Problem 1 (20pts) (a) Consider an investment in a portfolio V consisting of n securities with weights W1,..., Wn. Denote by V (0) the total investment in V, and by Vi(O) the investment in the ith security. Explain that Vi(0) = wiV (O). Show that V(0) = x=1 Vi (0) = = (b) Denote by V (T) the investment in V and by Vi(T) the investment of the ith security at time T. Explain V (T) = x1=1 V (T) Vi(T)- Vi(0) (c) Denote by Ki the return of the ith security. Recall that Ki = Vi (0) Show that Vi(T) = (1 + Kvi)Vi(0) (d) Denote by Kv the return of V. Apply (b) and (c) to the formula K = To show that : V(T)- VO V(0) Ky = X=1 W Ki Problem 1 (20pts) (a) Consider an investment in a portfolio V consisting of n securities with weights W1,..., Wn. Denote by V (0) the total investment in V, and by Vi(O) the investment in the ith security. Explain that Vi(0) = wiV (O). Show that V(0) = x=1 Vi (0) = = (b) Denote by V (T) the investment in V and by Vi(T) the investment of the ith security at time T. Explain V (T) = x1=1 V (T) Vi(T)- Vi(0) (c) Denote by Ki the return of the ith security. Recall that Ki = Vi (0) Show that Vi(T) = (1 + Kvi)Vi(0) (d) Denote by Kv the return of V. Apply (b) and (c) to the formula K = To show that : V(T)- VO V(0) Ky = X=1 W Ki