9 September 2012 Turning academic insight into investment performance™

Applied Quantitative Strategy

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Asset Allocation Model Horse Race Summary Wesley R. Gray, PhD [email protected] +1.773.230.4727 Yang Xu [email protected] +1.484.340.9126 Carl Kanner [email protected] +1.216.650.3832 Cliff Gray [email protected] +1.650.804.5712

“Risk Parity investing starts from the observation that traditional asset allocations, such as the market portfolio or the 60/40 portfolio in U.S. stocks/bonds, are insufficiently diversified when viewed from the perspective of how each investment contributes to the risk of the overall portfolio. Because stocks are so much more volatile than bonds, movement in the stock market dominates the risk in a 60/40 portfolio. Thus, when viewed from a risk perspective, 60/40 is mainly an equity portfolio since nearly all of the variation in the performance is explained by variation in equity markets. In this sense, 60/40 offers little diversification even though 60/40 looks well balanced when viewed from the perspective of dollars invested in each asset class.” --“Leverage Aversion and Risk Parity” by Asness, Frazinni, and Pederson (2012).  Risk parity (“RP”) shifts the weights between different asset classes so that each asset provides the same amount of volatility (measured by standard deviation) as other assets.  Since each asset provides the same amount of volatility, RP overweights less volatile assets, and underweights more volatile assets. In “Leverage Aversion and Risk Parity,” the most recent (June 2010) weighting (between CRSP value-weighted stock index or CRSP value-weighted bond index) was 86% in bonds and only 14% in stocks.  Leverage can be applied to an RP portfolio to match the ex-post volatility of any asset (such as SP500). Levered RP portfolios outperform unlevered 60/40 and 100% stock portfolios, hence the infatuation with the concept of risk parity.  We test RP portfolios constructed using 5 asset classes: REITs, non-U.S. and Canadian equity, Commodities, Long-term U.S. bond index, and SP500 from 1973-2011. We also test RP on the S&P 500 and 10-year government bonds from 1927 to 2011 to get a better sense of how RP performs over the longest time horizon available.  Historical RP weights estimated with the full dataset from 1927 to 2011 on the S&P 500 and 10-year government bonds suggest a 30% stocks and 70% bonds allocation. One can think of a 30/70 portfolio as a static portfolio, or the current RP weights using the full dataset to estimate volatility. The more dynamic RP estimated using shorter rolling horizons certainly has an interesting story and solid historical performance, however, it is unclear that RP adds any value over an allocation system that drew the 30/70 number out of a hat at the beginning of an investment period.  While risk parity does not reliably add value above a static allocation heavily weighted in bonds, risk parity does add a justification for being heavily weighted in bonds relative to stocks. Without a model to suggest that bonds should have a large allocation, it is unclear whether an asset allocator would choose this unorthodox static allocation at the outset.

PLEASE SEE THE DISLAIMER AND DISCLOSURES AT THE END OF THIS REPORT. The information set forth herein has been obtained or derived from sources believed by Empiritrage, LLC (“Empiritrage”) to be reliable. Empiritrage does not make any representation or warranty, express or implied, as to the information’s accuracy or completeness, nor does Empiritrage recommend that the attached information serve as the basis of any investment decision. This document has been provided to you solely for information purposes and does not constitute an offer or solicitation of an offer, or any advice or recommendation, to purchase any securities or other financial instruments, and may not be construed as such. This document is subject to further review and revision.

T: +1.773.230.4727 | F: +1.888.517.5529 | 3830 Kelley Ave. Cleveland, OH 44114 | [email protected]

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Research Design There is no shortage of tactical asset allocation models in the marketplace, nor is there a shortage of salesman willing to charge hefty fees for unproven, ad-hoc, and often ill-conceived shell games. The goal of this research piece is to pit some of the more popular TAA models against one another in a horse race to determine which strategy has historically performed the best. We hope you enjoy.

