# Is CAPM a cross sectional or time series model?

Given that CAPM is an equilibrium model, it prices the assets in absolute terms. Asset pricing studies use CAPM/ICAPM/CCAPM in a cross-sectional framework i.e. stocks with higher betas will have higher returns in a cross section (or relative to other stocks with lower betas). My question is that given CAPM is equilibrium model, can it be used as an absolute pricing tool in a time series i.e. to predict tomorrows return for instance of Apple? Also please compare the FF 3 factor model in the same light !

To answer your question directly: CAPM is a cross-sectional model, and is NOT a time series model.

CAPM aims at explaining variance of single asset's return by overall market return of the same period. This makes it impossible to predict return because once you have observed the market return, you will also observe the asset's return

On the other hand, a (predictive) time series model involves predicting future values at any point in time based on information up to that time.

FF model is similar. It is also cross-sectional but NOT time series model

• Exactly! The CAPM is a model for expected returns and not for returns! You could run a time-series regression of asset $i$ excess returns on market excess returns, obtain an $R^2$ of zero and still don't reject the CAPM if the intercept is not statistically significant! – fni May 21 '18 at 21:46
• No. If $R^2$ is zero you must reject the CAPM. No only intercept is relevant but also the slope coefficient ($\beta$). See Fama and MacBeth procedure here it.wikipedia.org/wiki/Regressione_Fama-MacBeth Its true that CAPM is "static model" no time series one, however time series concepts are involved in the "CAPM framework". The two dimension can be related. In fact the Fama MacBeth procedure sound like panel. – markowitz Feb 19 at 16:13

The standard CAPM is in the same time period.

If you are trying to predict a share price for example, you will have to use lags of variables.

RM(t) = c + DY(t-1) + e

for example.

I think a really good way to learn things like this is to practice yourself using econometrics software. Eviews is great for beginners, you can download data from Kenneth Frenchs data library and practice.

In reviews, if you're truing to make a prediction about the market index using the dividend yield, we can simple write,

RM c DY(-1)

Now you can see that there is a possible lead lag relationship if DY is significant.