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 - Sep 2021) Save

Note: The time period was constrained by the available data for SPDR Gold Shares (GLD) [Dec 2004 - Sep 2021].

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 11.89%. 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	63.15%
TLT	iShares 20+ Year Treasury Bond ETF	22.42%
GLD	SPDR Gold Shares	14.43%
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	$44,116	$33,919
CAGR	9.88%	8.06%
Expected Return	10.42%	8.82%
Stdev	9.90%	11.80%
Best Year	25.64%	23.38%
Worst Year	-18.32%	-21.23%
Max. Drawdown	-30.43%	-36.98%
Sharpe Ratio (ex-ante)	0.90	0.63
Sharpe Ratio (ex-post)	0.89	0.63
Sortino Ratio	1.41	0.94
US Stock Market Correlation	0.90	0.88
Results based on historical returns. Expected return is the annualized monthly arithmetic mean return.

Trailing Returns

Trailing Returns
Name	Annualized Return							Annualized Volatility
Name	3 Month	YTD	1 year	3 year	5 year	10 year	Full	3 year	5 year
Maximum Return at 10.00% Volatility	-0.04%	6.47%	15.74%	15.03%	12.65%	11.91%	9.88%	12.29%	10.10%
Equal Weighted	-1.73%	6.13%	18.17%	11.25%	8.99%	8.91%	8.06%	12.60%	10.30%
Trailing annualized return and volatility are for full months ending in September 2021 excluding portfolio cashflows.

Notes on results:

Past performance is no guarantee of future results, which may vary. All use is subject to terms of service.
Investing involves risk, including possible loss of principal. The value of the investments and the income derived from them may fluctuate over time.
All portfolio returns presented are hypothetical and backtested. Hypothetical returns do not reflect trading costs, transaction fees, or taxes.
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 information from a variety of sources we consider reliable, but we do not represent that the information is accurate or complete.
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.
The results are based on the total return of assets and assume that all received dividends and distributions are reinvested.
The annual results for 2021 are based on full calendar months from January to September
CAGR = Compound Annual Growth Rate
Stdev = Annualized standard deviation of monthly returns
Sharpe ratio is calculated and annualized from monthly excess returns over the risk free rate (3-month treasury bill)
Drawdowns are calculated based on monthly returns.
The backtested 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)	11.89%	15.43%	0.662	0.00%	100.00%
2	iShares S&P Small-Cap 600 Value ETF (IJS)	11.61%	20.78%	0.479	0.00%	100.00%
3	iShares MSCI EAFE ETF (EFA)	6.27%	17.40%	0.288	0.00%	100.00%
4	iShares MSCI Emerging Markets ETF (EEM)	8.02%	21.94%	0.304	0.00%	100.00%
5	Vanguard Real Estate ETF (VNQ)	10.81%	22.56%	0.409	0.00%	100.00%
6	iShares 20+ Year Treasury Bond ETF (TLT)	7.08%	13.40%	0.432	0.00%	100.00%
7	iShares iBoxx $ Invmt Grade Corp Bd ETF (LQD)	5.78%	7.36%	0.620	0.00%	100.00%
8	SPDR Gold Shares (GLD)	9.28%	17.60%	0.445	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	0.06
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	0.41	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	0.22
iShares iBoxx $ Invmt Grade Corp Bd ETF	LQD	0.34	0.25	0.41	0.38	0.46	0.49	1.00	0.27
SPDR Gold Shares	GLD	0.06	-0.01	0.15	0.29	0.10	0.22	0.27	1.00
Based on monthly returns from Jan 2006 to Sep 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	13.01%	0.26%	0.00%	0.00%	0.00%	12.94%	68.20%	5.59%	6.94%	7.09%	0.797
2	13.78%	0.13%	0.00%	0.00%	0.00%	13.46%	66.93%	5.70%	6.99%	7.09%	0.804
3	14.54%	0.00%	0.00%	0.00%	0.00%	13.99%	65.66%	5.81%	7.03%	7.09%	0.810
4	15.16%	0.00%	0.00%	0.00%	0.00%	14.55%	64.36%	5.93%	7.08%	7.09%	0.816
5	15.78%	0.00%	0.00%	0.00%	0.00%	15.10%	63.06%	6.05%	7.13%	7.09%	0.823
6	16.41%	0.00%	0.00%	0.00%	0.00%	15.66%	61.76%	6.17%	7.18%	7.10%	0.829
7	17.03%	0.00%	0.00%	0.00%	0.00%	16.22%	60.45%	6.29%	7.23%	7.10%	0.835
8	17.66%	0.00%	0.00%	0.00%	0.00%	16.77%	59.15%	6.42%	7.28%	7.11%	0.840
9	18.28%	0.00%	0.00%	0.00%	0.00%	17.33%	57.85%	6.54%	7.33%	7.12%	0.846
10	18.91%	0.00%	0.00%	0.00%	0.00%	17.89%	56.55%	6.66%	7.38%	7.12%	0.852
