is attained. Drawdown values are calculated based on monthly returns.
Value at Risk (VaR) measures the scale of loss at a given confidence level. If the 5% VaR is -3% the portfolio return is expected to be greater than -3% 95% of the time and less than -3% 5% of the time. Value at Risk can be calculated directly based on historical returns based on a given percentile or analytically based on the mean and standard deviation of the returns.
Conditional Value at Risk (CVaR) measures the scale of the expected loss once the specific Value at Risk (VaR) breakpoint has been breached, i.e., it calculates the average tail loss by taking a weighted average between the value at risk and losses exceeding the value at risk.
Beta is a measure of systematic risk and measures the volatility of a particular investment relative to the market or its benchmark. Alpha measures the active return of the investment compared to the market benchmark return. R-squared is the percentage of a portfolio's movements that can be explained by movements in the selected benchmark index.
Active return is the investment return minus the return of its benchmark. For periods longer than 12 months this is displayed as annualized value, i.e., annualized investment return minus annualized benchmark return.
Tracking error, also known as active risk, is the standard deviation of active return. This is displayed as annualized value based on the standard deviation of monthly active returns.
Information ratio is the active return divided by the tracking error. It measures whether the investment outperformed its benchmark consistently.
Gain/Loss ratio is a measure of downside risk, and it is calculated as the average positive return in up periods divided by the average negative return in down periods.
Upside Capture Ratio measures how well the fund performed relative to the benchmark when the market was up, and Downside Capture Ratio measures how well the fund performed relative to the benchmark when the market was down. An upside capture ratio greater than 100 would indicate that the fund outperformed its benchmark when the market was up, and a downside capture ratio below 100 would indicate that the fund lost less than its benchmark when the market was down. To calculate upside capture ratio a new series from the portfolio returns is constructed by dropping all time periods where the benchmark return is less than equal to zero. The up capture is then the quotient of the annualized return of the resulting manager series, divided by the annualized return of the resulting benchmark series. The downside capture ratio is calculated analogously.
All risk measures for the portfolio and portfolio assets are calculated based on monthly returns.
The optimization results assume monthly rebalancing of portfolio assets to match the specified allocation.

Efficient Frontier Assets
#	Asset	Expected Return	Standard Deviation	Sharpe Ratio	Min. Weight	Max. Weight
1	Vanguard Total Stock Market ETF (VTI)	12.32%	15.40%	0.689	0.00%	100.00%
2	iShares S&P Small-Cap 600 Value ETF (IJS)	11.72%	20.66%	0.488	0.00%	100.00%
3	iShares MSCI EAFE ETF (EFA)	6.37%	17.35%	0.296	0.00%	100.00%
4	iShares MSCI Emerging Markets ETF (EEM)	7.79%	21.80%	0.297	0.00%	100.00%
5	Vanguard Real Estate ETF (VNQ)	11.64%	22.56%	0.444	0.00%	100.00%
6	iShares 20+ Year Treasury Bond ETF (TLT)	7.18%	13.33%	0.442	0.00%	100.00%
7	iShares iBoxx $ Invmt Grade Corp Bd ETF (LQD)	5.71%	7.30%	0.618	0.00%	100.00%
8	SPDR Gold Shares (GLD)	9.41%	17.48%	0.456	0.00%	100.00%
Results based on historical returns. Expected return is the annualized monthly arithmetic mean return. Ex-ante Sharpe Ratio calculated using 3-month treasury bill returns as the risk-free rate.

Asset Correlations

Efficient Frontier Asset Correlations
Name	Ticker	VTI	IJS	EFA	EEM	VNQ	TLT	LQD	GLD
Vanguard Total Stock Market ETF	VTI	1.00	0.90	0.89	0.78	0.74	-0.32	0.34	0.07
iShares S&P Small-Cap 600 Value ETF	IJS	0.90	1.00	0.78	0.70	0.73	-0.38	0.25	-0.01
iShares MSCI EAFE ETF	EFA	0.89	0.78	1.00	0.87	0.70	-0.26	0.40	0.15
iShares MSCI Emerging Markets ETF	EEM	0.78	0.70	0.87	1.00	0.61	-0.25	0.38	0.29
Vanguard Real Estate ETF	VNQ	0.74	0.73	0.70	0.61	1.00	-0.01	0.46	0.10
iShares 20+ Year Treasury Bond ETF	TLT	-0.32	-0.38	-0.26	-0.25	-0.01	1.00	0.49	0.21
iShares iBoxx $ Invmt Grade Corp Bd ETF	LQD	0.34	0.25	0.40	0.38	0.46	0.49	1.00	0.27
SPDR Gold Shares	GLD	0.07	-0.01	0.15	0.29	0.10	0.21	0.27	1.00
Based on monthly returns from Jan 2006 to Dec 2021

