Michael Katz, Ph.D. and Christopher Palazzolo, CFA are both vice president's at AQR Capital Management.

1 While it is difficult to precisely define short-, medium- and long-term time periods, we generally define short-term as less than 1 year, medium-term as 1-5 years, and long-term as more than 5 years. These time periods have tended to coincide with business cycles which on average are 3-5 years, while major pricing adjustments occur in the short-term 1 year horizon and asset pricing reversals occur beyond the 5 year horizon due to mean reversion.

2 Inflation is defined as an increase in the cost of living. This is an abstract concept and varies by individual and entity. In this paper, we focus our analysis on the U.S. Consumer Price Index (CPI) which is a proxy for general price levels in the U.S. The relevance of the CPI to specific individuals or entities will vary in proportion to how closely liabilities match the basket of goods and services in the CPI. There are a wide variety of both supportive as well as critical studies on the methodologies used to calculate the CPI. Our view is that while there may be more accurate potential inflation measures, CPI does serve as a reasonable proxy for general inflation and will be highly correlated with the inflation sensitivity of most individual or entity liabilities.

3 There is much academic debate as to what may cause the short- to medium-term negative effect of unexpected inflation on equity prices. There are primarily two schools of thought that can broadly be categorized as Behavioral and Rational. Specifically, the Behavioral camp suggests that: 1) Investors may not properly account for the capital gain realized by indebted companies during unexpected increases in inflation, as the real cost of that debt declines and 2) Investors may improperly discount future real cash flows by using nominal rates, creating a negative inflation illusion that puts downward pressure on equity real values. The Rational camp suggests that 1) companies face real distortions as a result of unexpected increases in inflation which negatively impact earnings and 2) Investors may increase their real required rate of return as compensation for higher uncertainty during periods of increasing inflation. Of course, it is possible that a combination of both Behavioral and Rational theories explain the tendency for stock valuations to compress during periods of unexpected inflation. Exacerbating these effects are non-market factors such as the likelihood that real interest rates may be increased during inflationary periods if monetary authorities seek to combat inflation with higher borrowing costs which hurts corporate earnings and increases investors' required rate of return after an inflation shock.

4 An example of the inflation illusion in stock prices is captured in what is known as the "Fed Model" which relates Price-to-Earnings ratios to nominal government bond yields. There is wide empirical evidence which suggests that stock prices do respond to nominal yields, which contradicts the belief that stocks are good inflation hedges driven by real yields. For a comprehensive exposition on this inconsistency see "Fight the Fed Model" by Cliff Asness, Journal of Portfolio Management, Fall 2003.

5 It is generally assumed that governments do not adjust nominal tax brackets to compensate for inflation changes, since it may lower tax revenues.

6 The risk-free rate here is assumed to be U.S. T-bills which do reflect short-term inflation expectations.

7 It is important to note that many inflation-linked bonds including U.S. TIPS have an embedded principal "floor" which means that their inflation adjusted principal value on which the yield is determined will not decrease below the bond issuance par value (usually 100). This floor serves as a deflationary protection which mimics a call option on inflation with a strike price of CPI measured at time of issuance. This effect can be significant for TIPS that are issued in periods of deflationary pressure since the option value is more likely to be relevant. This also generates a premium for recently issued TIPS after a period of inflation since new issues have an inflation adjusted par value closer to a floor of 100, whereas an older issue may have a principal face value far in excess of its floor of 100 and be more sensitive to deflation.

8 AQR proprietary data includes performance of hedge fund sub-styles which may be used in inflation analyses. There are also other public sources of hedge fund sub-style returns.

9 For commodity returns we use the S&P GSCI Index. Although the Index is dominated by energies since it is production-weighted, cost of living (and CPI) is heavily driven by energies relative to other commodities.

10 Throughout the analysis we use excess returns over cash for consistency and comparison purposes. Returns on stocks, bonds and commodities are based on the returns of S&P 500 futures, 10 year bond futures and the GSCI index futures instead of the cash instruments themselves due to their superior liquidity and comparability.

11 60/40 portfolio defined as 60% S&P 500 Total Return / 40% U.S. 10-Year Government Bonds

12 TIPS are allocated weight in the portfolio after they were introduced in 1997. Before that TIPS weight is allocated to other assets proportionately. That is, in a 40/20/20/20 portfolio stock, bonds and commodities will receive the weights 50/25/25.

13 Equal risk portfolio calculated monthly using AQR proprietary risk model based on historical returns

14 We use index future contracts to hedge the beta exposure of the various equity related assets.

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