11	19.53%	0.00%	0.00%	0.00%	0.00%	18.45%	55.24%	6.78%	7.43%	7.13%	0.857
12	20.16%	0.00%	0.00%	0.00%	0.00%	19.00%	53.94%	6.90%	7.48%	7.14%	0.862
13	20.78%	0.00%	0.00%	0.00%	0.00%	19.56%	52.64%	7.02%	7.53%	7.15%	0.868
14	21.41%	0.00%	0.00%	0.00%	0.00%	20.12%	51.34%	7.14%	7.58%	7.16%	0.873
15	22.03%	0.00%	0.00%	0.00%	0.00%	20.68%	50.03%	7.26%	7.63%	7.17%	0.878
16	22.66%	0.00%	0.00%	0.00%	0.00%	21.23%	48.73%	7.38%	7.67%	7.19%	0.882
17	23.28%	0.00%	0.00%	0.00%	0.00%	21.79%	47.43%	7.50%	7.72%	7.20%	0.887
18	23.90%	0.00%	0.00%	0.00%	0.00%	22.35%	46.13%	7.62%	7.77%	7.22%	0.892
19	24.53%	0.00%	0.00%	0.00%	0.00%	22.90%	44.82%	7.74%	7.82%	7.23%	0.896
20	25.15%	0.00%	0.00%	0.00%	0.00%	23.46%	43.52%	7.86%	7.87%	7.25%	0.900
21	25.78%	0.00%	0.00%	0.00%	0.00%	24.02%	42.22%	7.98%	7.92%	7.27%	0.905
22	26.40%	0.00%	0.00%	0.00%	0.00%	24.58%	40.92%	8.10%	7.97%	7.28%	0.909
23	27.03%	0.00%	0.00%	0.00%	0.00%	25.13%	39.61%	8.22%	8.02%	7.30%	0.913
24	27.65%	0.00%	0.00%	0.00%	0.00%	25.69%	38.31%	8.35%	8.07%	7.32%	0.916
25	28.28%	0.00%	0.00%	0.00%	0.00%	26.25%	37.01%	8.47%	8.12%	7.34%	0.920
26	28.90%	0.00%	0.00%	0.00%	0.00%	26.80%	35.71%	8.59%	8.17%	7.37%	0.924
27	29.53%	0.00%	0.00%	0.00%	0.00%	27.36%	34.40%	8.71%	8.22%	7.39%	0.927
28	30.15%	0.00%	0.00%	0.00%	0.00%	27.92%	33.10%	8.83%	8.27%	7.41%	0.930
29	30.77%	0.00%	0.00%	0.00%	0.00%	28.48%	31.80%	8.95%	8.32%	7.43%	0.934
30	31.40%	0.00%	0.00%	0.00%	0.00%	29.03%	30.50%	9.07%	8.37%	7.46%	0.937
31	32.02%	0.00%	0.00%	0.00%	0.00%	29.59%	29.19%	9.19%	8.42%	7.48%	0.940
32	32.65%	0.00%	0.00%	0.00%	0.00%	30.15%	27.89%	9.31%	8.47%	7.51%	0.943
33	33.27%	0.00%	0.00%	0.00%	0.00%	30.71%	26.59%	9.43%	8.52%	7.54%	0.945
34	33.90%	0.00%	0.00%	0.00%	0.00%	31.26%	25.29%	9.55%	8.57%	7.57%	0.948
35	34.52%	0.00%	0.00%	0.00%	0.00%	31.82%	23.99%	9.67%	8.62%	7.59%	0.950
36	35.15%	0.00%	0.00%	0.00%	0.00%	32.38%	22.68%	9.79%	8.67%	7.62%	0.953
37	35.77%	0.00%	0.00%	0.00%	0.00%	32.93%	21.38%	9.91%	8.72%	7.65%	0.955
38	36.40%	0.00%	0.00%	0.00%	0.00%	33.49%	20.08%	10.03%	8.76%	7.68%	0.957
39	37.02%	0.00%	0.00%	0.00%	0.00%	34.05%	18.78%	10.16%	8.81%	7.72%	0.959
40	37.65%	0.00%	0.00%	0.00%	0.00%	34.61%	17.47%	10.28%	8.86%	7.75%	0.961
41	38.27%	0.00%	0.00%	0.00%	0.00%	35.16%	16.17%	10.40%	8.91%	7.78%	0.963
42	38.89%	0.00%	0.00%	0.00%	0.00%	35.72%	14.87%	10.52%	8.96%	7.81%	0.965
43	39.52%	0.00%	0.00%	0.00%	0.00%	36.28%	13.57%	10.64%	9.01%	7.85%	0.967
44	40.14%	0.00%	0.00%	0.00%	0.00%	36.84%	12.26%	10.76%	9.06%	7.88%	0.968
45	40.77%	0.00%	0.00%	0.00%	0.00%	37.39%	10.96%	10.88%	9.11%	7.92%	0.970
46	41.39%	0.00%	0.00%	0.00%	0.00%	37.95%	9.66%	11.00%	9.16%	7.96%	0.971
47	42.02%	0.00%	0.00%	0.00%	0.00%	38.51%	8.36%	11.12%	9.21%	7.99%	0.972
48	42.64%	0.00%	0.00%	0.00%	0.00%	39.06%	7.05%	11.24%	9.26%	8.03%	0.974
49	43.27%	0.00%	0.00%	0.00%	0.00%	39.62%	5.75%	11.36%	9.31%	8.07%	0.975
50	43.89%	0.00%	0.00%	0.00%	0.00%	40.18%	4.45%	11.48%	9.36%	8.11%	0.976
51	44.52%	0.00%	0.00%	0.00%	0.00%	40.74%	3.15%	11.60%	9.41%	8.15%	0.977
52	45.14%	0.00%	0.00%	0.00%	0.00%	41.29%	1.84%	11.72%	9.46%	8.19%	0.978
53	45.76%	0.00%	0.00%	0.00%	0.00%	41.85%	0.54%	11.84%	9.51%	8.23%	0.978
54	46.59%	0.00%	0.00%	0.00%	0.00%	41.43%	0.00%	11.98%	9.56%	8.27%	0.979
55	47.57%	0.00%	0.00%	0.00%	0.00%	40.31%	0.00%	12.12%	9.61%	8.32%	0.979
56	48.54%	0.00%	0.00%	0.00%	0.00%	39.19%	0.00%	12.27%	9.66%	8.37%	0.978
57	49.52%	0.00%	0.00%	0.00%	0.00%	38.07%	0.00%	12.41%	9.71%	8.44%	0.976
58	50.49%	0.00%	0.00%	0.00%	0.00%	36.96%	0.00%	12.55%	9.77%	8.50%	0.974
59	51.46%	0.00%	0.00%	0.00%	0.00%	35.84%	0.00%	12.70%	9.82%	8.58%	0.970
60	52.44%	0.00%	0.00%	0.00%	0.00%	34.72%	0.00%	12.84%	9.87%	8.66%	0.967
61	53.41%	0.00%	0.00%	0.00%	0.00%	33.60%	0.00%	12.99%	9.92%	8.75%	0.962
62	54.39%	0.00%	0.00%	0.00%	0.00%	32.48%	0.00%	13.13%	9.97%	8.84%	0.958
63	55.36%	0.00%	0.00%	0.00%	0.00%	31.37%	0.00%	13.27%	10.02%	8.94%	0.952
64	56.33%	0.00%	0.00%	0.00%	0.00%	30.25%	0.00%	13.42%	10.07%	9.04%	0.946
65	57.31%	0.00%	0.00%	0.00%	0.00%	29.13%	0.00%	13.56%	10.12%	9.15%	0.940
66	58.28%	0.00%	0.00%	0.00%	0.00%	28.01%	0.00%	13.71%	10.17%	9.26%	0.934
