Information Precision, Noise, and the Cross-Section of Stock Returns June 2009 Radu Burlacu Patrice Fontaine Sonia Jimenez-Garcès Mark S. Seasholes Hello Everyone, I’m Sonia Jimenez an assistant professor in finance at GIT. I have the pleasure to present you today this paper which is written with … As its title indicates, it deals with information, noise and stock returns. More precisely it studies the link between investors’ info and cross sectional asset prices. My presentation today will follow the 3 sections of the paper: i’ll present first our theoretical devpt, followed by our numerical analysis and the empirical part. I study frictions, trading behavior, and asset pricing Cross-Section of Returns © MSS 2009

Theoretical Derivation Economic Question Why do some stocks have high average returns while other stocks have low average returns? Our approach: Using a multi-asset rational expectations equilibrium (REE) model, we derive an estimate of expected returns that can be easily computed with recently available data Frictions: Investors have private info that cannot be traded Aggregate risk-aversion in the economy Existing measures: Theoretical CAPM Beta Found M/B Ratio Hypothesized FSRV Theoretical Derivation Empirical Analysis Numerical Analysis #1 The question we want to answer is the following: …. The littérature argue that high returns are a compensation for bearing high levels of risk. For instance, the weak explanatory power of the beta for realised returns raised the question of how to correctly specify the risks faced by investors? The goal of this article is precisely to explain the cross section of stock returns by a deeper understanding of the risks faced by investors. For doing so, we model the risks faced by investors in a market with a large number of investors who possess diverse and asymmetric pieces of private information. We use the Adamti multi asset model to derive an observable measure that is positively related to stocks’ expected returns. Cross-Section of Returns © MSS 2009

Theoretical Derivation Parameters: From Admati (1985) Corr 3.5 expected excess return (all stocks): Fit from a projection of stock i’s return on prices of all stocks: Substitute back to get an expression for expected return of stock i: #2 In a noisy market, (with supply shocks and/or noise trading) equilibrium prices partially reveal private information. Stock prices are below expected future values and these price discounts represent premia investors earn for holding risky assets. The premia are complicated functions of quantities such as the dividends covariance structure, precision of investors’ information, and supply uncertainty. On average stocks with high private info (low precisions) and/or high levels of sypply uncertainty ahve low prices and high premiums. In other words these stocks are viewed as risky by investors who must be compensated for holding them. Admati provides a closed form solution for the vector of equilibrium prices at date 0. the three constant expressions are complicated functions of the model parameters as the precision matrix Q of investors signals and covariance matrix of the supply. I'd plan on spending some time on this slide.  For example, you can discuss the Cov(P,r)<>0, while the Cov(P,r)=0 for CAPM. Here is an expression of expected returns as a function of investors’ precsions and supply uncertainty. The term in () is positive definite. On average low levels of investor precisions (Q) are associated with high expected returns. There may exist some individual stocks for which these relations do not hold. The situations are anomalous (see admati). Cross-Section of Returns © MSS 2009

Economic Intuition (1) Cross-sectional dimension Relations between price and E[r] are well understood See Berk (1995) for examples Time-Series dimension CAPM world Dividends are random; Prices are a deterministic function of model parameters R2 from a time-series projection of returns on prices is zero (0) REE world Dividends and prices are random variables R2 from a time-series projection of returns on prices is NOT zero In a noisy market, (with supply shocks and/or noise trading) equilibrium prices partially reveal private information. Stock prices are below expected future values and these price discounts represent premia investors earn for holding risky assets. The premia are complicated functions of quantities such as the dividends covariance structure, precision of investors’ information, and supply uncertainty. On average stocks with high private info (low precisions) and/or high levels of sypply uncertainty ahve low prices and high premiums. In other words these stocks are viewed as risky by investors who must be compensated for holding them. Admati provides a closed form solution for the vector of equilibrium prices at date 0. the three constant expressions are complicated functions of the model parameters as the precision matrix Q of investors signals and covariance matrix of the supply. I'd plan on spending some time on this slide.  For example, you can discuss the Cov(P,r)<>0, while the Cov(P,r)=0 for CAPM. Here is an expression of expected returns as a function of investors’ precsions and supply uncertainty. The term in () is positive definite. On average low levels of investor precisions (Q) are associated with high expected returns. There may exist some individual stocks for which these relations do not hold. The situations are anomalous (see admati). Cross-Section of Returns © MSS 2009

