Consider the following situation: State of Economy Probability of State of Econo
ID: 2744992 • Letter: C
Question
Consider the following situation:
State of Economy
Probability of State of Economy
Returns if State Occurs
Stock A
Stock B
Stock C
Boom
20%
25%
10%
5%
Recession
80%
-30%
5%
10%
The expected return on the market portfolio is 7% and the US Treasury bill yields 3%. The capital market is currently in equilibrium.
(5 points) Which stock has the most systematic risk? Provide all the steps and equations.
(5 points) Which stock has the most unsystematic risk? Explain why. Provide all the steps and equations.
(10 points) What is the standard deviation of a portfolio which is comprised of $8,400 invested in stock A, $3,600 in stock B, and $8,000 in stock C?
(5 points) If the expected inflation rate is 2.5%, what is the exact expected real return on the portfolio of part (c)?
State of Economy
Probability of State of Economy
Returns if State Occurs
Stock A
Stock B
Stock C
Boom
20%
25%
10%
5%
Recession
80%
-30%
5%
10%
Explanation / Answer
a) Systematic Risk = Beta Returns if State Occurs Expected Return State of Economy Probability of State of Economy Stock A Stock B Stock C Prob. x Stock A 's Return Prob. x Stock A 's Return Prob. x Stock A 's Return Boom 20.00% 25.00% 10.00% 5.00% 5.00% 2.00% 1.00% Recession 80.00% -30.00% 5.00% 10.00% -24.00% 4.00% 8.00% Total -19.00% 6.00% 9.00% According CAPM Expected Return E(R)= Risk free Rate + Beta x (Market Return - Risk free Rate) Risk Free Rate RF = 3.00% Return on market RM 7.00% Stock A 's Beta = -19% - 3% = Beta x (7% -3%) -5.5 Stock B 's Beta = 6% - 3% = Beta x (7% -3%) 0.75 Stock C 's Beta = 9% - 3% = Beta x (7% -3%) 1.5 Stock C has the most systematic risk because it has the highest beta. b) Stock A has the most unsystematic risk because it has the negative Beta.