Assume that you purchase stock at a price of $30 and that the risk-free (T-bill)
ID: 2801983 • Letter: A
Question
Assume that you purchase stock at a price of $30 and that the risk-free (T-bill) rate is 3%. Use the data in the following chart to answer parts A, B and C:
A) Calculate the expected return for the stock.
B) Calculate the standard deviation of the stock’s return.
C) If you invest 70% of your portfolio in the stock and 30% in T-bills, what would be the expected return and standard deviation of your portfolio?
State of EconomyProbability Recession Normal growth Boom 30% 50% 20% Stock price $15 $35 $50 Dividend $1 %3 $5Explanation / Answer
a) Expected Returns, M = sum of p(x) x X = 16.00%
where X = Returns = (Stock Price + Dividend) / Purchase Price
b) Standard Deviation = Square Root of sum of p(x) x (X - M)^2 = (2.74%)^0.5 = 16.54%
c) Expected Return of the portfolio = 70% x 16% + 30% x 3% = 12.10%
Std. Dev. of portfolio = 70% x 16.54% = 11.58%
State p(x) Returns (X) p(x)*X p(x)*(X-M)^2 Recession 30% -47% -14.00% 2.700% Normal 50% 27% 13.33% 0.036% Boom 20% 83% 16.67% 0.001% Mean (M) 16.00% 2.74% Std. Dev. 16.54%