Thank you for your reply. I talked to my professor and indeed I did not understand the problem correctly. I am sorry for that. The data consist of 878 montly observations, but Betas have to be calculated for each portfolio in two subsaples separately (1928:12-1963:6 and 1963:7-2001:12.) So for example, for portfolio FFS1BM1 I should get one cash-flow beta for years 1928:12-1963:6, another for the years 1963:7-2001:12 and discout-rate beta for the years 1963:7-2001:12 and different for years 1963:7-2001:12 (the same refers to any other portfolio in the data set; in total 45 portfolios). So for example for the first subsample I should get : 25 cash-flow Betas and 25 discount-rate Betas for 25 portfolios denoted with variables from FFS1BM1 to FFS5BM5 and 20 cash-flow Betas and 20 discount-rate Betas for 20 portfolios denoted with variables RISK1 to RISK20. (The same applies to the second subsample).
Here I rewrote the formulas that I attached in the Word document:
Beta i, CF = Cov(ri,t, NCF,t) / Var (NCF,t - NDR,t) + Cov(ri,t,NCF,t-1) / Var (NCF,t - NDR,t)
Beta i, DR= Cov(ri,t, -NDR,t) / Var (NCF,t - NDR,t) + Cov(ri,t,-NDR,t-1) / Var (NCF,t - NDR,t)
Cov and Var denote sample covariance and variance.
Subscript i denotes observation for particular month; ri, t denotes return of the portfolio (e.g. FFS1BM1) in particular month , CF = cash-flow and DR =discount-rate.
In the numerator of the Beta i, DR the covariance is calculated between portfolio return and good news about discount rates ( - NDR, t) ( thats why each observation of NDR enters formula with a minus).
The each Beta denominator ( variance of unexpected market return) : Var (NCF,t - NDR,t), can be equivalently written as Var ( R_Me - Et-1R_Me)
The second part of each Beta formula ( marked in red) includes one lag of NCF,t (NCF, t-1) and equivalently for NDR, t.
Adding one lag is motivated by the possibility that, especially during the early years of sample period not all assets were traded frequently and synchronously.
I Thank you for your time and appologies once again for not providing you with the exact problem description.
Here I rewrote the formulas that I attached in the Word document:
Beta i, CF = Cov(ri,t, NCF,t) / Var (NCF,t - NDR,t) + Cov(ri,t,NCF,t-1) / Var (NCF,t - NDR,t)
Beta i, DR= Cov(ri,t, -NDR,t) / Var (NCF,t - NDR,t) + Cov(ri,t,-NDR,t-1) / Var (NCF,t - NDR,t)
Cov and Var denote sample covariance and variance.
Subscript i denotes observation for particular month; ri, t denotes return of the portfolio (e.g. FFS1BM1) in particular month , CF = cash-flow and DR =discount-rate.
In the numerator of the Beta i, DR the covariance is calculated between portfolio return and good news about discount rates ( - NDR, t) ( thats why each observation of NDR enters formula with a minus).
The each Beta denominator ( variance of unexpected market return) : Var (NCF,t - NDR,t), can be equivalently written as Var ( R_Me - Et-1R_Me)
The second part of each Beta formula ( marked in red) includes one lag of NCF,t (NCF, t-1) and equivalently for NDR, t.
Adding one lag is motivated by the possibility that, especially during the early years of sample period not all assets were traded frequently and synchronously.
I Thank you for your time and appologies once again for not providing you with the exact problem description.
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