Table of Contents: 1. Tactical Asset Allocation (TAA) Entrants a) Risk Parity Portfolio Construction b) Momentum Portfolio Construction c) Min. Variance Construction d) Backtest outline 2. TAA Racing Forum a) Summary results for all systems b) Summary results for all systems with MA(1,12) rules 3. The Horse Race a) Summary results for all systems b) Summary results for all systems with MA(1,12) rules 4. Conclusions

Source: Empiritrage, LLC Research

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Constructing Risk Parity Portfolios: The risk parity portfolio (RP) is rebalanced at the end of every month. To construct the RP, we estimate the volatility 𝜎�𝑖 , of all the available asset classes (using data up to month t-1) and set the portfolio weight in asset class 𝑖 to: −1 𝑖 = 1, … , 𝑛 𝑤𝑡,𝑖 = 𝑘𝑡 𝜎�𝑡,𝑖

We estimate 𝜎�𝑡,𝑖 as the 3-year rolling volatility of monthly excess returns, but also test alternative estimation periods (e.g., 1-month, 1-year, etc.). The number 𝑘𝑡 is the same for all assets and controls the amount of leverage of the RP portfolio. The first portfolio is an unlevered RP, obtained by setting −1 𝑘𝑡 = 1�� 𝜎�𝑡,𝑖 𝑖

This corresponds to a simple volatility-weighted portfolio that over-weights less volatile assets and under-weights more volatile assets. The second portfolio is a levered RP obtained by keeping 𝑘𝑡 at a constant volatility over time: 𝑘𝑡 = 𝑘

For comparison purposes, we set k so that the annualized volatility of this portfolio matches the ex-post realized volatility of the benchmark (VW market or 60-40 portfolio). This portfolio corresponds to a portfolio targeting a constant volatility in each asset class, levered up to match the volatility of the benchmark.

Here is a quick example to explain how risk parity works. Let’s say that we have 3 assets A, B, and C which each have volatilities 5%, 10%, and 20%, respectively (this corresponds to 𝜎� above). Then 𝑘𝑡 = 1� 1�5 + 1�10 + 1�20 = 20�7 This means that for the unlevered portfolio, the weights would be: 𝑤𝐴 =

20 4 �5 = , 7 7

𝑤𝐵 =

20 2 �10 = , 7 7

𝑤𝐶 =

20 1 �20 = 7 7

Note how RP overweights the less volatile assets and underweights more volatile assets. Using a volatility of 10% we would get the following weights: 𝑤𝐴 = 10⁄5 = 2,

𝑤𝐵 = 10⁄10 = 1,

𝑤𝐶 = 10⁄20 =

1 2

With levered RP our weights add up to more than 1, and we use leverage to match the volatility of the benchmark portfolio. We can change the volatility to match any other underlying portfolio, such as the 60/40 portfolio or a specific stock market. Please note that this simple RP estimate does not consider covariance, which one may want to account for in the context of a portfolio. For example, if asset A has a volatility of 10% and a 90% correlation with the benchmark, and asset B has a volatility of 10% and a 0% correlation with the benchmark, the investor probably would prefer asset B. However, the simple RP model described above will allocated equally to assets A and B. Source: Leverage Aversion and Risk Parity (2012), Financial Analysts Journal, 68(1), 47-59. 3 9 September 2012 2011 © Empiritrage, LLC. All Rights Reserved.

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Constructing Momentum Portfolios: The momentum allocation (MOM) is rebalanced at the end of every month. We calculate the 12-month returns for all asset classes. We then rank the assets classes on momentum. Next, we allocate to asset classes using the following equation. R = .04 Base is equal to 20% for all 5 asset classes. In effect, the system shifts weights from the base rates in accordance with their relative momentum compared to the other asset classes.