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

Efficient Frontier Assets
#	VTI	IJS	EFA	EEM	VNQ	TLT	LQD	GLD	Expected Return^*	Standard Deviation^*	Sharpe Ratio^*
1	12.30%	0.61%	0.00%	0.00%	0.00%	12.74%	68.73%	5.61%	6.94%	7.04%	0.805
2	13.09%	0.45%	0.00%	0.00%	0.00%	13.26%	67.48%	5.72%	6.99%	7.04%	0.812
3	13.87%	0.29%	0.00%	0.00%	0.00%	13.78%	66.23%	5.82%	7.04%	7.04%	0.819
4	14.66%	0.14%	0.00%	0.00%	0.00%	14.29%	64.98%	5.93%	7.10%	7.04%	0.826
5	15.42%	0.00%	0.00%	0.00%	0.00%	14.82%	63.72%	6.04%	7.15%	7.04%	0.833
6	16.05%	0.00%	0.00%	0.00%	0.00%	15.38%	62.42%	6.15%	7.20%	7.05%	0.839
7	16.67%	0.00%	0.00%	0.00%	0.00%	15.94%	61.11%	6.27%	7.26%	7.05%	0.846
8	17.30%	0.00%	0.00%	0.00%	0.00%	16.50%	59.81%	6.39%	7.31%	7.06%	0.852
9	17.92%	0.00%	0.00%	0.00%	0.00%	17.07%	58.50%	6.51%	7.36%	7.07%	0.859
10	18.55%	0.00%	0.00%	0.00%	0.00%	17.63%	57.20%	6.63%	7.42%	7.07%	0.865
11	19.17%	0.00%	0.00%	0.00%	0.00%	18.19%	55.89%	6.74%	7.47%	7.08%	0.871
12	19.80%	0.00%	0.00%	0.00%	0.00%	18.76%	54.58%	6.86%	7.52%	7.09%	0.877
13	20.42%	0.00%	0.00%	0.00%	0.00%	19.32%	53.28%	6.98%	7.58%	7.10%	0.882
14	21.05%	0.00%	0.00%	0.00%	0.00%	19.88%	51.97%	7.10%	7.63%	7.11%	0.888
15	21.67%	0.00%	0.00%	0.00%	0.00%	20.44%	50.67%	7.22%	7.68%	7.13%	0.893
16	22.30%	0.00%	0.00%	0.00%	0.00%	21.01%	49.36%	7.33%	7.74%	7.14%	0.899
17	22.92%	0.00%	0.00%	0.00%	0.00%	21.57%	48.06%	7.45%	7.79%	7.15%	0.904
18	23.55%	0.00%	0.00%	0.00%	0.00%	22.13%	46.75%	7.57%	7.84%	7.17%	0.909
19	24.17%	0.00%	0.00%	0.00%	0.00%	22.69%	45.45%	7.69%	7.90%	7.18%	0.914
20	24.80%	0.00%	0.00%	0.00%	0.00%	23.26%	44.14%	7.81%	7.95%	7.20%	0.919
21	25.42%	0.00%	0.00%	0.00%	0.00%	23.82%	42.84%	7.92%	8.00%	7.22%	0.924
22	26.05%	0.00%	0.00%	0.00%	0.00%	24.38%	41.53%	8.04%	8.06%	7.24%	0.928
23	26.67%	0.00%	0.00%	0.00%	0.00%	24.95%	40.22%	8.16%	8.11%	7.26%	0.933
24	27.29%	0.00%	0.00%	0.00%	0.00%	25.51%	38.92%	8.28%	8.17%	7.28%	0.937
25	27.92%	0.00%	0.00%	0.00%	0.00%	26.07%	37.61%	8.39%	8.22%	7.30%	0.941
26	28.54%	0.00%	0.00%	0.00%	0.00%	26.63%	36.31%	8.51%	8.27%	7.32%	0.945
27	29.17%	0.00%	0.00%	0.00%	0.00%	27.20%	35.00%	8.63%	8.33%	7.34%	0.949
28	29.79%	0.00%	0.00%	0.00%	0.00%	27.76%	33.70%	8.75%	8.38%	7.36%	0.953
29	30.42%	0.00%	0.00%	0.00%	0.00%	28.32%	32.39%	8.87%	8.44%	7.39%	0.957
30	31.04%	0.00%	0.00%	0.00%	0.00%	28.89%	31.09%	8.98%	8.49%	7.41%	0.960
31	31.67%	0.00%	0.00%	0.00%	0.00%	29.45%	29.78%	9.10%	8.54%	7.44%	0.963
32	32.29%	0.00%	0.00%	0.00%	0.00%	30.01%	28.48%	9.22%	8.60%	7.47%	0.967
33	32.92%	0.00%	0.00%	0.00%	0.00%	30.57%	27.17%	9.34%	8.65%	7.49%	0.970
34	33.54%	0.00%	0.00%	0.00%	0.00%	31.14%	25.87%	9.46%	8.70%	7.52%	0.973
35	34.17%	0.00%	0.00%	0.00%	0.00%	31.70%	24.56%	9.57%	8.76%	7.55%	0.976
36	34.79%	0.00%	0.00%	0.00%	0.00%	32.26%	23.25%	9.69%	8.81%	7.58%	0.979
37	35.42%	0.00%	0.00%	0.00%	0.00%	32.82%	21.95%	9.81%	8.87%	7.61%	0.981
38	36.04%	0.00%	0.00%	0.00%	0.00%	33.39%	20.64%	9.93%	8.92%	7.64%	0.984
39	36.67%	0.00%	0.00%	0.00%	0.00%	33.95%	19.34%	10.05%	8.98%	7.67%	0.986
40	37.29%	0.00%	0.00%	0.00%	0.00%	34.51%	18.03%	10.16%	9.03%	7.70%	0.989
41	37.92%	0.00%	0.00%	0.00%	0.00%	35.08%	16.73%	10.28%	9.08%	7.74%	0.991
42	38.54%	0.00%	0.00%	0.00%	0.00%	35.64%	15.42%	10.40%	9.14%	7.77%	0.993
43	39.17%	0.00%	0.00%	0.00%	0.00%	36.20%	14.12%	10.52%	9.19%	7.81%	0.995
44	39.79%	0.00%	0.00%	0.00%	0.00%	36.76%	12.81%	10.64%	9.25%	7.84%	0.997
45	40.41%	0.00%	0.00%	0.00%	0.00%	37.33%	11.51%	10.75%	9.30%	7.88%	0.999
46	41.04%	0.00%	0.00%	0.00%	0.00%	37.89%	10.20%	10.87%	9.35%	7.91%	1.000
47	41.66%	0.00%	0.00%	0.00%	0.00%	38.45%	8.89%	10.99%	9.41%	7.95%	1.002
48	42.29%	0.00%	0.00%	0.00%	0.00%	39.01%	7.59%	11.11%	9.46%	7.99%	1.003
49	42.91%	0.00%	0.00%	0.00%	0.00%	39.58%	6.28%	11.22%	9.52%	8.03%	1.005
50	43.54%	0.00%	0.00%	0.00%	0.00%	40.14%	4.98%	11.34%	9.57%	8.07%	1.006
51	44.16%	0.00%	0.00%	0.00%	0.00%	40.70%	3.67%	11.46%	9.63%	8.11%	1.007
52	44.79%	0.00%	0.00%	0.00%	0.00%	41.27%	2.37%	11.58%	9.68%	8.15%	1.009
53	45.41%	0.00%	0.00%	0.00%	0.00%	41.83%	1.06%	11.70%	9.74%	8.19%	1.010
54	46.11%	0.00%	0.00%	0.00%	0.00%	42.08%	0.00%	11.81%	9.79%	8.23%	1.011
55	47.13%	0.00%	0.00%	0.00%	0.00%	40.96%	0.00%	11.91%	9.84%	8.28%	1.011
56	48.14%	0.00%	0.00%	0.00%	0.00%	39.85%	0.00%	12.01%	9.90%	8.33%	1.010
57	49.16%	0.00%	0.00%	0.00%	0.00%	38.74%	0.00%	12.11%	9.95%	8.39%	1.009
58	50.17%	0.00%	0.00%	0.00%	0.00%	37.62%	0.00%	12.21%	10.01%	8.46%	1.007
59	51.19%	0.00%	0.00%	0.00%	0.00%	36.51%	0.00%	12.31%	10.06%	8.53%	1.004
60	52.20%	0.00%	0.00%	0.00%	0.00%	35.39%	0.00%	12.41%	10.12%	8.61%	1.001
61	53.22%	0.00%	0.00%	0.00%	0.00%	34.28%	0.00%	12.50%	10.17%	8.70%	0.996
62	54.23%	0.00%	0.00%	0.00%	0.00%	33.16%	0.00%	12.60%	10.23%	8.79%	0.992
63	55.25%	0.00%	0.00%	0.00%	0.00%	32.05%	0.00%	12.70%	10.28%	8.89%	0.986
64	56.27%	0.00%	0.00%	0.00%	0.00%	30.93%	0.00%	12.80%	10.34%	8.99%	0.980
65	57.28%	0.00%	0.00%	0.00%	0.00%	29.82%	0.00%	12.90%	10.39%	9.10%	0.974
66	58.30%	0.00%	0.00%	0.00%	0.00%	28.70%	0.00%	13.00%	10.45%	9.22%	0.967
67	59.31%	0.00%	0.00%	0.00%	0.00%	27.59%	0.00%	13.10%	10.50%	9.34%	0.960
68	60.33%	0.00%	0.00%	0.00%	0.00%	26.47%	0.00%	13.20%	10.56%	9.46%	0.953
69	61.34%	0.00%	0.00%	0.00%	0.00%	25.36%	0.00%	13.30%	10.61%	9.59%	0.945
70	62.36%	0.00%	0.00%	0.00%	0.00%	24.25%	0.00%	13.40%	10.66%	9.73%	0.937
71	63.37%	0.00%	0.00%	0.00%	0.00%	23.13%	0.00%	13.50%	10.72%	9.87%	0.929
72	64.39%	0.00%	0.00%	0.00%	0.00%	22.02%	0.00%	13.59%	10.77%	10.01%	0.921
73	65.40%	0.00%	0.00%	0.00%	0.00%	20.90%	0.00%	13.69%	10.83%	10.16%	0.912
74	66.42%	0.00%	0.00%	0.00%	0.00%	19.79%	0.00%	13.79%	10.88%	10.31%	0.904
75	67.44%	0.00%	0.00%	0.00%	0.00%	18.67%	0.00%	13.89%	10.94%	10.46%	0.895
76	68.45%	0.00%	0.00%	0.00%	0.00%	17.56%	0.00%	13.99%	10.99%	10.62%	0.887
77	69.47%	0.00%	0.00%	0.00%	0.00%	16.44%	0.00%	14.09%	11.05%	10.78%	0.878
78	70.48%	0.00%	0.00%	0.00%	0.00%	15.33%	0.00%	14.19%	11.10%	10.94%	0.870
79	71.50%	0.00%	0.00%	0.00%	0.00%	14.21%	0.00%	14.29%	11.16%	11.11%	0.861
80	72.51%	0.00%	0.00%	0.00%	0.00%	13.10%	0.00%	14.39%	11.22%	11.28%	0.853
81	73.53%	0.00%	0.00%	0.00%	0.00%	11.99%	0.00%	14.49%	11.27%	11.46%	0.844
82	74.54%	0.00%	0.00%	0.00%	0.00%	10.87%	0.00%	14.59%	11.33%	11.63%	0.836
83	75.56%	0.00%	0.00%	0.00%	0.00%	9.76%	0.00%	14.68%	11.38%	11.81%	0.827
84	76.57%	0.00%	0.00%	0.00%	0.00%	8.64%	0.00%	14.78%	11.44%	11.99%	0.819
85	77.59%	0.00%	0.00%	0.00%	0.00%	7.53%	0.00%	14.88%	11.49%	12.17%	0.811
86	78.61%	0.00%	0.00%	0.00%	0.00%	6.41%	0.00%	14.98%	11.55%	12.36%	0.803
87	79.62%	0.00%	0.00%	0.00%	0.00%	5.30%	0.00%	15.08%	11.60%	12.55%	0.795
88	80.64%	0.00%	0.00%	0.00%	0.00%	4.18%	0.00%	15.18%	11.66%	12.73%	0.787
89	81.65%	0.00%	0.00%	0.00%	0.00%	3.07%	0.00%	15.28%	11.71%	12.93%	0.779
90	82.67%	0.00%	0.00%	0.00%	0.00%	1.95%	0.00%	15.38%	11.77%	13.12%	0.771
91	83.68%	0.00%	0.00%	0.00%	0.00%	0.84%	0.00%	15.48%	11.82%	13.31%	0.764
92	84.91%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	15.09%	11.88%	13.51%	0.756
93	86.80%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	13.20%	11.93%	13.71%	0.749
94	88.68%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	11.32%	11.99%	13.93%	0.741
95	90.57%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	9.43%	12.05%	14.15%	0.733
96	92.46%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	7.54%	12.10%	14.39%	0.724
97	94.34%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	5.66%	12.16%	14.63%	0.716
98	96.23%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	3.77%	12.21%	14.88%	0.707
99	98.11%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	1.89%	12.27%	15.14%	0.698
100	100.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	12.32%	15.40%	0.689
^*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 Return at 10.00% Volatility		Equal Weighted		Vanguard Total Stock Market ETF (VTI)	iShares 20+ Year Treasury Bond ETF (TLT)	SPDR Gold Shares (GLD)	iShares S&P Small-Cap 600 Value ETF (IJS)	iShares MSCI EAFE ETF (EFA)	iShares MSCI Emerging Markets ETF (EEM)	Vanguard Real Estate ETF (VNQ)	iShares iBoxx $ Invmt Grade Corp Bd ETF (LQD)
Year	Inflation	Return	Balance	Return	Balance	Vanguard Total Stock Market ETF (VTI)	iShares 20+ Year Treasury Bond ETF (TLT)	SPDR Gold Shares (GLD)	iShares S&P Small-Cap 600 Value ETF (IJS)	iShares MSCI EAFE ETF (EFA)	iShares MSCI Emerging Markets ETF (EEM)	Vanguard Real Estate ETF (VNQ)	iShares iBoxx $ Invmt Grade Corp Bd ETF (LQD)
2006	2.54%	13.24%	$11,324	19.39%	$11,939	15.69%	0.71%	22.55%	19.37%	25.81%	31.19%	35.30%	4.22%
2007	4.08%	9.94%	$12,450	8.39%	$12,941	5.37%	10.29%	30.45%	-5.56%	9.94%	33.31%	-16.50%	3.73%
2008	0.09%	-18.28%	$10,174	-21.23%	$10,194	-36.98%	33.93%	4.92%	-29.39%	-41.04%	-48.88%	-37.00%	2.40%
2009	2.72%	15.41%	$11,742	23.38%	$12,577	28.89%	-21.80%	24.03%	22.36%	26.95%	68.93%	30.08%	8.46%
2010	1.50%	18.10%	$13,868	18.79%	$14,941	17.42%	9.05%	29.27%	24.69%	8.15%	16.51%	28.37%	9.33%
2011	2.96%	10.30%	$15,296	4.04%	$15,545	0.97%	33.96%	9.57%	-1.65%	-12.25%	-18.82%	8.62%	9.73%
2012	1.74%	12.31%	$17,179	14.22%	$17,756	16.45%	2.63%	6.60%	18.24%	18.82%	19.10%	17.63%	10.58%
2013	1.50%	11.68%	$19,186	4.45%	$18,546	33.45%	-13.37%	-28.33%	39.34%	21.40%	-3.69%	2.31%	-2.00%
2014	0.76%	13.87%	$21,846	8.88%	$20,193	12.54%	27.30%	-2.19%	7.56%	-6.20%	-3.93%	30.36%	8.21%
2015	0.73%	-1.11%	$21,605	-3.92%	$19,401	0.36%	-1.79%	-10.67%	-6.90%	-1.00%	-16.18%	2.42%	-1.25%
2016	2.07%	10.04%	$23,774	10.46%	$21,431	12.83%	1.18%	8.03%	31.25%	1.37%	10.87%	8.60%	6.21%
2017	2.11%	17.28%	$27,882	15.92%	$24,842	21.21%	9.18%	12.81%	11.35%	25.10%	37.28%	4.91%	7.06%
2018	1.91%	-3.48%	$26,912	-7.18%	$23,059	-5.21%	-1.61%	-1.94%	-12.84%	-13.81%	-15.31%	-6.02%	-3.79%
2019	2.29%	25.64%	$33,813	22.27%	$28,195	30.67%	14.12%	17.86%	24.12%	22.03%	18.20%	28.87%	17.37%
2020	1.36%	22.35%	$41,371	13.35%	$31,960	21.03%	18.15%	24.81%	2.63%	7.59%	17.03%	-4.68%	10.97%
2021	7.04%	14.09%	$47,200	11.08%	$35,502	25.67%	-4.60%	-4.15%	30.53%	11.46%	-3.61%	40.52%	-1.85%