Economic Intuition (2) Our measure helps differentiate between stocks with: High E[ri] Low E[ri] Little private info about Lots of private info dividends or close substitutes about dividends Prices are relatively informative Prices are relatively i.e., investors must glean most of their non-informative information from observing prices R2 from time-series R2 from time-series projection is high projection is low In a noisy market, (with supply shocks and/or noise trading) equilibrium prices partially reveal private information. Stock prices are below expected future values and these price discounts represent premia investors earn for holding risky assets. The premia are complicated functions of quantities such as the dividends covariance structure, precision of investors’ information, and supply uncertainty. On average stocks with high private info (low precisions) and/or high levels of sypply uncertainty ahve low prices and high premiums. In other words these stocks are viewed as risky by investors who must be compensated for holding them. Admati provides a closed form solution for the vector of equilibrium prices at date 0. the three constant expressions are complicated functions of the model parameters as the precision matrix Q of investors signals and covariance matrix of the supply. I'd plan on spending some time on this slide.  For example, you can discuss the Cov(P,r)<>0, while the Cov(P,r)=0 for CAPM. Here is an expression of expected returns as a function of investors’ precsions and supply uncertainty. The term in () is positive definite. On average low levels of investor precisions (Q) are associated with high expected returns. There may exist some individual stocks for which these relations do not hold. The situations are anomalous (see admati). Cross-Section of Returns © MSS 2009

Numerical: E[r] and Our Measure More importantly, theses figures show that expected returns increase roughly linearly with our fit measure. The figures support the idea that our measure can be used on the RHS of a linear predictive regression in which future returns are on the LHS. Cross-Section of Returns © MSS 2009

Creating Our Measure with CRSP Data Calculate daily normalized prices of stock i and four industry portfolios Industry portfolios SIC 4\i Same 4-digit SIC code but not including stock i SIC 3\4 Same 3-digit SIC code but not including SIC 4\i & stock i SIC 2\3 Same 2-digit SIC code but not including… SIC 1\2 Same 1-digit SIC code but not including… Project a stock’s daily returns onto normalized prices & measure the “fit” Our measure is the logistic transformation of “fit” Cross-Section of Returns © MSS 2009

Table 2: Cross-Sectional Regressions (1) (2) (3) (4) (5) Our Measure 0.21 0.15 0.17 0.25 (T-stat) (3.90) (3.01) (3.83) (3.19) (4.26) Beta -0.14 -0.13 -0.18 (-1.91) (-1.70) (-2.07) (-1.72) (-1.58) ln (MktCap) 0.01 -0.01 0.18 (0.18) (0.26) (0.16) (2.76) ln (Bk-to-Mkt) 0.27 0.29 0.14 (5.35) (5.58) (5.47) (1.64) FSRV (-0.33) Delay(1) -0.07 (0.65) PIN 3.53 (4.49) Economic significance of our measure: Stocks 1s above and 1s below the mean, have expected returns that differ of 4.44% per annum #3 Many, many robustness checks - Portfolio of stocks - Control for past returns - Control for turnover and Amihud Illiquid - Sorts by industry and size portfolios Cross-Section of Returns © MSS 2009

Theoretical Derivation Conclusions We explain cross-sectional difference in stock returns Theoretically derived measure of expected returns from a multi-asset rational expectations equilibrium mode Numerical analysis Empirical analysis with CRSP data—our measure works Theoretical Derivation Empirical Analysis Numerical Analysis Cross-Section of Returns © MSS 2009