67	59.26%	0.00%	0.00%	0.00%	0.00%	26.89%	0.00%	13.85%	10.22%	9.38%	0.927
68	60.23%	0.00%	0.00%	0.00%	0.00%	25.78%	0.00%	14.00%	10.27%	9.51%	0.919
69	61.20%	0.00%	0.00%	0.00%	0.00%	24.66%	0.00%	14.14%	10.32%	9.63%	0.912
70	62.18%	0.00%	0.00%	0.00%	0.00%	23.54%	0.00%	14.28%	10.37%	9.77%	0.904
71	63.15%	0.00%	0.00%	0.00%	0.00%	22.42%	0.00%	14.43%	10.42%	9.90%	0.896
72	64.13%	0.00%	0.00%	0.00%	0.00%	21.30%	0.00%	14.57%	10.47%	10.04%	0.888
73	65.10%	0.00%	0.00%	0.00%	0.00%	20.19%	0.00%	14.72%	10.52%	10.19%	0.880
74	66.07%	0.00%	0.00%	0.00%	0.00%	19.07%	0.00%	14.86%	10.57%	10.34%	0.872
75	67.05%	0.00%	0.00%	0.00%	0.00%	17.95%	0.00%	15.00%	10.62%	10.49%	0.864
76	68.02%	0.00%	0.00%	0.00%	0.00%	16.83%	0.00%	15.15%	10.67%	10.64%	0.856
77	68.99%	0.00%	0.00%	0.00%	0.00%	15.71%	0.00%	15.29%	10.72%	10.80%	0.847
78	69.97%	0.00%	0.00%	0.00%	0.00%	14.60%	0.00%	15.44%	10.77%	10.96%	0.839
79	70.94%	0.00%	0.00%	0.00%	0.00%	13.48%	0.00%	15.58%	10.82%	11.13%	0.831
80	71.92%	0.00%	0.00%	0.00%	0.00%	12.36%	0.00%	15.72%	10.88%	11.30%	0.823
81	72.89%	0.00%	0.00%	0.00%	0.00%	11.24%	0.00%	15.87%	10.93%	11.47%	0.815
82	73.86%	0.00%	0.00%	0.00%	0.00%	10.12%	0.00%	16.01%	10.98%	11.64%	0.806
83	74.84%	0.00%	0.00%	0.00%	0.00%	9.01%	0.00%	16.16%	11.03%	11.81%	0.798
84	75.81%	0.00%	0.00%	0.00%	0.00%	7.89%	0.00%	16.30%	11.08%	11.99%	0.790
85	76.79%	0.00%	0.00%	0.00%	0.00%	6.77%	0.00%	16.44%	11.13%	12.17%	0.783
86	77.76%	0.00%	0.00%	0.00%	0.00%	5.65%	0.00%	16.59%	11.18%	12.35%	0.775
87	78.73%	0.00%	0.00%	0.00%	0.00%	4.53%	0.00%	16.73%	11.23%	12.54%	0.767
88	79.71%	0.00%	0.00%	0.00%	0.00%	3.41%	0.00%	16.88%	11.28%	12.72%	0.760
89	80.68%	0.00%	0.00%	0.00%	0.00%	2.30%	0.00%	17.02%	11.33%	12.91%	0.752
90	81.66%	0.00%	0.00%	0.00%	0.00%	1.18%	0.00%	17.16%	11.38%	13.10%	0.745
91	82.63%	0.00%	0.00%	0.00%	0.00%	0.06%	0.00%	17.31%	11.43%	13.29%	0.737
92	84.51%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	15.49%	11.48%	13.49%	0.730
93	86.45%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	13.55%	11.54%	13.70%	0.722
94	88.39%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	11.61%	11.59%	13.91%	0.714
95	90.32%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	9.68%	11.64%	14.14%	0.706
96	92.26%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	7.74%	11.69%	14.38%	0.697
97	94.19%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	5.81%	11.74%	14.63%	0.689
98	96.13%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	3.87%	11.79%	14.89%	0.680
99	98.06%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	1.94%	11.84%	15.15%	0.671
100	100.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	11.89%	15.43%	0.662
^*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%	13.42%	$11,342	19.39%	$11,939	15.69%	0.71%	22.55%	19.37%	25.81%	31.19%	35.30%	4.22%
2007	4.08%	10.13%	$12,491	8.39%	$12,941	5.37%	10.29%	30.45%	-5.56%	9.94%	33.31%	-16.50%	3.73%
2008	0.09%	-18.32%	$10,202	-21.23%	$10,194	-36.98%	33.93%	4.92%	-29.39%	-41.04%	-48.88%	-37.00%	2.40%
2009	2.72%	15.80%	$11,814	23.38%	$12,577	28.89%	-21.80%	24.03%	22.36%	26.95%	68.93%	30.08%	8.46%
2010	1.50%	18.26%	$13,972	18.79%	$14,941	17.42%	9.05%	29.27%	24.69%	8.15%	16.51%	28.37%	9.33%
2011	2.96%	10.16%	$15,392	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%	$17,287	14.22%	$17,756	16.45%	2.63%	6.60%	18.24%	18.82%	19.10%	17.63%	10.58%
2013	1.50%	11.39%	$19,256	4.45%	$18,546	33.45%	-13.37%	-28.33%	39.34%	21.40%	-3.69%	2.31%	-2.00%
2014	0.76%	13.62%	$21,879	8.88%	$20,193	12.54%	27.30%	-2.19%	7.56%	-6.20%	-3.93%	30.36%	8.21%
2015	0.73%	-1.19%	$21,617	-3.92%	$19,401	0.36%	-1.79%	-10.67%	-6.90%	-1.00%	-16.18%	2.42%	-1.25%
2016	2.07%	10.09%	$23,799	10.46%	$21,431	12.83%	1.18%	8.03%	31.25%	1.37%	10.87%	8.60%	6.21%
2017	2.11%	17.29%	$27,913	15.92%	$24,842	21.21%	9.18%	12.81%	11.35%	25.10%	37.28%	4.91%	7.06%
2018	1.91%	-3.47%	$26,944	-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%	$33,852	22.27%	$28,195	30.67%	14.12%	17.86%	24.12%	22.03%	18.20%	28.87%	17.37%
2020	1.36%	22.40%	$41,434	13.35%	$31,960	21.03%	18.15%	24.81%	2.63%	7.59%	17.03%	-4.68%	10.97%
2021	5.31%	6.47%	$44,116	6.13%	$33,919	15.18%	-7.55%	-7.93%	25.15%	8.38%	-2.07%	22.15%	-2.21%