Monthly returns for the configured portfolios
Year	Month	Maximum Return at 10.00% Volatility		Equal Weighted		Vanguard Total Stock Market ETF (VTI)	iShares 20+ Year Treasury Bond ETF (TLT)	SPDR Gold Shares (GLD)	iShares S&P Small-Cap 600 Value ETF (IJS)	iShares MSCI EAFE ETF (EFA)	iShares MSCI Emerging Markets ETF (EEM)	Vanguard Real Estate ETF (VNQ)	iShares iBoxx $ Invmt Grade Corp Bd ETF (LQD)
Year	Month	Return	Balance	Return	Balance	Vanguard Total Stock Market ETF (VTI)	iShares 20+ Year Treasury Bond ETF (TLT)	SPDR Gold Shares (GLD)	iShares S&P Small-Cap 600 Value ETF (IJS)	iShares MSCI EAFE ETF (EFA)	iShares MSCI Emerging Markets ETF (EEM)	Vanguard Real Estate ETF (VNQ)	iShares iBoxx $ Invmt Grade Corp Bd ETF (LQD)
2006	1	3.07%	$10,307	5.95%	$10,595	3.22%	-1.34%	9.93%	8.75%	5.77%	14.20%	7.54%	-0.44%
2006	2	0.25%	$10,332	-0.19%	$10,575	0.22%	1.11%	-1.11%	0.27%	-0.70%	-3.85%	1.86%	0.68%
2006	3	0.73%	$10,408	1.90%	$10,776	2.05%	-4.57%	3.62%	4.86%	4.01%	2.17%	4.73%	-1.68%
2006	4	1.59%	$10,574	2.26%	$11,020	0.96%	-2.75%	12.03%	0.18%	4.79%	6.52%	-3.40%	-0.20%
2006	5	-2.26%	$10,334	-3.39%	$10,646	-3.22%	-0.19%	-1.32%	-4.55%	-3.82%	-11.14%	-2.70%	-0.19%
2006	6	-0.28%	$10,306	0.21%	$10,669	0.13%	1.18%	-4.67%	0.04%	-0.06%	0.21%	4.95%	-0.09%
2006	7	0.85%	$10,393	1.33%	$10,810	-0.12%	2.16%	3.15%	-3.10%	0.81%	2.34%	3.89%	1.46%
2006	8	1.98%	$10,599	2.07%	$11,033	2.30%	3.06%	-1.38%	2.70%	2.55%	1.58%	3.48%	2.22%
2006	9	1.26%	$10,733	0.38%	$11,075	2.26%	1.91%	-4.53%	1.19%	0.22%	-0.87%	1.96%	0.87%
2006	10	2.61%	$11,013	3.63%	$11,477	3.53%	0.85%	1.29%	5.52%	3.75%	7.06%	6.03%	1.00%
2006	11	2.94%	$11,336	3.65%	$11,896	2.33%	2.31%	6.89%	2.38%	3.07%	5.98%	4.78%	1.46%
2006	12	-0.11%	$11,324	0.36%	$11,939	1.20%	-2.69%	-1.83%	0.32%	3.20%	5.44%	-1.83%	-0.90%
2007	1	1.30%	$11,471	1.99%	$12,177	1.86%	-1.00%	2.56%	2.14%	1.39%	0.11%	8.78%	0.09%
2007	2	0.10%	$11,482	-0.08%	$12,167	-1.62%	3.39%	2.55%	-0.92%	-0.12%	-3.24%	-2.70%	2.00%
2007	3	0.17%	$11,501	0.59%	$12,238	1.12%	-1.70%	-1.11%	0.91%	2.90%	5.33%	-2.07%	-0.68%
2007	4	3.04%	$11,850	2.13%	$12,499	4.02%	0.90%	2.05%	1.84%	3.75%	3.73%	-0.13%	0.89%
2007	5	1.51%	$12,030	1.19%	$12,649	3.72%	-2.31%	-2.31%	4.63%	2.36%	5.06%	-0.38%	-1.23%
2007	6	-1.61%	$11,836	-1.67%	$12,437	-1.76%	-1.01%	-1.94%	-2.24%	-0.32%	3.68%	-8.99%	-0.81%
2007	7	-1.15%	$11,699	-1.85%	$12,207	-3.53%	3.32%	2.37%	-6.26%	-2.29%	0.71%	-8.26%	-0.82%
2007	8	1.50%	$11,874	1.90%	$12,440	1.47%	1.79%	1.11%	1.33%	-0.63%	1.04%	6.74%	2.38%
2007	9	3.91%	$12,339	4.55%	$13,006	3.85%	0.23%	10.51%	0.31%	5.32%	11.57%	3.90%	0.73%
2007	10	2.49%	$12,646	3.85%	$13,507	1.79%	1.81%	6.95%	1.06%	4.25%	11.87%	2.10%	0.97%
2007	11	-1.85%	$12,412	-3.46%	$13,039	-4.52%	5.35%	-1.65%	-7.15%	-3.62%	-7.65%	-9.47%	1.02%
2007	12	0.31%	$12,450	-0.75%	$12,941	-0.70%	-0.64%	6.65%	-0.71%	-2.99%	-1.43%	-5.41%	-0.81%
2008	1	-1.96%	$12,206	-1.53%	$12,743	-6.17%	2.10%	10.84%	-4.00%	-7.85%	-8.92%	-0.78%	2.57%
2008	2	-0.98%	$12,086	-0.50%	$12,680	-2.50%	-0.46%	5.23%	-3.36%	-1.02%	1.99%	-3.18%	-0.71%
2008	3	-0.88%	$11,980	-0.17%	$12,658	-0.90%	2.14%	-6.00%	0.83%	0.42%	-3.75%	6.48%	-0.60%
2008	4	1.96%	$12,215	2.89%	$13,023	4.89%	-2.48%	-4.16%	2.64%	5.44%	9.14%	6.38%	1.25%
2008	5	0.78%	$12,310	0.76%	$13,122	2.02%	-2.69%	0.92%	3.92%	1.19%	3.16%	-0.21%	-2.21%
2008	6	-3.92%	$11,827	-4.92%	$12,477	-8.12%	2.65%	4.52%	-8.41%	-8.80%	-9.29%	-10.62%	-1.29%
2008	7	-0.68%	$11,747	-0.61%	$12,401	-0.62%	-0.37%	-1.44%	2.87%	-3.32%	-5.50%	3.12%	0.39%
2008	8	0.30%	$11,783	-1.05%	$12,271	1.46%	2.74%	-9.29%	4.76%	-4.25%	-6.32%	2.37%	0.15%
2008	9	-4.96%	$11,199	-5.68%	$11,574	-9.24%	1.47%	4.11%	-4.82%	-11.44%	-14.68%	-0.11%	-10.73%
2008	10	-13.69%	$9,666	-16.93%	$9,615	-17.48%	-1.86%	-16.14%	-19.86%	-20.83%	-25.58%	-31.73%	-1.95%
2008	11	-0.07%	$9,660	-3.55%	$9,273	-8.01%	14.34%	12.57%	-11.80%	-6.37%	-9.75%	-22.72%	3.35%
2008	12	5.32%	$10,174	9.93%	$10,194	1.78%	13.64%	7.73%	6.57%	8.88%	10.35%	16.67%	13.80%
2009	1	-7.38%	$9,424	-8.98%	$9,278	-8.05%	-13.07%	5.54%	-13.94%	-13.73%	-9.29%	-17.53%	-1.80%
2009	2	-6.83%	$8,780	-8.25%	$8,512	-10.53%	-1.54%	1.45%	-13.03%	-10.39%	-6.27%	-20.53%	-5.20%
2009	3	5.83%	$9,292	5.84%	$9,009	8.26%	4.04%	-2.54%	7.58%	8.39%	16.86%	3.61%	0.47%
2009	4	4.91%	$9,748	10.02%	$9,911	10.99%	-6.95%	-3.33%	18.89%	11.52%	15.56%	30.68%	2.78%
2009	5	3.99%	$10,137	5.84%	$10,491	5.46%	-3.69%	10.23%	0.67%	13.19%	15.94%	2.62%	2.32%