Source: Using a Z-score Approach to Combine Value and Momentum in Tactical Asset Allocation, Peng Wang and Larry Kochard, working paper, http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1726443 4

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Constructing Minimum Variance Portfolios: The minimum variance portfolio utilizes the minimum variance algorithm applied to rolling 3-year samples. The portfolio is rebalanced monthly and does not have short sell constraints. Information on the minimum variance algorithm and basic portfolio theory can be accessed via the following document: http://faculty.washington.edu/ezivot/econ424/portfolioTheoryMatrix.pdf Below we visually depict the meaning of the minimum variance portfolio. In words, the minimum variance portfolio is the portfolio of assets that has the lowest possible total variance (the portfolio variance calculation involves N variance terms and N^2-N covariance terms).

Lowest possible variance using risky assets

Source: Empiritrage, LLC Research 5

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Backtest Outline 1. Our risk parity and minimum variance TAA models use 3-year rolling data samples to estimate required parameters. 2. The following 5 asset classes are used in the back-test (referred to as the “IVY 5”): a. FTSE NAREIT All Equity REITS Total Return Index - benchmark for REITs - FNERTR b. MSCI EAFE Index – benchmark for investment in equity markets outside of U.S. and Canada - NDDUEAFE c. S&P GSCI – benchmark for investment in commodity markets - SPGSITR d. Merrill Lynch 7-10 year government bond index – ML 7-10 e. SP500 Index - SPTR 3. Each month we determine the weights of each asset class based on the output from a given TAA model. 4. We utilized long-term simple moving average rules as a risk-management technique that is overlayed on various TAA models. The benefits of long-term MA rules as an effective risk-management tool was brought to the mainstream by Mebane Faber. We analyze a 12-month moving average rule (MA (1,12)) that compares the latest price and the 12 month simple moving averages (~250 day). The MA(1,12) rule is triggered if the most recent price goes below the 12 month MA. All MA rules are calculated off each asset class. When an MA rule is triggered, proceeds earn risk-free rate of return (measured by US T-bill). 5. All basic results are from December 1, 1978 through June 30, 2012. 6. The momentum-based TAA system sometimes uses a small amount of leverage (up to 10% in our analysis) and the minimum variance algorithm often requires shorting asset classes. We do not include fees for these aspects of these strategies. 7. No transaction costs are included in any of our analysis. All results are gross of any transaction fees, management fees, or any other fees that might be associated with executing the models in real-time.

Source: Empiritrage, LLC Research

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TAA Racing Forum

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Summary Statistics (December 1, 1978 through June 30, 2012) CAGR Standard Deviation Downside Deviation Sharpe Ratio Sortino Ratio (MAR=5%) Worst Drawdown Worst Month Return Best Month Return Profitable Months Rolling 5-Year Win % Rolling 10-Year Win % DrawDown Total

Correlation CAGR Standard Deviation Downside Deviation Sharpe Ratio Sortino Ratio (MAR=5%) Worst Drawdown Worst Month Return Best Month Return Profitable Months Rolling 5-Year Win % Rolling 10-Year Win % DrawDown Total

Correlation

CAGR Standard Deviation Downside Deviation Sharpe Ratio Sortino Ratio (MAR=5%) Worst Drawdown Worst Month Return Best Month Return Profitable Months Rolling 5-Year Win % Rolling 10-Year Win % DrawDown Total