Annual return for 2021 is from 01/01/2021 to 09/30/2021

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	3.16%	$10,316	5.95%	$10,595	3.22%	-1.34%	9.93%	8.75%	5.77%	14.20%	7.54%	-0.44%
2006	2	0.23%	$10,340	-0.19%	$10,575	0.22%	1.11%	-1.11%	0.27%	-0.70%	-3.85%	1.86%	0.68%
2006	3	0.79%	$10,422	1.90%	$10,776	2.05%	-4.57%	3.62%	4.86%	4.01%	2.17%	4.73%	-1.68%
2006	4	1.72%	$10,602	2.26%	$11,020	0.96%	-2.75%	12.03%	0.18%	4.79%	6.52%	-3.40%	-0.20%
2006	5	-2.27%	$10,361	-3.39%	$10,646	-3.22%	-0.19%	-1.32%	-4.55%	-3.82%	-11.14%	-2.70%	-0.19%
2006	6	-0.33%	$10,327	0.21%	$10,669	0.13%	1.18%	-4.67%	0.04%	-0.06%	0.21%	4.95%	-0.09%
2006	7	0.86%	$10,416	1.33%	$10,810	-0.12%	2.16%	3.15%	-3.10%	0.81%	2.34%	3.89%	1.46%
2006	8	1.94%	$10,618	2.07%	$11,033	2.30%	3.06%	-1.38%	2.70%	2.55%	1.58%	3.48%	2.22%
2006	9	1.20%	$10,746	0.38%	$11,075	2.26%	1.91%	-4.53%	1.19%	0.22%	-0.87%	1.96%	0.87%
2006	10	2.61%	$11,026	3.63%	$11,477	3.53%	0.85%	1.29%	5.52%	3.75%	7.06%	6.03%	1.00%
2006	11	2.98%	$11,355	3.65%	$11,896	2.33%	2.31%	6.89%	2.38%	3.07%	5.98%	4.78%	1.46%
2006	12	-0.11%	$11,342	0.36%	$11,939	1.20%	-2.69%	-1.83%	0.32%	3.20%	5.44%	-1.83%	-0.90%
2007	1	1.32%	$11,492	1.99%	$12,177	1.86%	-1.00%	2.56%	2.14%	1.39%	0.11%	8.78%	0.09%
2007	2	0.10%	$11,504	-0.08%	$12,167	-1.62%	3.39%	2.55%	-0.92%	-0.12%	-3.24%	-2.70%	2.00%
2007	3	0.17%	$11,523	0.59%	$12,238	1.12%	-1.70%	-1.11%	0.91%	2.90%	5.33%	-2.07%	-0.68%
2007	4	3.04%	$11,873	2.13%	$12,499	4.02%	0.90%	2.05%	1.84%	3.75%	3.73%	-0.13%	0.89%
2007	5	1.50%	$12,051	1.19%	$12,649	3.72%	-2.31%	-2.31%	4.63%	2.36%	5.06%	-0.38%	-1.23%
2007	6	-1.62%	$11,856	-1.67%	$12,437	-1.76%	-1.01%	-1.94%	-2.24%	-0.32%	3.68%	-8.99%	-0.81%
2007	7	-1.15%	$11,720	-1.85%	$12,207	-3.53%	3.32%	2.37%	-6.26%	-2.29%	0.71%	-8.26%	-0.82%
2007	8	1.49%	$11,895	1.90%	$12,440	1.47%	1.79%	1.11%	1.33%	-0.63%	1.04%	6.74%	2.38%
2007	9	4.00%	$12,370	4.55%	$13,006	3.85%	0.23%	10.51%	0.31%	5.32%	11.57%	3.90%	0.73%
2007	10	2.54%	$12,685	3.85%	$13,507	1.79%	1.81%	6.95%	1.06%	4.25%	11.87%	2.10%	0.97%
2007	11	-1.90%	$12,444	-3.46%	$13,039	-4.52%	5.35%	-1.65%	-7.15%	-3.62%	-7.65%	-9.47%	1.02%
2007	12	0.38%	$12,491	-0.75%	$12,941	-0.70%	-0.64%	6.65%	-0.71%	-2.99%	-1.43%	-5.41%	-0.81%
2008	1	-1.86%	$12,259	-1.53%	$12,743	-6.17%	2.10%	10.84%	-4.00%	-7.85%	-8.92%	-0.78%	2.57%
2008	2	-0.92%	$12,146	-0.50%	$12,680	-2.50%	-0.46%	5.23%	-3.36%	-1.02%	1.99%	-3.18%	-0.71%
2008	3	-0.95%	$12,030	-0.17%	$12,658	-0.90%	2.14%	-6.00%	0.83%	0.42%	-3.75%	6.48%	-0.60%
2008	4	1.93%	$12,262	2.89%	$13,023	4.89%	-2.48%	-4.16%	2.64%	5.44%	9.14%	6.38%	1.25%
2008	5	0.80%	$12,361	0.76%	$13,122	2.02%	-2.69%	0.92%	3.92%	1.19%	3.16%	-0.21%	-2.21%
2008	6	-3.88%	$11,881	-4.92%	$12,477	-8.12%	2.65%	4.52%	-8.41%	-8.80%	-9.29%	-10.62%	-1.29%
2008	7	-0.68%	$11,800	-0.61%	$12,401	-0.62%	-0.37%	-1.44%	2.87%	-3.32%	-5.50%	3.12%	0.39%
2008	8	0.20%	$11,823	-1.05%	$12,271	1.46%	2.74%	-9.29%	4.76%	-4.25%	-6.32%	2.37%	0.15%
2008	9	-4.91%	$11,242	-5.68%	$11,574	-9.24%	1.47%	4.11%	-4.82%	-11.44%	-14.68%	-0.11%	-10.73%
2008	10	-13.78%	$9,692	-16.93%	$9,615	-17.48%	-1.86%	-16.14%	-19.86%	-20.83%	-25.58%	-31.73%	-1.95%
2008	11	-0.03%	$9,689	-3.55%	$9,273	-8.01%	14.34%	12.57%	-11.80%	-6.37%	-9.75%	-22.72%	3.35%
2008	12	5.30%	$10,202	9.93%	$10,194	1.78%	13.64%	7.73%	6.57%	8.88%	10.35%	16.67%	13.80%
2009	1	-7.21%	$9,466	-8.98%	$9,278	-8.05%	-13.07%	5.54%	-13.94%	-13.73%	-9.29%	-17.53%	-1.80%
2009	2	-6.78%	$8,824	-8.25%	$8,512	-10.53%	-1.54%	1.45%	-13.03%	-10.39%	-6.27%	-20.53%	-5.20%
2009	3	5.76%	$9,333	5.84%	$9,009	8.26%	4.04%	-2.54%	7.58%	8.39%	16.86%	3.61%	0.47%
2009	4	4.90%	$9,790	10.02%	$9,911	10.99%	-6.95%	-3.33%	18.89%	11.52%	15.56%	30.68%	2.78%
2009	5	4.10%	$10,191	5.84%	$10,491	5.46%	-3.69%	10.23%	0.67%	13.19%	15.94%	2.62%	2.32%
2009	6	-0.35%	$10,155	-0.82%	$10,404	0.36%	0.76%	-5.22%	1.52%	-1.43%	-2.25%	-3.23%	2.89%
2009	7	5.36%	$10,699	7.27%	$11,160	7.74%	0.58%	2.38%	11.00%	10.04%	11.01%	10.77%	4.63%
2009	8	2.85%	$11,005	3.54%	$11,555	3.71%	2.24%	0.05%	3.48%	4.50%	-1.31%	14.32%	1.31%
2009	9	4.01%	$11,446	4.88%	$12,119	4.14%	2.46%	5.84%	4.21%	3.80%	10.20%	6.63%	1.76%