2009	6	-0.30%	$10,106	-0.82%	$10,404	0.36%	0.76%	-5.22%	1.52%	-1.43%	-2.25%	-3.23%	2.89%
2009	7	5.36%	$10,648	7.27%	$11,160	7.74%	0.58%	2.38%	11.00%	10.04%	11.01%	10.77%	4.63%
2009	8	2.88%	$10,954	3.54%	$11,555	3.71%	2.24%	0.05%	3.48%	4.50%	-1.31%	14.32%	1.31%
2009	9	3.98%	$11,390	4.88%	$12,119	4.14%	2.46%	5.84%	4.21%	3.80%	10.20%	6.63%	1.76%
2009	10	-1.77%	$11,188	-2.32%	$11,838	-2.63%	-2.62%	3.72%	-6.07%	-2.52%	-3.44%	-4.46%	-0.49%
2009	11	5.61%	$11,816	5.36%	$12,473	5.69%	1.21%	12.79%	2.90%	3.92%	7.85%	6.57%	1.95%
2009	12	-0.63%	$11,742	0.84%	$12,577	2.86%	-6.34%	-7.20%	8.10%	0.70%	3.27%	7.37%	-2.07%
2010	1	-1.81%	$11,530	-2.72%	$12,235	-3.57%	2.69%	-1.26%	-2.54%	-5.07%	-7.76%	-5.52%	1.25%
2010	2	2.54%	$11,823	2.41%	$12,530	3.44%	-0.34%	3.27%	4.76%	0.27%	1.78%	5.58%	0.51%
2010	3	3.52%	$12,239	4.63%	$13,110	6.40%	-2.06%	-0.44%	7.80%	6.39%	8.11%	10.18%	0.65%
2010	4	2.95%	$12,600	3.01%	$13,505	2.18%	3.32%	5.88%	6.63%	-2.80%	-0.17%	7.15%	1.91%
2010	5	-3.40%	$12,171	-4.44%	$12,906	-7.88%	5.11%	3.05%	-8.54%	-11.19%	-9.39%	-5.33%	-1.31%
2010	6	-2.04%	$11,923	-1.42%	$12,723	-5.83%	5.80%	2.36%	-8.27%	-2.07%	-1.40%	-5.19%	3.28%
2010	7	3.54%	$12,346	5.24%	$13,390	7.02%	-0.95%	-5.09%	6.71%	11.61%	10.93%	9.59%	2.11%
2010	8	-0.27%	$12,312	-0.50%	$13,323	-4.71%	8.40%	5.71%	-7.91%	-3.80%	-3.24%	-1.28%	2.86%
2010	9	6.05%	$13,057	6.16%	$14,144	9.45%	-2.51%	4.78%	10.93%	9.97%	11.76%	4.45%	0.46%
2010	10	2.01%	$13,320	2.32%	$14,472	4.03%	-4.47%	3.68%	4.04%	3.81%	3.02%	4.74%	-0.26%
2010	11	0.22%	$13,349	-0.97%	$14,331	0.51%	-1.69%	2.11%	2.47%	-4.82%	-2.91%	-1.85%	-1.62%
2010	12	3.89%	$13,868	4.25%	$14,941	6.96%	-3.68%	2.44%	8.97%	8.30%	7.27%	4.54%	-0.75%
2011	1	-0.28%	$13,830	-0.76%	$14,827	2.05%	-3.08%	-6.38%	-0.24%	2.10%	-3.84%	3.25%	0.04%
2011	2	3.53%	$14,319	3.11%	$15,287	3.70%	1.65%	6.00%	4.21%	3.55%	-0.04%	4.71%	1.08%
2011	3	0.49%	$14,388	0.75%	$15,402	0.42%	0.03%	1.60%	2.21%	-2.39%	6.29%	-1.62%	-0.54%
2011	4	3.58%	$14,904	3.98%	$16,015	2.90%	2.34%	8.94%	1.06%	5.63%	2.73%	5.75%	2.50%
2011	5	-0.12%	$14,886	-0.46%	$15,941	-1.06%	3.42%	-1.79%	-1.77%	-2.21%	-2.94%	1.37%	1.27%
2011	6	-2.00%	$14,587	-1.80%	$15,655	-1.79%	-2.33%	-2.43%	-1.59%	-1.19%	-0.93%	-3.30%	-0.80%
2011	7	0.72%	$14,692	1.05%	$15,819	-2.27%	4.42%	8.42%	-2.77%	-2.38%	-1.03%	1.56%	2.43%
2011	8	0.03%	$14,697	-1.93%	$15,514	-6.09%	9.66%	12.27%	-7.98%	-8.75%	-9.25%	-5.62%	0.34%
2011	9	-3.24%	$14,221	-6.90%	$14,443	-7.57%	13.20%	-11.06%	-10.57%	-10.81%	-17.89%	-10.85%	0.35%
2011	10	7.11%	$15,232	8.93%	$15,733	11.37%	-3.84%	5.87%	15.34%	9.63%	16.27%	14.29%	2.51%
2011	11	0.45%	$15,300	-0.90%	$15,592	-0.37%	1.98%	1.67%	0.63%	-2.18%	-1.96%	-3.80%	-3.16%
2011	12	-0.02%	$15,296	-0.30%	$15,545	0.98%	3.44%	-10.66%	2.02%	-2.21%	-4.30%	4.85%	3.49%
2012	1	4.67%	$16,011	6.10%	$16,493	5.07%	-0.33%	11.40%	7.90%	5.27%	10.99%	6.38%	2.14%
2012	2	1.67%	$16,279	1.37%	$16,719	4.22%	-2.59%	-2.96%	1.71%	4.83%	5.27%	-1.15%	1.63%
2012	3	0.78%	$16,407	0.18%	$16,750	3.06%	-4.23%	-1.32%	2.89%	0.42%	-3.11%	5.19%	-1.42%
2012	4	0.69%	$16,521	0.29%	$16,798	-0.64%	4.83%	-0.15%	-1.91%	-2.08%	-1.70%	2.86%	1.08%
2012	5	-2.71%	$16,072	-4.54%	$16,036	-6.23%	9.03%	-6.34%	-7.18%	-11.14%	-10.71%	-4.51%	0.76%
2012	6	2.50%	$16,474	3.48%	$16,594	4.05%	-1.68%	2.35%	4.54%	7.11%	5.08%	5.52%	0.87%
2012	7	1.55%	$16,729	1.30%	$16,809	0.88%	3.82%	0.84%	-0.69%	0.08%	-0.03%	2.00%	3.48%
2012	8	2.07%	$17,076	1.74%	$17,102	2.70%	-1.32%	4.94%	4.08%	3.20%	0.41%	-0.01%	-0.05%
2012	9	1.62%	$17,354	1.87%	$17,422	2.49%	-2.53%	4.67%	3.14%	2.71%	5.22%	-1.86%	1.10%
2012	10	-1.65%	$17,067	-0.76%	$17,289	-1.81%	-0.48%	-2.94%	-1.96%	1.09%	-0.44%	-0.91%	1.35%
2012	11	0.75%	$17,194	0.87%	$17,440	0.77%	1.38%	-0.47%	1.65%	2.78%	1.56%	-0.26%	-0.42%
2012	12	-0.09%	$17,179	1.81%	$17,756	1.29%	-2.49%	-2.43%	3.55%	4.37%	6.80%	3.72%	-0.33%
2013	1	2.63%	$17,631	1.62%	$18,043	5.42%	-3.19%	-0.51%	5.35%	3.73%	-0.29%	3.74%	-1.30%
2013	2	0.41%	$17,704	-0.28%	$17,993	1.28%	1.24%	-5.09%	1.63%	-1.29%	-2.28%	1.22%	1.08%
2013	3	2.53%	$18,152	1.46%	$18,256	3.95%	-0.42%	0.95%	4.11%	1.31%	-1.02%	2.87%	-0.05%
2013	4	1.08%	$18,348	1.75%	$18,575	1.61%	4.68%	-7.56%	0.12%	5.02%	1.22%	6.73%	2.17%
2013	5	-0.85%	$18,191	-2.91%	$18,035	2.44%	-6.76%	-6.20%	4.29%	-3.02%	-4.83%	-5.98%	-3.22%
2013	6	-3.16%	$17,617	-3.65%	$17,377	-1.43%	-3.27%	-11.06%	-0.14%	-2.70%	-5.35%	-1.98%	-3.27%
2013	7	4.12%	$18,343	3.27%	$17,945	5.75%	-2.26%	7.43%	6.56%	5.32%	1.32%	0.90%	1.11%
