1 Question 1 Let's specialize the concept of returns we have seen generically for securities to stocks. The gross return of stock 3' between time t and t + 1 in state 8 (given available information at t) is H,t+1(3) + Di,t+1(9) Pig: Ri,t:t+1(3) E Ri,t+1(3) E where a P": price at time t of stock 1' - D,t+1(s): dividend paid at time t + 1 by stock 1' in state 3 a H,t+1(8): price of stock 3' at time t + 1 in state 3 (after the dividend is paid; ex-dividend price) Answer the following two conceptual questions 1. Why PE; is not a function of the states of the world? 2. Given the denition of linear return T'f:f+1(8) E r1t+1(3) E Ri+1(s) 1, if we dene cap ital gain/ loss as CG,t+1('5l = W what is the implied denition of dividend yield DK+1(3)? Suppose ABC stock price is currently $120. Assume that the (ex-dividend) stock price will either be $135 or $90 next month. (The state will be either "good" or "bad," 9 or 5?.) Either way, the rm will pay a $7 dividend. 1. Compute the stock capital gain/loss, CGABC+1(3), dividend yield, DYA BC,t+1(3) and linear return TABCJ+1(8) in the good and the bad state 2. Without computing the log return r3130; +1 3), do you expect it to be higher or lower than T 4430,1944 (S) ? Why? 3. Given a risk-free rate of 0.0025 compute the excess return r534 36,: +1(s) in the good and the bad state 2 Question 2 Consider the following setup: a 3 states of the world: p1 : Prob(81) : 0.3,p2 : Prob(sl) : 0.4 and p3 : Pr0b(31) : 0.3