Can somebody give the definition of cross section in “cross section of stock return”?
Cochrane (p. 435, 2005) gives a simple explanation between the difference of looking at expected returns in the time series and in the cross section:
- Time series: How average returns change over time.
- Cross section: How average returns change across different stock or portfolios.
So intuitively, if you study the cross section of stock returns, you want to answer the question why stock A earns higher/lower returns than stock B. That’s why you call it cross section: at one point in time, you check the cross section of many stocks. Note that you do not need a time series for that, you really need only one point in time (and in some corporate finance studies this is also done because they only want to explain the cross section for one shock, let’s say the default of Lehman; however, in most studies, you check the cross section during an interval, probably to increase the sample size).
So for instance, if you look at the CAPM, that’s a model that explains the cross section of stock returns with only one factor, the systematic risk of a stock. Since the CAPM is empirically not successful in explaining the stock returns completely, there are other models, such as the Fama-French 3 factor-model. Note that those models do not help in explaining the time series. The CAPM does not tell you if the market risk premium should be high or low today, only that given a certain risk premium and risk-free rate, how much higher the return of stock A compared to stock B should be.
Reference: Cochrane, John (2005): Asset Pricing, Revised Edition, Princeton University Press