2013	8	-1.53%	$18,063	-1.88%	$17,607	-3.03%	-1.34%	5.20%	-3.41%	-1.96%	-2.54%	-6.98%	-1.00%
2013	9	1.98%	$18,420	3.20%	$18,171	3.90%	0.66%	-4.78%	6.59%	7.82%	7.21%	3.49%	0.74%
2013	10	2.99%	$18,971	2.82%	$18,684	4.27%	1.43%	-0.34%	3.48%	3.26%	4.17%	4.52%	1.81%
2013	11	0.34%	$19,036	-0.79%	$18,536	2.70%	-2.70%	-5.51%	4.25%	0.55%	-0.26%	-5.25%	-0.14%
2013	12	0.79%	$19,186	0.05%	$18,546	2.73%	-1.87%	-3.79%	1.29%	2.16%	-0.42%	0.10%	0.22%
2014	1	-0.09%	$19,169	-0.58%	$18,438	-3.17%	6.30%	3.42%	-3.51%	-5.20%	-8.64%	4.28%	1.88%
2014	2	4.05%	$19,945	4.00%	$19,176	4.87%	0.52%	6.27%	4.63%	6.13%	3.38%	5.07%	1.14%
2014	3	0.07%	$19,959	0.41%	$19,255	0.51%	0.73%	-3.14%	1.34%	-0.46%	3.88%	0.49%	-0.03%
2014	4	0.59%	$20,076	0.93%	$19,434	0.06%	2.10%	0.49%	-2.29%	1.67%	0.78%	3.29%	1.33%
2014	5	1.60%	$20,398	1.38%	$19,703	2.10%	2.95%	-3.05%	0.62%	1.60%	2.95%	2.40%	1.51%
2014	6	2.46%	$20,899	2.13%	$20,122	2.62%	-0.25%	6.32%	3.85%	0.92%	2.40%	1.13%	0.01%
2014	7	-1.60%	$20,565	-1.44%	$19,832	-1.99%	0.67%	-3.63%	-5.07%	-2.60%	1.36%	0.08%	-0.32%
2014	8	3.77%	$21,341	2.72%	$20,372	4.15%	4.72%	0.38%	4.46%	0.18%	2.83%	3.04%	2.00%
2014	9	-2.65%	$20,775	-4.46%	$19,463	-2.10%	-2.11%	-6.18%	-5.94%	-3.88%	-7.77%	-6.04%	-1.68%
2014	10	1.98%	$21,186	2.74%	$19,997	2.75%	2.81%	-3.05%	7.13%	-0.27%	1.42%	9.94%	1.23%
2014	11	2.19%	$21,651	0.86%	$20,169	2.48%	2.97%	-0.49%	0.48%	0.06%	-1.54%	2.00%	0.91%
2014	12	0.90%	$21,846	0.12%	$20,193	-0.04%	3.25%	1.31%	2.56%	-4.00%	-3.99%	1.88%	-0.02%
2015	1	1.71%	$22,220	2.62%	$20,723	-2.74%	9.82%	8.69%	-5.32%	0.62%	-0.69%	6.85%	3.75%
2015	2	1.42%	$22,536	0.65%	$20,858	5.74%	-6.14%	-5.91%	5.86%	6.34%	4.41%	-3.67%	-1.42%
2015	3	-0.77%	$22,362	-0.27%	$20,801	-1.16%	1.10%	-2.15%	1.03%	-1.43%	-1.50%	1.74%	0.20%
2015	4	-0.43%	$22,267	-0.17%	$20,766	0.62%	-3.43%	-0.17%	-1.82%	3.65%	6.85%	-5.85%	-1.19%
2015	5	0.35%	$22,345	-0.64%	$20,634	1.30%	-2.37%	0.56%	0.75%	0.20%	-4.10%	-0.30%	-1.12%
2015	6	-2.21%	$21,852	-2.43%	$20,133	-1.67%	-4.07%	-1.52%	0.42%	-3.12%	-2.93%	-4.68%	-1.88%
2015	7	1.24%	$22,122	-0.09%	$20,114	1.70%	4.55%	-6.62%	-2.70%	2.03%	-6.31%	5.77%	0.83%
2015	8	-3.52%	$21,343	-3.88%	$19,333	-6.09%	-0.69%	3.71%	-4.62%	-7.43%	-8.84%	-6.29%	-0.83%
2015	9	-1.64%	$20,993	-1.23%	$19,095	-2.92%	1.97%	-1.80%	-3.77%	-4.42%	-3.13%	3.05%	1.19%
2015	10	5.23%	$22,091	4.46%	$19,946	7.91%	-0.41%	2.28%	6.57%	6.61%	6.38%	5.76%	0.57%
2015	11	-0.73%	$21,929	-1.08%	$19,732	0.60%	-0.87%	-6.75%	2.47%	-0.75%	-2.52%	-0.63%	-0.15%
2015	12	-1.48%	$21,605	-1.67%	$19,401	-2.13%	-0.30%	-0.45%	-5.08%	-2.34%	-3.83%	1.82%	-1.08%
2016	1	-1.61%	$21,257	-1.81%	$19,051	-5.72%	5.57%	5.41%	-5.85%	-5.52%	-5.03%	-3.44%	0.12%
2016	2	2.18%	$21,721	1.58%	$19,351	-0.01%	3.09%	10.93%	2.08%	-3.33%	-0.82%	-0.36%	1.05%
2016	3	4.37%	$22,671	6.15%	$20,542	7.11%	-0.09%	-0.84%	9.41%	6.58%	12.96%	10.48%	3.62%
2016	4	0.94%	$22,883	1.12%	$20,773	0.66%	-0.74%	5.11%	2.13%	2.22%	0.41%	-2.35%	1.55%
2016	5	0.46%	$22,988	-0.65%	$20,638	1.73%	0.81%	-6.14%	0.44%	-0.09%	-3.69%	2.25%	-0.51%
2016	6	2.99%	$23,675	3.65%	$21,391	0.27%	6.93%	8.97%	0.83%	-2.42%	4.56%	6.92%	3.09%
2016	7	3.27%	$24,450	3.50%	$22,140	3.98%	2.10%	1.98%	5.06%	3.98%	5.38%	4.26%	1.29%
2016	8	-0.54%	$24,317	-0.64%	$21,999	0.21%	-1.01%	-3.26%	1.13%	0.53%	0.88%	-3.76%	0.18%
2016	9	-0.12%	$24,287	0.25%	$22,054	0.21%	-1.51%	0.69%	0.87%	1.34%	2.52%	-1.82%	-0.32%
2016	10	-2.80%	$23,607	-2.95%	$21,404	-2.19%	-4.38%	-2.94%	-3.74%	-2.22%	-0.83%	-5.74%	-1.53%
2016	11	-0.18%	$23,564	-1.22%	$21,142	4.49%	-8.21%	-8.36%	13.34%	-1.78%	-4.42%	-1.68%	-3.17%
2016	12	0.89%	$23,774	1.37%	$21,431	1.98%	-0.46%	-1.91%	3.20%	2.71%	-0.25%	4.82%	0.84%
2017	1	2.10%	$24,272	2.10%	$21,881	1.86%	0.81%	5.42%	-1.21%	3.29%	6.66%	-0.19%	0.15%
2017	2	3.14%	$25,034	2.20%	$22,361	3.69%	1.59%	3.18%	1.35%	1.19%	1.74%	3.51%	1.32%
2017	3	-0.17%	$24,991	0.32%	$22,432	0.06%	-0.65%	-0.43%	-0.65%	3.23%	3.69%	-2.42%	-0.29%
2017	4	1.27%	$25,308	1.30%	$22,724	1.06%	1.57%	1.73%	0.51%	2.42%	1.70%	0.24%	1.19%
2017	5	1.06%	$25,577	0.94%	$22,938	1.01%	1.89%	-0.12%	-2.26%	3.54%	2.85%	-0.72%	1.33%
2017	6	0.49%	$25,703	0.81%	$23,124	0.95%	0.79%	-2.16%	2.96%	0.31%	0.93%	2.23%	0.48%
2017	7	1.35%	$26,050	1.85%	$23,551	1.88%	-0.66%	2.31%	0.75%	2.65%	5.82%	1.24%	0.77%
2017	8	1.45%	$26,428	0.97%	$23,779	0.15%	3.41%	4.20%	-2.72%	-0.04%	2.35%	-0.26%	0.68%
2017	9	0.55%	$26,574	0.94%	$24,002	2.44%	-2.32%	-3.37%	8.58%	2.36%	-0.04%	-0.11%	-0.05%
2017	10	1.27%	$26,911	0.76%	$24,184	2.17%	-0.04%	-0.75%	0.59%	1.68%	3.28%	-1.07%	0.19%
