Question

Consider a security with the stock prices
S(1) =



80 with probability 1/8
90 with probability 2/8
100 with probability 3/8
110 with probability 2/8
(a) What is the current price of the stock for which the expected return
would be 12%?
(b) What is the current price of the stock for which the standard deviation
would be 18%

Answer 1

We find the expected price and Variance of the stock at end of year 1.

Expected price is the sum of the multiple of price and probability

Variance, we find the square of the deviation, multiply it by probability, sum it.

Expected Price at time 1 (S1) = 97.5

Variance at time 1 (Var 1) = 93.75

1) Expected price at time 0 (S0) = S1 / (1+ Return) = 97.5 / 1.12 = 87.05

2) Variance (K) = 18%^2 = 0.0324

Now, Variance (K) = 1/ S(0)^2 * Variance (S1)

i.e 0.0324 = 1/ S(0)^2 * 93.75

i.e S(0) = Square root (93.75 / 0.0324)

i.e S(0) = 53.79