Correlation

8

IVY5_EW 10.65% 10.42% 9.27% 0.54 0.62 -46.47% -19.60% 9.91% 68.73% ---4816.49% --

SP500TR 11.58% 15.50% 11.39% 0.46 0.63 -50.21% -21.58% 13.52% 63.03% 48.26% 33.80% -8868.20% 0.796

EAFE 8.86% 17.72% 12.37% 0.28 0.41 -56.68% -20.18% 15.58% 59.31% 68.31% 69.37% -9906.87% 0.803

GSCI 6.67% 19.53% 13.62% 0.17 0.25 -67.65% -28.20% 22.94% 56.82% ---11274.52% --

ML 7-10 8.88% 7.96% 4.77% 0.47 0.81 -15.18% -8.61% 11.96% 65.01% 40.41% 40.14% -2503.48% -0.085

REIT 13.14% 17.68% 15.20% 0.50 0.59 -68.30% -31.67% 31.02% 61.29% 25.58% 23.94% -8220.45% 0.170

RP 10.80% 8.23% 6.91% 0.67 0.82 -30.85% -13.17% 6.72% 69.73% ---3537.54% --

MOMO 12.34% 11.66% 10.47% 0.62 0.71 -49.10% -21.59% 10.15% 69.23% 14.83% 8.80% -5195.99% 0.951

RP_MOMO_ 12.52% 9.52% 8.19% 0.75 0.89 -34.09% -15.17% 7.97% 70.97% 3.78% 0.00% -4041.25% 0.978

9 September 2012

KEY:  IVY5_EW=IVY5 EW returns  SP500TR=S&P 500 Total Return  EAFE=EAFE Total Return  GSCI=Goldman Sachs Commodity Index  ML 7-10=Merril Lynch US Treasury 7-10y  REIT= All Equity REITS Total Return Index  RP=Risk parity model  MOMO=Momentum model  RP_MOMO=RP MOMO model

model,

shifted

with

 Min Var=Minimum Variance model Min Var 8.22% 6.78% 4.80% 0.44 0.66 -13.70% -7.28% 10.67% 67.49% 87.79% 99.65% -2478.37% 0.689

Source: Empiritrage, LLC Research

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The Horse Race

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Annual Returns (December 1, 1978 through June 30, 2012) RP

MOMO

RP_MOMO_

1979

15.02%

21.16%

17.14%

Min Var 5.86%

1980

16.45%

21.26%

19.29%

6.27%

1981

-2.56%

-3.52%

-2.66%

-0.31%

1982

17.61%

19.20%

19.38%

24.83%

1983

19.15%

21.66%

21.29%

15.50%

1984

10.72%

10.31%

10.69%

10.91%

1985

26.48%

31.28%

29.28%

15.68%

1986

22.06%

31.56%

28.97%

6.95%

1987

6.85%

12.44%

8.75%

-1.41%

1988

17.07%

18.76%

16.86%

13.89%

1989

20.49%

24.36%

23.76%

19.66%

1990

3.83%

2.07%

6.56%

7.44%

1991

20.65%

19.18%

22.01%

17.95%

1992

6.39%

6.69%

8.77%

7.97%

1993

11.93%

14.62%

14.58%

9.74%

1994

0.78%

2.47%

0.71%

-3.92%

1995

23.22%

23.25%

25.02%

25.62%

1996

17.94%

23.89%

22.29%

9.18%

1997

11.08%

11.22%

12.41%

5.42%

1998

2.79%

3.40%

6.86%

5.69%

1999

8.50%

16.68%

9.94%

-2.92%

2000

12.62%

15.27%

15.50%

12.35%

2001

-3.05%

-8.69%

-1.84%

4.16%

2002

4.39%

2.91%

5.60%

9.50%

2003

20.44%

28.33%

23.05%

9.76%

2004

15.05%

19.89%

17.40%

5.80%

2005

9.97%

13.99%

11.64%

3.95%

2006

12.50%

15.88%

16.25%

2.97%

2007

8.15%

7.43%

7.17%

10.91%

2008

-17.48%

-32.05%

-19.36%

-2.05%

2009

11.60%

19.98%

11.73%

-2.31%

2010

12.59%

15.54%

13.81%

11.36%

2011

6.21%

1.58%

5.28%

14.70%

2012_YTD

4.39%

6.16%

5.75%

3.48%

 Consistent and generally positive results. 2008 is an extraordinary year where diversification proponents were tested. Source: Empiritrage, LLC Research

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Invested Growth (December 1, 1978 through June 30, 2012)

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 The straight momentum and the RP combined with momentum strategies compounded at the highest rates of return. 11

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Market Cycle Performance (December 1, 1978 through June 30, 2012)

 RP is more conservative; MOMO is more aggressive; Min Var is for the most defensive investors. 12

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Rolling CAGR Analysis (December 1, 1978 through June 30, 2012)

