What Process Does the Market Follow in the CAPM?

What Process Does the Market Follow in the CAPM?

Consider a multiperiod version of the CAPM E_tr_i,t1-r_f,t1beta_i,tE_tr_m,t1-r_f,t1 where E_tr_i,t1-r_f,t1 is the time t expectation of the time t1 excess return on asset i, E_tr_m,t1-r_f,t1 is the time t expectation of the time t1 market risk premium, and beta_i,t is the time t measure of co-movement between returns on asset i and returns on the market portfolio defined as beta_i,tfracCov_tr_i,t1,r_m,t1Var_tr_m,t1 The discount factor used to compute the time t present value of time t1 cash flows from asset i is then frac11E_tr_i,t1t1-t As the discounting becomes increasingly large with time i.e. discounting for cash flows at time t2, t3 etc., my intuition is that the systematic uncertainty becomes increasingly large with time, i.e. that the probability of very highlow levels of both the cash flows and the market compared to today: time t become increasingly large with time. I find it natural to think about the distribution of the future market returns as normal, sort of like the many possible paths of a Brownian motion. Hence, I am wondering what process the market is assumed to follow in the CAPM, if any Could it be a geometric Brownian motion Is it some other stochastic process Suggestions for academic articles that discuss this issue are also very welcome.

About which cash flows are you talking and from where do you get your t. The basic CAPM is not a time series model. One of the assumptions of CAPM is, that the returns follow a multivariate normal distribution. CAPM introduces furthermore the idea of equilibrium and can thus tell us which asset prices will result if market participants invest in efficient portfolios according to Markowitz.