2009	10	-1.71%	$11,250	-2.32%	$11,838	-2.63%	-2.62%	3.72%	-6.07%	-2.52%	-3.44%	-4.46%	-0.49%
2009	11	5.71%	$11,892	5.36%	$12,473	5.69%	1.21%	12.79%	2.90%	3.92%	7.85%	6.57%	1.95%
2009	12	-0.66%	$11,814	0.84%	$12,577	2.86%	-6.34%	-7.20%	8.10%	0.70%	3.27%	7.37%	-2.07%
2010	1	-1.83%	$11,598	-2.72%	$12,235	-3.57%	2.69%	-1.26%	-2.54%	-5.07%	-7.76%	-5.52%	1.25%
2010	2	2.57%	$11,896	2.41%	$12,530	3.44%	-0.34%	3.27%	4.76%	0.27%	1.78%	5.58%	0.51%
2010	3	3.51%	$12,314	4.63%	$13,110	6.40%	-2.06%	-0.44%	7.80%	6.39%	8.11%	10.18%	0.65%
2010	4	2.97%	$12,680	3.01%	$13,505	2.18%	3.32%	5.88%	6.63%	-2.80%	-0.17%	7.15%	1.91%
2010	5	-3.39%	$12,250	-4.44%	$12,906	-7.88%	5.11%	3.05%	-8.54%	-11.19%	-9.39%	-5.33%	-1.31%
2010	6	-2.04%	$11,999	-1.42%	$12,723	-5.83%	5.80%	2.36%	-8.27%	-2.07%	-1.40%	-5.19%	3.28%
2010	7	3.49%	$12,418	5.24%	$13,390	7.02%	-0.95%	-5.09%	6.71%	11.61%	10.93%	9.59%	2.11%
2010	8	-0.27%	$12,384	-0.50%	$13,323	-4.71%	8.40%	5.71%	-7.91%	-3.80%	-3.24%	-1.28%	2.86%
2010	9	6.09%	$13,139	6.16%	$14,144	9.45%	-2.51%	4.78%	10.93%	9.97%	11.76%	4.45%	0.46%
2010	10	2.07%	$13,411	2.32%	$14,472	4.03%	-4.47%	3.68%	4.04%	3.81%	3.02%	4.74%	-0.26%
2010	11	0.25%	$13,445	-0.97%	$14,331	0.51%	-1.69%	2.11%	2.47%	-4.82%	-2.91%	-1.85%	-1.62%
2010	12	3.92%	$13,972	4.25%	$14,941	6.96%	-3.68%	2.44%	8.97%	8.30%	7.27%	4.54%	-0.75%
2011	1	-0.32%	$13,927	-0.76%	$14,827	2.05%	-3.08%	-6.38%	-0.24%	2.10%	-3.84%	3.25%	0.04%
2011	2	3.57%	$14,424	3.11%	$15,287	3.70%	1.65%	6.00%	4.21%	3.55%	-0.04%	4.71%	1.08%
2011	3	0.50%	$14,497	0.75%	$15,402	0.42%	0.03%	1.60%	2.21%	-2.39%	6.29%	-1.62%	-0.54%
2011	4	3.64%	$15,025	3.98%	$16,015	2.90%	2.34%	8.94%	1.06%	5.63%	2.73%	5.75%	2.50%
2011	5	-0.16%	$15,001	-0.46%	$15,941	-1.06%	3.42%	-1.79%	-1.77%	-2.21%	-2.94%	1.37%	1.27%
2011	6	-2.01%	$14,700	-1.80%	$15,655	-1.79%	-2.33%	-2.43%	-1.59%	-1.19%	-0.93%	-3.30%	-0.80%
2011	7	0.77%	$14,813	1.05%	$15,819	-2.27%	4.42%	8.42%	-2.77%	-2.38%	-1.03%	1.56%	2.43%
2011	8	0.09%	$14,827	-1.93%	$15,514	-6.09%	9.66%	12.27%	-7.98%	-8.75%	-9.25%	-5.62%	0.34%
2011	9	-3.42%	$14,320	-6.90%	$14,443	-7.57%	13.20%	-11.06%	-10.57%	-10.81%	-17.89%	-10.85%	0.35%
2011	10	7.16%	$15,346	8.93%	$15,733	11.37%	-3.84%	5.87%	15.34%	9.63%	16.27%	14.29%	2.51%
2011	11	0.45%	$15,415	-0.90%	$15,592	-0.37%	1.98%	1.67%	0.63%	-2.18%	-1.96%	-3.80%	-3.16%
2011	12	-0.15%	$15,392	-0.30%	$15,545	0.98%	3.44%	-10.66%	2.02%	-2.21%	-4.30%	4.85%	3.49%
2012	1	4.77%	$16,126	6.10%	$16,493	5.07%	-0.33%	11.40%	7.90%	5.27%	10.99%	6.38%	2.14%
2012	2	1.65%	$16,393	1.37%	$16,719	4.22%	-2.59%	-2.96%	1.71%	4.83%	5.27%	-1.15%	1.63%
2012	3	0.79%	$16,523	0.18%	$16,750	3.06%	-4.23%	-1.32%	2.89%	0.42%	-3.11%	5.19%	-1.42%
2012	4	0.66%	$16,632	0.29%	$16,798	-0.64%	4.83%	-0.15%	-1.91%	-2.08%	-1.70%	2.86%	1.08%
2012	5	-2.82%	$16,163	-4.54%	$16,036	-6.23%	9.03%	-6.34%	-7.18%	-11.14%	-10.71%	-4.51%	0.76%
2012	6	2.52%	$16,570	3.48%	$16,594	4.05%	-1.68%	2.35%	4.54%	7.11%	5.08%	5.52%	0.87%
2012	7	1.53%	$16,824	1.30%	$16,809	0.88%	3.82%	0.84%	-0.69%	0.08%	-0.03%	2.00%	3.48%
2012	8	2.12%	$17,181	1.74%	$17,102	2.70%	-1.32%	4.94%	4.08%	3.20%	0.41%	-0.01%	-0.05%
2012	9	1.68%	$17,470	1.87%	$17,422	2.49%	-2.53%	4.67%	3.14%	2.71%	5.22%	-1.86%	1.10%
2012	10	-1.67%	$17,177	-0.76%	$17,289	-1.81%	-0.48%	-2.94%	-1.96%	1.09%	-0.44%	-0.91%	1.35%
2012	11	0.73%	$17,303	0.87%	$17,440	0.77%	1.38%	-0.47%	1.65%	2.78%	1.56%	-0.26%	-0.42%
2012	12	-0.09%	$17,287	1.81%	$17,756	1.29%	-2.49%	-2.43%	3.55%	4.37%	6.80%	3.72%	-0.33%
2013	1	2.63%	$17,742	1.62%	$18,043	5.42%	-3.19%	-0.51%	5.35%	3.73%	-0.29%	3.74%	-1.30%
2013	2	0.35%	$17,805	-0.28%	$17,993	1.28%	1.24%	-5.09%	1.63%	-1.29%	-2.28%	1.22%	1.08%
2013	3	2.53%	$18,256	1.46%	$18,256	3.95%	-0.42%	0.95%	4.11%	1.31%	-1.02%	2.87%	-0.05%
2013	4	0.97%	$18,434	1.75%	$18,575	1.61%	4.68%	-7.56%	0.12%	5.02%	1.22%	6.73%	2.17%
2013	5	-0.87%	$18,274	-2.91%	$18,035	2.44%	-6.76%	-6.20%	4.29%	-3.02%	-4.83%	-5.98%	-3.22%
2013	6	-3.23%	$17,683	-3.65%	$17,377	-1.43%	-3.27%	-11.06%	-0.14%	-2.70%	-5.35%	-1.98%	-3.27%
2013	7	4.19%	$18,425	3.27%	$17,945	5.75%	-2.26%	7.43%	6.56%	5.32%	1.32%	0.90%	1.11%
2013	8	-1.46%	$18,155	-1.88%	$17,607	-3.03%	-1.34%	5.20%	-3.41%	-1.96%	-2.54%	-6.98%	-1.00%
