I want to understand how to do this question and an explanation of the answer ( I have limited Finance knowledge ( specifically parts c to f) ( in part C where did the 1.67 come from, what is that ? In part d where is this 1.8 and 0.8 coming from and what is that ? Could you explain part e and f in simple language i don't really understand it , also where did the 1.2 and later on 1.05 came from in f? Thank you very much

a) Calculate the expected returns on ABC and on the market. (2pts) b) What is the beta of stock ABC? (2 pts) c) What is the risk-free rate, assuming CAPM holds? (2 pts) d) What are the prices of stock ABC in the two states? (2 pts) e) Suppose that you want to write a one-year European put option on the stock of ABC with an exercise price of $35. How much is the option worth? Show your work. (3 pts) f) If in the Boom state, the return of ABC stock becomes 0.2 and in the Recession state, its return becomes -0.2, for the same option as in part e) do you think the value of the option will be higher, lower or the same as that in part e)? Explain

Answer :

a) ER(ABC) = 0.4*.8+.6*(-.2) = 0.2; ER(m) = 0.4*.5+.6*(-.1) = 0.14

b) var(m) = .4*(.5-0.14)^2+.6*(-.1-.14)^2 = 0.0864; cov =0.4*(.8-0.2)*(.5-0.14)+.6*(-.2- 0.2)*(-.1-.14) = .144; Beta = .144/0.0864 = 1.6

c) .2 = rf + 1.67*(.14- rf) rf = (.2-1.67*.14)/(1-1.67) = 0.05

d) P(B) = 35*1.8 = 63; P(R) = 35*.8 = 28

e) Put: Su=0; Sd=35-28 = 7; Short stock: Pu=-63; Pd=-28 Lend PV of 63 Su = 0; Sd = 63-28 = 35 hedge ratio = 7/35 P put = 7/35*(63/1.05-35) = 5

f) fall: Pu = -35*1.2= -42 lend PV of 42; Sd = 42-28 = 14 P put = 7/14*(42/1.05-35) = 2.5

7. In a most simplified world, we suppose there are two states of the economy in one year. The returns on stock ABC and on the market are as given below. Stock ABC is currently traded at $35. 7. In a most simplified world, we suppose there are two states of the economy in one year. The returns on stock ABC and on the market are as given below. Stock ABC is currently traded at $35