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 MOMO has historically been the top performer, but has recently struggled. 13

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Draw Down Analysis (December 1, 1978 through June 30, 2012)

 Min Variance excels. 14

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Short-Term Stress Test Analysis (December 1, 1978 through June 30, 2012)

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 Most systems hold up well during extraordinary markets; MOMO gets crushed in Financial Crisis. 15

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Rolling Drawdown Analysis (December 1, 1978 through June 30, 2012)

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 Min Var is the best; RP systems are next best; MOMO gets hurt during recent chaos. 16

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Risk-Managed Risk Parity: MA Rules and Risk Parity Performance

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Summary Statistics* (December 1, 1978 through June 30, 2012)

Source: Empiritrage, LLC Research

KEY:  RP_IVY5_3y_MA=Risk parity applied to IVY5 using 3 years of data to compute risk parity weights, then using MA rules (12-month MA).  MOMIVY5=Momentum weighted IVY5 returns , then using MA rules.  RP_IVY5_3yr_Lever=Risk parity applied to IVY5 using 3 years of data to compute risk parity weights, then using leverage to match the volatility of IVY5, then using MA rules.  IVY5=IVY5 EW returns , then using MA rules. *Asset Pricing Model Descriptions CAPM=Capital Asset Pricing Model 3-Factor=Fama and French Model 4-Factor=Fama and French Model plus Carhart Momentum Factor 5-Factor=Fama and French Model plus Carhart Momentum Factor plus Pastor Stambaugh Liquidity Factor 18

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 IVY5 with MA and RP with MA perform about the same; levered RP outperforms. 19

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 Risk Parity with leverage outperforms. 20

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Draw Down Analysis (December 1, 1978 through June 30, 2012)

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Source: Empiritrage, LLC Research

 Unlevered risk parity with an MA rule has solid performance, but the standard IVY5 with MA also performs similarly.  Levered risk parity is clearly the best, but we do not include a cost for leverage, nor do we examine leverage exposures. 22 9 September 2012 2011 © Empiritrage, LLC. All Rights Reserved.

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Source: Empiritrage, LLC Research

 MA provides robust drawdown protection when applied to risk parity. 23

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Risk Parity Robustness: 3-Year Volatility versus 10-year Volatility

24

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Summary Statistics* (December 1, 1985 through June 30, 2012)

Source: Empiritrage, LLC Research

 Results appear to be robust using 3 or 10 years, with 3 years outperforming by a small amount. The difference is not significant given the large estimate variance. KEY:  RP_IVY5_3y=Risk parity applied to IVY5 using 3 years of data to compute risk parity weights.  RP_IVY5_10y=Risk parity applied to IVY5 using 10 years of data to compute risk parity weights.  RP_IVY5_3y_Lever=Risk parity applied to IVY5 using 3 years of data to compute risk parity weights , then using leverage to match the volatility of IVY5.  RP_IVY5_10y_Lever=Risk parity applied to IVY5 using 10 years of data to compute risk parity weights , then using leverage to match the volatility of IVY5. *Asset Pricing Model Descriptions CAPM=Capital Asset Pricing Model 3-Factor=Fama and French Model 4-Factor=Fama and French Model plus Carhart Momentum Factor 5-Factor=Fama and French Model plus Carhart Momentum Factor plus Pastor Stambaugh Liquidity Factor 25

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Risk Parity Robustness: 3-Year Volatility versus 10-year Volatility with MA Rules.