2013	9	1.92%	$18,504	3.20%	$18,171	3.90%	0.66%	-4.78%	6.59%	7.82%	7.21%	3.49%	0.74%
2013	10	2.97%	$19,052	2.82%	$18,684	4.27%	1.43%	-0.34%	3.48%	3.26%	4.17%	4.52%	1.81%
2013	11	0.31%	$19,111	-0.79%	$18,536	2.70%	-2.70%	-5.51%	4.25%	0.55%	-0.26%	-5.25%	-0.14%
2013	12	0.76%	$19,256	0.05%	$18,546	2.73%	-1.87%	-3.79%	1.29%	2.16%	-0.42%	0.10%	0.22%
2014	1	-0.10%	$19,237	-0.58%	$18,438	-3.17%	6.30%	3.42%	-3.51%	-5.20%	-8.64%	4.28%	1.88%
2014	2	4.09%	$20,025	4.00%	$19,176	4.87%	0.52%	6.27%	4.63%	6.13%	3.38%	5.07%	1.14%
2014	3	0.03%	$20,031	0.41%	$19,255	0.51%	0.73%	-3.14%	1.34%	-0.46%	3.88%	0.49%	-0.03%
2014	4	0.58%	$20,147	0.93%	$19,434	0.06%	2.10%	0.49%	-2.29%	1.67%	0.78%	3.29%	1.33%
2014	5	1.55%	$20,459	1.38%	$19,703	2.10%	2.95%	-3.05%	0.62%	1.60%	2.95%	2.40%	1.51%
2014	6	2.51%	$20,973	2.13%	$20,122	2.62%	-0.25%	6.32%	3.85%	0.92%	2.40%	1.13%	0.01%
2014	7	-1.63%	$20,631	-1.44%	$19,832	-1.99%	0.67%	-3.63%	-5.07%	-2.60%	1.36%	0.08%	-0.32%
2014	8	3.73%	$21,401	2.72%	$20,372	4.15%	4.72%	0.38%	4.46%	0.18%	2.83%	3.04%	2.00%
2014	9	-2.69%	$20,826	-4.46%	$19,463	-2.10%	-2.11%	-6.18%	-5.94%	-3.88%	-7.77%	-6.04%	-1.68%
2014	10	1.92%	$21,226	2.74%	$19,997	2.75%	2.81%	-3.05%	7.13%	-0.27%	1.42%	9.94%	1.23%
2014	11	2.16%	$21,685	0.86%	$20,169	2.48%	2.97%	-0.49%	0.48%	0.06%	-1.54%	2.00%	0.91%
2014	12	0.89%	$21,879	0.12%	$20,193	-0.04%	3.25%	1.31%	2.56%	-4.00%	-3.99%	1.88%	-0.02%
2015	1	1.73%	$22,256	2.62%	$20,723	-2.74%	9.82%	8.69%	-5.32%	0.62%	-0.69%	6.85%	3.75%
2015	2	1.40%	$22,568	0.65%	$20,858	5.74%	-6.14%	-5.91%	5.86%	6.34%	4.41%	-3.67%	-1.42%
2015	3	-0.79%	$22,388	-0.27%	$20,801	-1.16%	1.10%	-2.15%	1.03%	-1.43%	-1.50%	1.74%	0.20%
2015	4	-0.40%	$22,298	-0.17%	$20,766	0.62%	-3.43%	-0.17%	-1.82%	3.65%	6.85%	-5.85%	-1.19%
2015	5	0.37%	$22,380	-0.64%	$20,634	1.30%	-2.37%	0.56%	0.75%	0.20%	-4.10%	-0.30%	-1.12%
2015	6	-2.19%	$21,890	-2.43%	$20,133	-1.67%	-4.07%	-1.52%	0.42%	-3.12%	-2.93%	-4.68%	-1.88%
2015	7	1.14%	$22,139	-0.09%	$20,114	1.70%	4.55%	-6.62%	-2.70%	2.03%	-6.31%	5.77%	0.83%
2015	8	-3.47%	$21,372	-3.88%	$19,333	-6.09%	-0.69%	3.71%	-4.62%	-7.43%	-8.84%	-6.29%	-0.83%
2015	9	-1.66%	$21,016	-1.23%	$19,095	-2.92%	1.97%	-1.80%	-3.77%	-4.42%	-3.13%	3.05%	1.19%
2015	10	5.23%	$22,116	4.46%	$19,946	7.91%	-0.41%	2.28%	6.57%	6.61%	6.38%	5.76%	0.57%
2015	11	-0.79%	$21,941	-1.08%	$19,732	0.60%	-0.87%	-6.75%	2.47%	-0.75%	-2.52%	-0.63%	-0.15%
2015	12	-1.48%	$21,617	-1.67%	$19,401	-2.13%	-0.30%	-0.45%	-5.08%	-2.34%	-3.83%	1.82%	-1.08%
2016	1	-1.58%	$21,275	-1.81%	$19,051	-5.72%	5.57%	5.41%	-5.85%	-5.52%	-5.03%	-3.44%	0.12%
2016	2	2.26%	$21,756	1.58%	$19,351	-0.01%	3.09%	10.93%	2.08%	-3.33%	-0.82%	-0.36%	1.05%
2016	3	4.35%	$22,703	6.15%	$20,542	7.11%	-0.09%	-0.84%	9.41%	6.58%	12.96%	10.48%	3.62%
2016	4	0.99%	$22,927	1.12%	$20,773	0.66%	-0.74%	5.11%	2.13%	2.22%	0.41%	-2.35%	1.55%
2016	5	0.39%	$23,016	-0.65%	$20,638	1.73%	0.81%	-6.14%	0.44%	-0.09%	-3.69%	2.25%	-0.51%
2016	6	3.02%	$23,712	3.65%	$21,391	0.27%	6.93%	8.97%	0.83%	-2.42%	4.56%	6.92%	3.09%
2016	7	3.27%	$24,487	3.50%	$22,140	3.98%	2.10%	1.98%	5.06%	3.98%	5.38%	4.26%	1.29%
2016	8	-0.57%	$24,348	-0.64%	$21,999	0.21%	-1.01%	-3.26%	1.13%	0.53%	0.88%	-3.76%	0.18%
2016	9	-0.11%	$24,322	0.25%	$22,054	0.21%	-1.51%	0.69%	0.87%	1.34%	2.52%	-1.82%	-0.32%
2016	10	-2.79%	$23,643	-2.95%	$21,404	-2.19%	-4.38%	-2.94%	-3.74%	-2.22%	-0.83%	-5.74%	-1.53%
2016	11	-0.21%	$23,593	-1.22%	$21,142	4.49%	-8.21%	-8.36%	13.34%	-1.78%	-4.42%	-1.68%	-3.17%
2016	12	0.87%	$23,799	1.37%	$21,431	1.98%	-0.46%	-1.91%	3.20%	2.71%	-0.25%	4.82%	0.84%
2017	1	2.14%	$24,307	2.10%	$21,881	1.86%	0.81%	5.42%	-1.21%	3.29%	6.66%	-0.19%	0.15%
2017	2	3.15%	$25,073	2.20%	$22,361	3.69%	1.59%	3.18%	1.35%	1.19%	1.74%	3.51%	1.32%
2017	3	-0.17%	$25,029	0.32%	$22,432	0.06%	-0.65%	-0.43%	-0.65%	3.23%	3.69%	-2.42%	-0.29%
2017	4	1.27%	$25,348	1.30%	$22,724	1.06%	1.57%	1.73%	0.51%	2.42%	1.70%	0.24%	1.19%
2017	5	1.04%	$25,613	0.94%	$22,938	1.01%	1.89%	-0.12%	-2.26%	3.54%	2.85%	-0.72%	1.33%
2017	6	0.47%	$25,732	0.81%	$23,124	0.95%	0.79%	-2.16%	2.96%	0.31%	0.93%	2.23%	0.48%
2017	7	1.37%	$26,085	1.85%	$23,551	1.88%	-0.66%	2.31%	0.75%	2.65%	5.82%	1.24%	0.77%
