Skewness in Stock Returns: Reconciling the Evidence on Firm versus Aggregate Returns Rui Albuquerque Discussion by: Marcin Kacperczyk (NYU and NBER)

2 Motivation: Firm-Level Skewness

3 Motivation: Aggregate Skewness

4 This Paper: Firm Skewness Propose a unified framework based on the timing of firms’ cash flows that explains both results –Value of cash-flow news depends on how close it is to the next payout –News that is more distant from payout time is more discounted and contributes less to risk –Volatility goes up as we approach “news date” –Expected returns go up at the same time –The unconditional moments of the return distribution come from a mixture of Normals model –=> positive skewness on average

5 This Paper: Aggregate Skewness Implications for aggregate skewness –Skewness of aggregate returns = –average stock skewness (positive on average) + –coskewness (negative on average) [low return on one stock coincides with high volatility of the remaining stocks] –Negative coskewness induced by heterogeneity in news timing => negative portfolio skewness

6 Summary of the Results Firm-level skewness is positive on average Firm-level skewness is greater than the aggregate skewness Market skewness is almost always negative Skewness of a portfolio of first-week announcers and k-week announcers (within quarter) is U-shaped in k Industries with greater dispersion of earnings announcement dates have more negative coskewness Skewness of a portfolio with different k’s decreases in the number of k’s and can be negative

7 Comment 1: Motivation The paper lays out a model to explain particular features of the data (skewness) –Why is this particular focus economically important? (negative skewness can arise naturally in a statistical exercise) Suggestions: –Focus the paper on the mechanism rather than outcome (few of the previous “skew” papers aim to merely explain skewness) –Derive asset pricing predictions that nest skewness results (e.g., following Kraus & Litzenberger (1976) and other studies) –Implications for portfolio diversification / volatility patterns in options –Does your framework reject competing hypotheses (leverage effect; asymmetric volatility)? Where do they fail? –Why do firms not internalize the impact of their disclosure on equilibrium pricing (cost of capital)? How about dividend policy? Do managers alter their policy?

8 Comment 2: Theoretical Setup This is a model in which skewness plays a central role, yet the preferences do not incorporate it directly –Justifiable from modeling perspective, but this is a paper about skewness…and investors do not care about it In the model, volatility and conditional mean returns increase as we come closer to the payout date –Effect on volatility is pretty clear (discounting of news) –Effect on mean less clear: why do variance terms (↑ with k) dominate covariance terms (ambiguous)? In the paper, only 12 stocks form the market, so volatility may dominate; diversification should matter more as we increase N. Need to explain better how N affects conditional mean (otherwise the positive skewness story is not clear) –A possible effect on kurtosis (fat tails) Market is defined as an equal-weighted portfolio. Why?

9 Comment 3: Model-Data Mapping The model tested in a qualitative fashion –Can you provide evidence on its quantitative performance (calibration)? Model only explains skewness. Test other auxiliary predictions? –How does the model operate for other important moments of the returns? Can you recover reasonable equity premium? Risk-free rates? –Volatility is an important feature of the model: test predictions! Returns in the model are expressed in terms of absolute not relative payoffs (simplifies math dramatically)… but it creates the disconnect between model and data –Can you prove that your predictions go through with a proper definition of returns (theoretically or via simulations)?

10 Comment 3: Time-Series Variation The motivating regularities change over time. Can you explain these differences within your (static) model? PeriodAggregate SkewFirm Skew *** (0.0608)(0.0257) ***0.1622*** (0.0892)(0.0433) *** (0.0527)(0.0273)

11 Comment 4: Empirical Results This paper: relate skewness to heterogeneity in announcements (dividends/earnings) –Model: All companies pay out dividends; Data: ~50% pay out –Focus on earnings announcements (less sample selection bias)

12 Comment 4: Empirical Results Focus on earnings announcement week within quarters (k:1-13) Test 1: Group firms with respect to announcement weeks (P1- P13). Form portfolios between P1 and each alternate portfolio from P2 to P13 and calculate skewness of the portfolio returns –Prediction: U-shape in k Identifying assumption: Firms (portfolios) only differ in terms of their k (and not other characteristics correlated with skewness)

13 Distribution of Announcements

14 Test 1: Results

15 Announcement Week and Skewness

16 Announcement Week and Firm Size

17 Announcement Week and Firm Volume

18 Announcement Week and Firm B/M

19 Comment 4: Empirical Results Test 2: Form portfolios between P1 and each additional portfolio from P2 to P13 –Prediction: Decreasing in k Earnings are assumed to be the only news items. Other news items might be relevant: Information flow becomes continuous –Portfolios with more continuous flow should have less declining pattern –Condition on firm size: large firms are likely to have more continuous flow –Large (Small) portfolio: 33% largest (smallest) firms in the empirical distribution

20 Test 2: Results

21 Test 2: Small Stocks

22 Test 2: Large Stocks

23 Conclusions Ambitious model with interesting predictions Room for improvement: –Economic motivation –Theoretical setup –Calibration to the data –Empirical evidence