26

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Summary Statistics* (December 1, 1985 through June 30, 2012)

Source: Empiritrage, LLC Research

 Similar to the non-MA analysis, using a longer volatility estimation period does not help results. KEY:  RP_IVY5_3y_MA=Risk parity applied to IVY5 using 3 years of data to compute risk parity weights, with MA rules  RP_IVY5_10y_MA=Risk parity applied to IVY5 using 10 years of data to compute risk parity weights, with MA rules.  RP_IVY5_3y_MA_Lever=Risk parity applied to IVY5 using 3 years of data to compute risk parity weights, then using leverage to match the volatility of IVY5, with MA rules.  RP_IVY5_10y_MA_Lever=Risk parity applied to IVY5 using 10 years of data to compute risk parity weights, then using leverage to match the volatility of IVY5, with MA rules. *Asset Pricing Model Descriptions CAPM=Capital Asset Pricing Model 3-Factor=Fama and French Model 4-Factor=Fama and French Model plus Carhart Momentum Factor 5-Factor=Fama and French Model plus Carhart Momentum Factor plus Pastor Stambaugh Liquidity Factor 27

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Risk Parity Robustness: Risk Parity versus Static Allocations

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Summary Statistics* (December 1, 1978 through June 30, 2012)

 A simple allocation tilted to bonds significantly outperforms a more complicated risk parity allocation system.

Source: Empiritrage, LLC Research

KEY:  RP_IVY5_3y=Risk parity applied to IVY5 using 3 years of data to compute risk parity weights.  IVY5(80,5)=IVY5 with 80% in long term US bonds, and 5% in the other 4 asset classes each month.  IVY5(60,10)=IVY5 with 60% in long term US bonds, and 10% in the other 4 asset classes each month.  IVY5(40,15)=IVY5 with 40% in long term US bonds, and 15% in the other 4 asset classes each month. *Asset Pricing Model Descriptions CAPM=Capital Asset Pricing Model 3-Factor=Fama and French Model 4-Factor=Fama and French Model plus Carhart Momentum Factor 5-Factor=Fama and French Model plus Carhart Momentum Factor plus Pastor Stambaugh Liquidity Factor 29

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Source: Empiritrage, LLC Research

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Source: Empiritrage, LLC Research

 Risk parity outperforms a static allocation on a rolling CAGR basis, but this analysis does not account for the underlying risk of the strategy. 31

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Draw Down Analysis (December 1, 1978 through June 30, 2012)

Source: Empiritrage, LLC Research

 Risk Parity does significantly worse than a simple allocation to long term bonds. A static allocation that shifts heavily into bonds is the clear winner. 32

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Source: Empiritrage, LLC Research

 There is a risk/reward trade-off between risk parity and static allocations—no free lunch. 33

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Source: Empiritrage, LLC Research

 A static allocation protects capital much better than risk parity. 34

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Risk Parity Robustness: Risk Parity versus Static Allocations with MA Rules

35

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Summary Statistics* (December 1, 1978 through June 30, 2012)

Source: Empiritrage, LLC Research

 Static allocations perform as well, if not better than risk parity. The static allocations in the other 4 asset portfolio have less return, but also have lower max drawdowns. KEY:  RP_IVY5_3y_MA=Risk parity applied to IVY5 using 3 years of data to compute risk parity weights, then using MA rules.  IVY5(80,5) MA=IVY5 with 80% in long term US bonds, and 5% in the other 4 asset classes each month , then using MA rules.  IVY5(60,10) MA=IVY5 with 60% in long term US bonds, and 10% in the other 4 asset classes each month , then using MA rules.  IVY5(40,15) MA=IVY5 with 40% in long term US bonds, and 15% in the other 4 asset classes each month , then using MA rules. *Asset Pricing Model Descriptions CAPM=Capital Asset Pricing Model 3-Factor=Fama and French Model 4-Factor=Fama and French Model plus Carhart Momentum Factor 5-Factor=Fama and French Model plus Carhart Momentum Factor plus Pastor Stambaugh Liquidity Factor 36

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Source: Empiritrage, LLC Research

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 Risk parity shows little systematic outperformance on a CAGR basis, even with MA rules. 38

9 September 2012

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Draw Down Analysis (December 1, 1978 through June 30, 2012)

 Risk Parity does worse than a simple allocation to long term bonds for drawdowns, even with MA rules. 39

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Source: Empiritrage, LLC Research

40

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Source: Empiritrage, LLC Research

 Static portfolio protects capital relative to risk parity. 41

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Risk Parity using only Long-term Bonds and S&P 500