2017	11	2.14%	$27,486	1.34%	$24,508	3.03%	0.74%	0.36%	3.76%	0.69%	-0.39%	2.66%	-0.12%
2017	12	1.44%	$27,882	1.36%	$24,842	1.16%	1.81%	2.11%	-0.37%	1.35%	3.77%	-0.14%	1.22%
2018	1	3.00%	$28,718	1.80%	$25,289	5.23%	-3.26%	3.23%	1.33%	5.02%	8.30%	-4.25%	-1.23%
2018	2	-3.37%	$27,751	-4.20%	$24,228	-3.76%	-3.04%	-2.08%	-4.04%	-4.83%	-5.90%	-7.68%	-2.24%
2018	3	-0.49%	$27,615	0.88%	$24,441	-1.95%	2.86%	0.63%	1.37%	-0.84%	0.54%	3.88%	0.56%
2018	4	-0.33%	$27,525	-0.36%	$24,353	0.45%	-2.09%	-0.95%	1.76%	1.52%	-2.82%	0.82%	-1.57%
2018	5	2.03%	$28,082	1.14%	$24,630	2.72%	2.01%	-1.20%	5.87%	-1.89%	-2.62%	3.68%	0.52%
2018	6	0.11%	$28,113	-0.48%	$24,511	0.70%	0.65%	-3.61%	0.80%	-1.57%	-4.54%	4.20%	-0.49%
2018	7	1.47%	$28,525	1.32%	$24,835	3.32%	-1.44%	-2.24%	2.62%	2.85%	3.53%	0.60%	1.34%
2018	8	2.19%	$29,150	0.29%	$24,908	3.43%	1.31%	-2.14%	3.14%	-2.24%	-3.77%	2.58%	0.02%
2018	9	-0.63%	$28,967	-1.10%	$24,635	0.20%	-2.86%	-0.66%	-3.05%	0.97%	-0.58%	-2.64%	-0.14%
2018	10	-5.09%	$27,494	-5.00%	$23,402	-7.41%	-2.93%	2.12%	-9.94%	-8.13%	-8.76%	-2.93%	-2.05%
2018	11	1.74%	$27,971	1.80%	$23,824	2.01%	1.79%	0.34%	0.57%	0.50%	4.90%	4.67%	-0.36%
2018	12	-3.79%	$26,912	-3.21%	$23,059	-9.16%	5.85%	4.94%	-12.38%	-5.35%	-3.50%	-7.96%	1.86%
2019	1	5.89%	$28,496	7.03%	$24,681	8.54%	0.38%	2.89%	12.26%	6.63%	10.34%	11.85%	3.37%
2019	2	1.86%	$29,025	0.90%	$24,903	3.56%	-1.38%	-0.61%	4.13%	2.54%	-1.53%	0.70%	-0.20%
2019	3	1.97%	$29,597	1.33%	$25,235	1.42%	5.57%	-1.60%	-3.91%	0.92%	1.13%	4.21%	2.93%
2019	4	1.94%	$30,171	1.39%	$25,587	3.93%	-1.99%	-0.66%	4.32%	2.93%	2.35%	-0.16%	0.44%
2019	5	-2.27%	$29,487	-2.30%	$24,998	-6.45%	6.84%	1.76%	-9.98%	-5.03%	-7.33%	0.14%	1.65%
2019	6	5.78%	$31,192	5.07%	$26,266	7.08%	0.95%	8.00%	7.66%	5.91%	6.20%	1.54%	3.25%
2019	7	0.96%	$31,490	0.04%	$26,277	1.41%	0.26%	0.01%	1.30%	-1.95%	-2.66%	1.70%	0.25%
2019	8	2.30%	$32,216	1.71%	$26,726	-2.08%	11.04%	7.91%	-5.14%	-1.92%	-3.78%	3.75%	3.88%
2019	9	0.05%	$32,232	0.91%	$26,970	1.78%	-2.68%	-3.39%	5.57%	3.16%	1.69%	1.93%	-0.76%
2019	10	1.42%	$32,690	1.84%	$27,466	2.11%	-1.11%	2.56%	2.00%	3.39%	4.18%	1.13%	0.44%
2019	11	1.87%	$33,303	0.39%	$27,572	3.79%	-0.41%	-3.21%	2.71%	1.13%	-0.09%	-1.30%	0.47%
2019	12	1.53%	$33,813	2.26%	$28,195	2.80%	-3.20%	3.66%	2.84%	2.98%	7.71%	0.76%	0.53%
2020	1	2.35%	$34,606	0.07%	$28,213	-0.06%	7.69%	4.50%	-6.31%	-2.82%	-6.15%	1.23%	2.45%
2020	2	-3.62%	$33,353	-3.70%	$27,168	-8.00%	6.63%	-0.64%	-10.15%	-7.77%	-3.78%	-7.03%	1.09%
2020	3	-7.37%	$30,895	-11.14%	$24,142	-13.91%	6.38%	-0.22%	-25.76%	-14.11%	-15.77%	-19.42%	-6.31%
2020	4	9.58%	$33,856	7.81%	$26,027	13.13%	1.22%	7.26%	13.89%	5.82%	7.35%	8.96%	4.85%
2020	5	3.36%	$34,994	2.67%	$26,722	5.40%	-1.76%	2.59%	2.55%	5.43%	2.97%	1.73%	2.46%
2020	6	1.90%	$35,659	2.95%	$27,511	2.29%	0.34%	2.74%	3.58%	3.51%	6.61%	2.41%	2.13%
2020	7	6.12%	$37,842	5.06%	$28,903	5.74%	4.44%	10.79%	2.58%	1.94%	8.25%	3.64%	3.10%
2020	8	3.29%	$39,088	1.63%	$29,375	7.10%	-5.05%	-0.32%	5.07%	4.72%	2.89%	0.44%	-1.78%
2020	9	-2.63%	$38,059	-2.29%	$28,703	-3.54%	0.77%	-4.17%	-5.18%	-2.05%	-1.01%	-2.68%	-0.44%
2020	10	-2.09%	$37,265	-0.98%	$28,421	-1.95%	-3.39%	-0.52%	3.66%	-3.55%	1.41%	-3.00%	-0.51%
2020	11	7.13%	$39,923	8.00%	$30,694	11.80%	1.66%	-5.41%	19.21%	14.27%	8.99%	9.67%	3.77%
2020	12	3.63%	$41,371	4.12%	$31,960	4.68%	-1.23%	7.01%	7.50%	5.01%	7.14%	2.72%	0.15%
2021	1	-1.49%	$40,756	-0.04%	$31,946	-0.33%	-3.63%	-3.22%	6.25%	-0.78%	3.17%	0.04%	-1.83%
2021	2	-0.18%	$40,682	0.77%	$32,191	3.14%	-5.73%	-6.26%	10.80%	2.24%	0.79%	3.43%	-2.26%
2021	3	0.94%	$41,066	1.04%	$32,526	3.65%	-5.24%	-1.14%	5.61%	2.51%	-0.73%	5.15%	-1.48%
2021	4	4.25%	$42,811	3.23%	$33,576	5.04%	2.49%	3.56%	1.69%	2.95%	1.20%	7.86%	1.04%
2021	5	1.33%	$43,378	2.32%	$34,356	0.46%	0.00%	7.68%	3.89%	3.48%	1.65%	0.81%	0.62%
2021	6	1.63%	$44,085	0.47%	$34,517	2.48%	4.42%	-7.15%	-0.71%	-1.08%	0.95%	2.64%	2.21%
2021	7	2.30%	$45,100	0.47%	$34,681	1.74%	3.72%	2.53%	-4.36%	0.77%	-6.44%	4.42%	1.42%
2021	8	1.72%	$45,876	1.14%	$35,075	2.86%	-0.34%	-0.08%	1.82%	1.45%	1.57%	2.15%	-0.34%
2021	9	-3.94%	$44,070	-3.30%	$33,919	-4.46%	-2.91%	-3.22%	-1.46%	-3.26%	-3.87%	-5.68%	-1.51%
2021	10	5.01%	$46,277	3.18%	$34,997	6.69%	2.46%	1.48%	2.86%	3.18%	1.07%	7.13%	0.53%
2021	11	-0.38%	$46,103	-1.61%	$34,435	-1.46%	2.77%	-0.69%	-2.62%	-4.53%	-4.08%	-2.11%	-0.12%
2021	12	2.38%	$47,200	3.10%	$35,502	3.79%	-2.01%	3.30%	4.12%	4.41%	1.53%	9.69%	-0.03%