2017	8	1.46%	$26,467	0.97%	$23,779	0.15%	3.41%	4.20%	-2.72%	-0.04%	2.35%	-0.26%	0.68%
2017	9	0.53%	$26,609	0.94%	$24,002	2.44%	-2.32%	-3.37%	8.58%	2.36%	-0.04%	-0.11%	-0.05%
2017	10	1.25%	$26,942	0.76%	$24,184	2.17%	-0.04%	-0.75%	0.59%	1.68%	3.28%	-1.07%	0.19%
2017	11	2.13%	$27,516	1.34%	$24,508	3.03%	0.74%	0.36%	3.76%	0.69%	-0.39%	2.66%	-0.12%
2017	12	1.44%	$27,913	1.36%	$24,842	1.16%	1.81%	2.11%	-0.37%	1.35%	3.77%	-0.14%	1.22%
2018	1	3.04%	$28,762	1.80%	$25,289	5.23%	-3.26%	3.23%	1.33%	5.02%	8.30%	-4.25%	-1.23%
2018	2	-3.36%	$27,797	-4.20%	$24,228	-3.76%	-3.04%	-2.08%	-4.04%	-4.83%	-5.90%	-7.68%	-2.24%
2018	3	-0.50%	$27,657	0.88%	$24,441	-1.95%	2.86%	0.63%	1.37%	-0.84%	0.54%	3.88%	0.56%
2018	4	-0.32%	$27,568	-0.36%	$24,353	0.45%	-2.09%	-0.95%	1.76%	1.52%	-2.82%	0.82%	-1.57%
2018	5	2.00%	$28,118	1.14%	$24,630	2.72%	2.01%	-1.20%	5.87%	-1.89%	-2.62%	3.68%	0.52%
2018	6	0.07%	$28,137	-0.48%	$24,511	0.70%	0.65%	-3.61%	0.80%	-1.57%	-4.54%	4.20%	-0.49%
2018	7	1.45%	$28,545	1.32%	$24,835	3.32%	-1.44%	-2.24%	2.62%	2.85%	3.53%	0.60%	1.34%
2018	8	2.15%	$29,160	0.29%	$24,908	3.43%	1.31%	-2.14%	3.14%	-2.24%	-3.77%	2.58%	0.02%
2018	9	-0.61%	$28,981	-1.10%	$24,635	0.20%	-2.86%	-0.66%	-3.05%	0.97%	-0.58%	-2.64%	-0.14%
2018	10	-5.03%	$27,523	-5.00%	$23,402	-7.41%	-2.93%	2.12%	-9.94%	-8.13%	-8.76%	-2.93%	-2.05%
2018	11	1.72%	$27,997	1.80%	$23,824	2.01%	1.79%	0.34%	0.57%	0.50%	4.90%	4.67%	-0.36%
2018	12	-3.76%	$26,944	-3.21%	$23,059	-9.16%	5.85%	4.94%	-12.38%	-5.35%	-3.50%	-7.96%	1.86%
2019	1	5.89%	$28,532	7.03%	$24,681	8.54%	0.38%	2.89%	12.26%	6.63%	10.34%	11.85%	3.37%
2019	2	1.85%	$29,060	0.90%	$24,903	3.56%	-1.38%	-0.61%	4.13%	2.54%	-1.53%	0.70%	-0.20%
2019	3	1.91%	$29,617	1.33%	$25,235	1.42%	5.57%	-1.60%	-3.91%	0.92%	1.13%	4.21%	2.93%
2019	4	1.94%	$30,190	1.39%	$25,587	3.93%	-1.99%	-0.66%	4.32%	2.93%	2.35%	-0.16%	0.44%
2019	5	-2.29%	$29,500	-2.30%	$24,998	-6.45%	6.84%	1.76%	-9.98%	-5.03%	-7.33%	0.14%	1.65%
2019	6	5.84%	$31,222	5.07%	$26,266	7.08%	0.95%	8.00%	7.66%	5.91%	6.20%	1.54%	3.25%
2019	7	0.95%	$31,519	0.04%	$26,277	1.41%	0.26%	0.01%	1.30%	-1.95%	-2.66%	1.70%	0.25%
2019	8	2.30%	$32,245	1.71%	$26,726	-2.08%	11.04%	7.91%	-5.14%	-1.92%	-3.78%	3.75%	3.88%
2019	9	0.03%	$32,256	0.91%	$26,970	1.78%	-2.68%	-3.39%	5.57%	3.16%	1.69%	1.93%	-0.76%
2019	10	1.45%	$32,723	1.84%	$27,466	2.11%	-1.11%	2.56%	2.00%	3.39%	4.18%	1.13%	0.44%
2019	11	1.84%	$33,325	0.39%	$27,572	3.79%	-0.41%	-3.21%	2.71%	1.13%	-0.09%	-1.30%	0.47%
2019	12	1.58%	$33,852	2.26%	$28,195	2.80%	-3.20%	3.66%	2.84%	2.98%	7.71%	0.76%	0.53%
2020	1	2.34%	$34,642	0.07%	$28,213	-0.06%	7.69%	4.50%	-6.31%	-2.82%	-6.15%	1.23%	2.45%
2020	2	-3.66%	$33,375	-3.70%	$27,168	-8.00%	6.63%	-0.64%	-10.15%	-7.77%	-3.78%	-7.03%	1.09%
2020	3	-7.39%	$30,910	-11.14%	$24,142	-13.91%	6.38%	-0.22%	-25.76%	-14.11%	-15.77%	-19.42%	-6.31%
2020	4	9.61%	$33,882	7.81%	$26,027	13.13%	1.22%	7.26%	13.89%	5.82%	7.35%	8.96%	4.85%
2020	5	3.39%	$35,029	2.67%	$26,722	5.40%	-1.76%	2.59%	2.55%	5.43%	2.97%	1.73%	2.46%
2020	6	1.92%	$35,701	2.95%	$27,511	2.29%	0.34%	2.74%	3.58%	3.51%	6.61%	2.41%	2.13%
2020	7	6.18%	$37,907	5.06%	$28,903	5.74%	4.44%	10.79%	2.58%	1.94%	8.25%	3.64%	3.10%
2020	8	3.31%	$39,161	1.63%	$29,375	7.10%	-5.05%	-0.32%	5.07%	4.72%	2.89%	0.44%	-1.78%
2020	9	-2.67%	$38,117	-2.29%	$28,703	-3.54%	0.77%	-4.17%	-5.18%	-2.05%	-1.01%	-2.68%	-0.44%
2020	10	-2.07%	$37,329	-0.98%	$28,421	-1.95%	-3.39%	-0.52%	3.66%	-3.55%	1.41%	-3.00%	-0.51%
2020	11	7.05%	$39,960	8.00%	$30,694	11.80%	1.66%	-5.41%	19.21%	14.27%	8.99%	9.67%	3.77%
2020	12	3.69%	$41,434	4.12%	$31,960	4.68%	-1.23%	7.01%	7.50%	5.01%	7.14%	2.72%	0.15%
2021	1	-1.49%	$40,817	-0.04%	$31,946	-0.33%	-3.63%	-3.22%	6.25%	-0.78%	3.17%	0.04%	-1.83%
2021	2	-0.21%	$40,733	0.77%	$32,191	3.14%	-5.73%	-6.26%	10.80%	2.24%	0.79%	3.43%	-2.26%
2021	3	0.96%	$41,124	1.04%	$32,526	3.65%	-5.24%	-1.14%	5.61%	2.51%	-0.73%	5.15%	-1.48%
2021	4	4.25%	$42,874	3.23%	$33,576	5.04%	2.49%	3.56%	1.69%	2.95%	1.20%	7.86%	1.04%
2021	5	1.40%	$43,472	2.32%	$34,356	0.46%	0.00%	7.68%	3.89%	3.48%	1.65%	0.81%	0.62%
2021	6	1.53%	$44,135	0.47%	$34,517	2.48%	4.42%	-7.15%	-0.71%	-1.08%	0.95%	2.64%	2.21%