42

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Backtest Outline 1. At the end of each month, calculate the past N years volatility (measured by standard deviation) for each asset class. We allow N to vary from 1 month to 10 years, showing results for 1 month through 5 years. 2. The following 2 asset classes are used in the back-test: a. 10 year government bond index b. SP500 Index 3. MA (1,12) looks at the latest price and the 12 month simple moving averages (~250 day). The rule is triggered if the most recent price goes below the 12 month MA. All MA rules are calculated off the S&P 500. 4. When an MA rule is triggered, proceeds are invested in the long-term bond. 5. All results are from January 1, 1932 through December 31, 2011. Note: A “static” allocation is monthly rebalanced to the static weights.

Source: Empiritrage, LLC Research

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2011 © Empiritrage, LLC. All Rights Reserved.

Empiritrage, LLC

Applied Quantitative Strategy

Risk Parity Allocation over time using 3-year estimation windows (January 1, 1932 through December 31, 2011)

Source: Empiritrage, LLC Research

 How different is this from a static 20/80 or a 30/70 allocation? 44

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2011 © Empiritrage, LLC. All Rights Reserved.

Empiritrage, LLC

Applied Quantitative Strategy

Summary Statistics* (January 1, 1932 through December 31, 2011)

Source: Empiritrage, LLC Research

 The 30% stocks and 70% bonds would be the risk parity portfolio if you used the volatility over the entire time period for stocks and bonds.  Overall risk parity is not substantially better than a simple 30/70 portfolio. KEY:  RP_3yr=Risk parity applied to Sp500 and Long-term U.S. bonds using last 3 years of data to compute risk parity weights.  RP_1yr=Risk parity applied to Sp500 and Long-term U.S. bonds using last 1 year of data to compute risk parity weights.  RP_3m=Risk parity applied to Sp500 and Long-term U.S. bonds using last 3 months of data to compute risk parity weights.  30_70=Portfolio that allocates 30% to stocks and 70% to bonds. *Asset Pricing Model Descriptions CAPM=Capital Asset Pricing Model 3-Factor=Fama and French Model 4-Factor=Fama and French Model plus Carhart Momentum Factor 5-Factor=Fama and French Model plus Carhart Momentum Factor plus Pastor Stambaugh Liquidity Factor 45

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2011 © Empiritrage, LLC. All Rights Reserved.

Empiritrage, LLC

Applied Quantitative Strategy

Source: Empiritrage, LLC Research

46

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Empiritrage, LLC

Applied Quantitative Strategy

 Dynamic risk parity shows little systematic outperformance on a CAGR basis. 47

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Source: Empiritrage, LLC Research

2011 © Empiritrage, LLC. All Rights Reserved.

Empiritrage, LLC

Applied Quantitative Strategy

Source: Empiritrage, LLC Research

 Risk parity does not outperform a 30/70 allocation in terms of drawdowns. 48

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2011 © Empiritrage, LLC. All Rights Reserved.

Empiritrage, LLC

Applied Quantitative Strategy

Source: Empiritrage, LLC Research

 No substantial difference between dynamic risk parity and the static 30/70 portfolio. 49

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2011 © Empiritrage, LLC. All Rights Reserved.

Empiritrage, LLC

Applied Quantitative Strategy

Risk Parity on Long-term Bonds and S&P 500, adding MA rules

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2011 © Empiritrage, LLC. All Rights Reserved.

