The price of some stock today is $300. Assume that the stock\'s value in one yea

Question

The price of some stock today is $300. Assume that the stock's value in one year is a random
variable X with the following probability distribution: P(x=400)=0.1; P(x=350)=0.4; P(x=300)=0.3; P(x=270)=0.2.
a. Compute the expected value, E(x), which represents the expected price of the stock in one year.
b. What is the expected return of investing into this stock? (Hint, ignoring dividends,
the expected return on the stock is given by (E(x))/(Price today)
c. Assume there is a riskless bond in the economy that yields a (certain) return of 4% a
year. This is lower than the expected return from the stock you found above. Will
some people in this economy choose to hold the bond? Why would they do so?
Explain.

Explanation / Answer

a) E(x) = Sum(pi * xi ) (where i = 1,2,3,4) E(x) = 0.1*400+0.4*350*+0.3*300+0.2*270 = 324 (ANSWER)) b) Expected return =( E(x)- today's price)/ today's price = (324-300)/300 = 24/300 = 8% ((ANSWER) c) Some people are risk averse and are willing to accept lesser return.This is the reason why they prefer risk less bonds with lower returns rather than higher returns on risky investments.

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