2021	7	2.30%	$45,148	0.47%	$34,681	1.74%	3.72%	2.53%	-4.36%	0.77%	-6.44%	4.42%	1.42%
2021	8	1.72%	$45,924	1.14%	$35,075	2.86%	-0.34%	-0.08%	1.82%	1.45%	1.57%	2.15%	-0.34%
2021	9	-3.94%	$44,116	-3.30%	$33,919	-4.46%	-2.91%	-3.22%	-1.46%	-3.26%	-3.87%	-5.68%	-1.51%

Portfolio return and risk metrics
Metric	Maximum Return at 10.00% Volatility	Equal Weighted
Arithmetic Mean (monthly)	0.83%	0.71%
Arithmetic Mean (annualized)	10.42%	8.82%
Geometric Mean (monthly)	0.79%	0.65%
Geometric Mean (annualized)	9.88%	8.06%
Volatility (monthly)	2.86%	3.41%
Volatility (annualized)	9.90%	11.80%
Downside Deviation (monthly)	1.79%	2.25%
Max. Drawdown	-30.43%	-36.98%
US Market Correlation	0.90	0.88
Beta^(*)	0.58	0.67
Alpha (annualized)	3.47%	0.99%
R²	81.65%	76.92%
Sharpe Ratio	0.89	0.63
Sortino Ratio	1.41	0.94
Treynor Ratio (%)	15.32	11.06
Calmar Ratio	1.40	0.78
Active Return	-0.57%	-2.39%
Tracking Error	7.76%	7.62%
Information Ratio	-0.07	-0.31
Skewness	-0.78	-0.82
Excess Kurtosis	3.66	4.39
Historical Value-at-Risk (5%)	-3.58%	-4.45%
Analytical Value-at-Risk (5%)	-3.86%	-4.88%
Conditional Value-at-Risk (5%)	-6.03%	-7.68%
Upside Capture Ratio (%)	62.58	64.15
Downside Capture Ratio (%)	49.10	61.89
Safe Withdrawal Rate	10.19%	9.90%
Perpetual Withdrawal Rate	7.39%	5.76%
Positive Periods	125 out of 189 (66.14%)	120 out of 189 (63.49%)
Gain/Loss Ratio	1.12	1.03
^* 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	-30.43%	-36.98%
COVID-19 Start	Jan 2020	Mar 2020	-10.77%	-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	-30.43%
2	Feb 2020	Mar 2020	2 months	May 2020	2 months	4 months	-10.77%
3	Sep 2018	Dec 2018	4 months	Mar 2019	3 months	7 months	-7.60%
4	Mar 2015	Sep 2015	7 months	Mar 2016	6 months	1 year 1 month	-6.88%
5	May 2011	Sep 2011	5 months	Oct 2011	1 month	6 months	-4.69%
6	Sep 2020	Oct 2020	2 months	Nov 2020	1 month	3 months	-4.68%
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	-4.07%
9	Sep 2021	Sep 2021	1 month				-3.94%
10	Aug 2016	Nov 2016	4 months	Feb 2017	3 months	7 months	-3.65%
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	US Mkt Correlation
VTI	Vanguard Total Stock Market ETF	10.57%	15.43%	33.45%	-36.98%	-50.84%	0.66	0.97	1.00
TLT	iShares 20+ Year Treasury Bond ETF	6.15%	13.40%	33.96%	-21.80%	-21.80%	0.43	0.75	-0.32
GLD	SPDR Gold Shares	7.63%	17.60%	30.45%	-28.33%	-42.91%	0.45	0.72	0.06
IJS	iShares S&P Small-Cap 600 Value ETF	9.20%	20.78%	39.34%	-29.39%	-54.13%	0.48	0.70	0.90
EFA	iShares MSCI EAFE ETF	4.65%	17.40%	26.95%	-41.04%	-57.38%	0.29	0.41	0.89
EEM	iShares MSCI Emerging Markets ETF	5.44%	21.94%	68.93%	-48.88%	-60.44%	0.30	0.45	0.78
VNQ	Vanguard Real Estate ETF	7.94%	22.56%	35.30%	-37.00%	-68.30%	0.41	0.58	0.74
LQD	iShares iBoxx $ Invmt Grade Corp Bd ETF	5.50%	7.36%	17.37%	-3.79%	-15.11%	0.62	1.00	0.34

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	0.06	0.90	0.89	0.78	0.74	0.34	0.90	0.88
TLT	iShares 20+ Year Treasury Bond ETF	-0.32	1.00	0.22	-0.38	-0.26	-0.25	-0.01	0.49	0.04	-0.02
GLD	SPDR Gold Shares	0.06	0.22	1.00	-0.01	0.15	0.29	0.10	0.27	0.38	0.36
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	0.76	0.81
EFA	iShares MSCI EAFE ETF	0.89	-0.26	0.15	0.78	1.00	0.87	0.70	0.41	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	0.77	0.87
VNQ	Vanguard Real Estate ETF	0.74	-0.01	0.10	0.73	0.70	0.61	1.00	0.46	0.75	0.84
LQD	iShares iBoxx $ Invmt Grade Corp Bd ETF	0.34	0.49	0.27	0.25	0.41	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	88.81%	14.34%
TLT	iShares 20+ Year Treasury Bond ETF	1.34%	-0.34%
GLD	SPDR Gold Shares	9.85%	6.78%
IJS	iShares S&P Small-Cap 600 Value ETF		17.86%
EFA	iShares MSCI EAFE ETF		16.45%
EEM	iShares MSCI Emerging Markets ETF		20.21%
VNQ	Vanguard Real Estate ETF		20.19%
LQD	iShares iBoxx $ Invmt Grade Corp Bd ETF		4.53%

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	10.33%	34.81%	-27.34%	8.45%	47.20%	-32.87%
3 years	9.35%	22.93%	-5.15%	7.17%	25.23%	-6.98%
5 years	9.91%	17.81%	5.91%	7.72%	17.64%	3.02%
7 years	9.88%	13.76%	7.63%	7.54%	12.50%	4.07%
10 years	9.87%	12.66%	7.51%	7.58%	11.33%	5.92%
15 years	9.91%	10.27%	9.57%	7.89%	8.14%	7.63%