Empiritrage, LLC

Applied Quantitative Strategy

Summary Statistics* (January 1, 1932 through December 31, 2011)

Source: Empiritrage, LLC Research

 The 30% stocks and 70% bonds would be the risk parity portfolio if you used the volatility over the entire time period for stocks and bonds.  The MA rule (1,12) will put portfolio entirely into bonds is the SP500 MA rule is broken.  While MA rules appear to help with drawdowns, overall risk parity is not substantially better than a simple 30/70 portfolio. KEY:  RP_3yr=Risk parity applied to Sp500 and Long-term U.S. bonds using last 3 years of data to compute risk parity weights, then applying SP500 MA rule.  RP_1yr=Risk parity applied to Sp500 and Long-term U.S. bonds using last 1 year of data to compute risk parity weights , then applying SP500 MA rule.  RP_3m=Risk parity applied to Sp500 and Long-term U.S. bonds using last 3 months of data to compute risk parity weights, then applying SP500 MA rule.  30_70=Portfolio that allocates 30% to stocks and 70% to bonds, then applying SP500 MA rule. *Asset Pricing Model Descriptions CAPM=Capital Asset Pricing Model 3-Factor=Fama and French Model 4-Factor=Fama and French Model plus Carhart Momentum Factor 5-Factor=Fama and French Model plus Carhart Momentum Factor plus Pastor Stambaugh Liquidity Factor 51

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2011 © Empiritrage, LLC. All Rights Reserved.

Empiritrage, LLC

Applied Quantitative Strategy

Source: Empiritrage, LLC Research

52

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2011 © Empiritrage, LLC. All Rights Reserved.

Empiritrage, LLC

Applied Quantitative Strategy

 Risk parity with MA shows outperformance over the past 30 years; underperforms slighly before that. 53

9 September 2012

Source: Empiritrage, LLC Research

2011 © Empiritrage, LLC. All Rights Reserved.

Empiritrage, LLC

Applied Quantitative Strategy

 Little difference in drawdowns. 54

9 September 2012

Source: Empiritrage, LLC Research

2011 © Empiritrage, LLC. All Rights Reserved.

Empiritrage, LLC

Applied Quantitative Strategy

DISCLAIMER The views expressed are the views of the authors and are subject to change at any time based on market and other conditions. This document shall not constitute an offer to sell or the solicitation of any offer to buy any security and should not be construed as such. References to specific securities and issuers are for illustrative purposes only and not intended to be, and should not be interpreted as, recommendations to purchase or sell such securities. While all the information prepared for this document is believed to be accurate, Empiritrage, LLC makes no express warranty as to the completeness or accuracy, nor can it accept responsibility for errors appearing in the document. DISCLOSURES Performance figures contained herein are unaudited and prepared by Empiritrage, LLC. They are intended for illustrative purposes only. Past performance is not indicative of future results, which may vary. There is a risk of substantial loss associated with trading commodities, futures, options and other financial instruments. Before trading, investors should carefully consider their financial position and risk tolerance to determine if the proposed trading style is appropriate. Investors should realize that when trading futures, commodities and/or granting/writing options one could lose the full balance of their account. It is also possible to lose more than the initial deposit when trading futures and/or granting/writing options. All funds committed to such a trading strategy should be purely risk capital. Hypothetical performance results (e.g., quantitative backtests) have many inherent limitations, some of which, but not all, are described herein. No representation is being made that any fund or account will or is likely to achieve profits or losses similar to those shown herein. In fact, there are frequently sharp differences between hypothetical performance results and the actual results subsequently realized by any particular trading program. One of the limitations of hypothetical performance results is that they are generally prepared with the benefit of hindsight. In addition, hypothetical trading does not involve financial risk, and no hypothetical trading record can completely account for the impact of financial risk in actual trading. For example, the ability to withstand losses or adhere to a particular trading program in spite of trading losses are material points which can adversely affect actual trading results. The hypothetical performance results contained herein represent the application of the quantitative models as currently in effect on the date first written above and there can be no assurance that the models will remain the same in the future or that an application of the current models in the future will produce similar results because the relevant market and economic conditions that prevailed during the hypothetical performance period will not necessarily recur. There are numerous other factors related to the markets in general or to the implementation of any specific trading program which cannot be fully accounted for in the preparation of hypothetical performance results, all of which can adversely affect actual trading results. Hypothetical performance results are presented for illustrative purposes only. There is no guarantee, express or implied, that long-term return and/or volatility targets will be achieved. Realized returns and/or volatility may come in higher or lower than expected.

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