Portfolio return and risk metrics
Metric	Maximum Return at 10.00% Volatility	Equal Weighted
Arithmetic Mean (monthly)	0.85%	0.72%
Arithmetic Mean (annualized)	10.72%	8.99%
Geometric Mean (monthly)	0.81%	0.66%
Geometric Mean (annualized)	10.18%	8.24%
Standard Deviation (monthly)	2.85%	3.39%
Standard Deviation (annualized)	9.87%	11.75%
Downside Deviation (monthly)	1.78%	2.24%
Maximum Drawdown	-30.57%	-36.98%
Stock Market Correlation	0.91	0.88
Beta^(*)	0.58	0.67
Alpha (annualized)	3.51%	0.90%
R²	82.18%	76.98%
Sharpe Ratio	0.93	0.64
Sortino Ratio	1.46	0.97
Treynor Ratio (%)	15.80	11.34
Calmar Ratio	1.92	1.07
Active Return	-0.70%	-2.64%
Tracking Error	7.70%	7.61%
Information Ratio	-0.09	-0.35
Skewness	-0.79	-0.82
Excess Kurtosis	3.62	4.40
Historical Value-at-Risk (5%)	-3.57%	-4.45%
Analytical Value-at-Risk (5%)	-3.82%	-4.85%
Conditional Value-at-Risk (5%)	-6.06%	-7.68%
Upside Capture Ratio (%)	62.70	63.95
Downside Capture Ratio (%)	49.01	62.16
Safe Withdrawal Rate	9.86%	9.52%
Perpetual Withdrawal Rate	7.25%	5.58%
Positive Periods	127 out of 192 (66.15%)	122 out of 192 (63.54%)
Gain/Loss Ratio	1.14	1.04
^* 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 Return at 10.00% Volatility	Equal Weighted
Subprime Crisis	Nov 2007	Mar 2009	-30.57%	-36.98%
COVID-19 Start	Jan 2020	Mar 2020	-10.73%	-14.43%

