Assume that you purchase stock at a price of $30 and that the risk-free (T-bill)
ID: 2801984 • 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
Stock Price = $30
a) Expected return of the stock = weighted average of the returns from three states of economy
= Summation(Probability * stock return) = 30% * -46.67 + 50% * 30% + 20% * 83.33% = 17.67%
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b) Average of the 3 returns = (-46.67% + 30% + 83.33% )/ 3 = 22.22%
Standard Deviation = Underroot[ Summation of( ( rate - mean return)2 )/ number of states]
= underroot[(-46.67%-22.22%)2 + (30%-22.22%)2 + (83.33%- 22.22%)2/3]
=53.36%
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c) Expected return of portfolio = weight of stock * return of stock + weight of TBill * Return of TBill
= 0.7 * 17.67% + 0.3 * 3% = 13.27%
Standard deviation of portfolio = weight of stock * Standard deviation of Stock + weight of Tbill * standard deviation of Tbill
= 0.7 * 53.36% + 0.3 * 0
= 37.35%
state of the economy Probability stock price Dividend STOCK RETURNS SD Recession 30% $15 $1 =($15+$1-$30)/$30 =-46.67 % 50% $36 $3 =($36+$3 -$30)/$30 =30 % 20% $50 $5 =($50+$5 -$30)/$30 =83.33%