Drawdowns for Maximum Return at 10.00% Volatility

Drawdowns for Maximum Return at 10.00% Volatility (worst 10)
Rank	Start	End	Length	Recovery By	Recovery Time	Underwater Period	Drawdown
1	Nov 2007	Feb 2009	1 year 4 months	Sep 2010	1 year 7 months	2 years 11 months	-30.57%
2	Feb 2020	Mar 2020	2 months	May 2020	2 months	4 months	-10.73%
3	Sep 2018	Dec 2018	4 months	Mar 2019	3 months	7 months	-7.68%
4	Mar 2015	Sep 2015	7 months	Mar 2016	6 months	1 year 1 month	-6.85%
5	Sep 2020	Oct 2020	2 months	Nov 2020	1 month	3 months	-4.66%
6	May 2011	Sep 2011	5 months	Oct 2011	1 month	6 months	-4.58%
7	Feb 2018	Apr 2018	3 months	Aug 2018	4 months	7 months	-4.15%
8	May 2013	Jun 2013	2 months	Sep 2013	3 months	5 months	-3.98%
9	Sep 2021	Sep 2021	1 month	Oct 2021	1 month	2 months	-3.94%
10	Aug 2016	Nov 2016	4 months	Feb 2017	3 months	7 months	-3.62%
Worst 10 drawdowns included above

Drawdowns for Equal Weighted

Drawdowns for Equal Weighted (worst 10)
Rank	Start	End	Length	Recovery By	Recovery Time	Underwater Period	Drawdown
1	Nov 2007	Feb 2009	1 year 4 months	Sep 2010	1 year 7 months	2 years 11 months	-36.98%
2	Feb 2020	Mar 2020	2 months	Jul 2020	4 months	6 months	-14.43%
3	May 2011	Sep 2011	5 months	Jan 2012	4 months	9 months	-9.81%
4	Feb 2018	Dec 2018	11 months	Apr 2019	4 months	1 year 3 months	-8.82%
5	Mar 2015	Jan 2016	11 months	Jun 2016	5 months	1 year 4 months	-8.66%
6	May 2013	Jun 2013	2 months	Oct 2013	4 months	6 months	-6.45%
7	May 2012	May 2012	1 month	Jul 2012	2 months	3 months	-4.54%
8	Aug 2016	Nov 2016	4 months	Feb 2017	3 months	7 months	-4.51%
9	Sep 2014	Sep 2014	1 month	Jan 2015	4 months	5 months	-4.46%
10	Jun 2007	Jul 2007	2 months	Sep 2007	2 months	4 months	-3.49%
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
VTI	Vanguard Total Stock Market ETF	11.00%	15.40%	33.45%	-36.98%	-50.84%	0.69	1.02	1.00
TLT	iShares 20+ Year Treasury Bond ETF	6.26%	13.33%	33.96%	-21.80%	-21.80%	0.44	0.76	-0.31
GLD	SPDR Gold Shares	7.78%	17.48%	30.45%	-28.33%	-42.91%	0.46	0.74	0.06
IJS	iShares S&P Small-Cap 600 Value ETF	9.34%	20.66%	39.34%	-29.39%	-54.13%	0.49	0.71	0.90
EFA	iShares MSCI EAFE ETF	4.76%	17.35%	26.95%	-41.04%	-57.38%	0.30	0.42	0.89
EEM	iShares MSCI Emerging Markets ETF	5.25%	21.80%	68.93%	-48.88%	-60.44%	0.30	0.44	0.78
VNQ	Vanguard Real Estate ETF	8.76%	22.56%	40.52%	-37.00%	-68.30%	0.44	0.63	0.74
LQD	iShares iBoxx $ Invmt Grade Corp Bd ETF	5.44%	7.30%	17.37%	-3.79%	-15.11%	0.61	1.00	0.34

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
Vanguard Total Stock Market ETF	9.11%	25.67%	25.67%	25.73%	17.96%	16.29%	0.03%	0.03%
iShares 20+ Year Treasury Bond ETF	3.18%	-4.60%	-4.60%	8.75%	6.68%	4.51%	0.15%	0.15%
SPDR Gold Shares	4.10%	-4.15%	-4.15%	12.13%	9.30%	1.18%	0.40%	0.40%
iShares S&P Small-Cap 600 Value ETF	4.30%	30.53%	30.53%	18.47%	10.04%	13.33%	0.18%	0.18%
iShares MSCI EAFE ETF	2.84%	11.46%	11.46%	13.53%	9.55%	7.92%	0.32%	0.32%
iShares MSCI Emerging Markets ETF	-1.57%	-3.61%	-3.61%	10.06%	9.16%	4.73%	0.68%	0.68%
Vanguard Real Estate ETF	15.03%	40.52%	40.52%	19.96%	11.22%	11.50%	0.12%	0.12%
iShares iBoxx $ Invmt Grade Corp Bd ETF	0.38%	-1.85%	-1.85%	8.53%	5.66%	4.94%	0.14%	0.14%
Trailing returns as of last calendar month ending December 2021

Monthly Correlations

Correlations for the portfolio assets
Ticker	Name	VTI	TLT	GLD	IJS	EFA	EEM	VNQ	LQD	Maximum Return at 10.00% Volatility	Equal Weighted
VTI	Vanguard Total Stock Market ETF	1.00	-0.32	0.07	0.90	0.89	0.78	0.74	0.34	0.91	0.88
TLT	iShares 20+ Year Treasury Bond ETF	-0.32	1.00	0.21	-0.38	-0.26	-0.25	-0.01	0.49	0.05	-0.03
GLD	SPDR Gold Shares	0.07	0.21	1.00	-0.01	0.15	0.29	0.10	0.27	0.37	0.37
IJS	iShares S&P Small-Cap 600 Value ETF	0.90	-0.38	-0.01	1.00	0.78	0.70	0.73	0.25	0.77	0.81
EFA	iShares MSCI EAFE ETF	0.89	-0.26	0.15	0.78	1.00	0.87	0.70	0.40	0.83	0.89
EEM	iShares MSCI Emerging Markets ETF	0.78	-0.25	0.29	0.70	0.87	1.00	0.61	0.38	0.76	0.87
VNQ	Vanguard Real Estate ETF	0.74	-0.01	0.10	0.73	0.70	0.61	1.00	0.46	0.76	0.85
LQD	iShares iBoxx $ Invmt Grade Corp Bd ETF	0.34	0.49	0.27	0.25	0.40	0.38	0.46	1.00	0.55	0.58

Portfolio Risk Decomposition

Portfolio risk decomposition
Ticker	Name	Maximum Return at 10.00% Volatility	Equal Weighted
VTI	Vanguard Total Stock Market ETF	89.59%	14.37%
TLT	iShares 20+ Year Treasury Bond ETF	1.54%	-0.38%
GLD	SPDR Gold Shares	8.87%	6.79%
IJS	iShares S&P Small-Cap 600 Value ETF		17.83%
EFA	iShares MSCI EAFE ETF		16.48%
EEM	iShares MSCI Emerging Markets ETF		20.13%
VNQ	Vanguard Real Estate ETF		20.28%
LQD	iShares iBoxx $ Invmt Grade Corp Bd ETF		4.49%
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	Maximum Return at 10.00% Volatility			Equal Weighted
Roll Period	Average	High	Low	Average	High	Low
1 year	10.46%	34.66%	-27.36%	8.57%	47.20%	-32.87%
3 years	9.55%	22.85%	-5.28%	7.31%	25.23%	-6.98%
5 years	10.04%	17.83%	5.79%	7.78%	17.64%	3.02%
7 years	9.97%	13.81%	7.61%	7.56%	12.50%	4.07%
10 years	9.98%	12.70%	7.51%	7.61%	11.33%	5.92%
15 years	9.92%	10.28%	9.57%	7.80%	8.14%	7.34%