Consider the following situation: State of Economy Probability of State of Econo
ID: 2744946 • 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)?
****PLEASE SHOW EVERY DETAILED STEP OF EVERY EQUATION
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
b. Most Unsystematic Risk - Stock A - Unsystematic Risk is measure through measuring standard deviation. Standard Deviation of Stock A is the highest as shown below
E(R) = weighted average probability of returns
Std. Dev. = Square Root ( weighted average(square of difference between xi and average x))
For Stock A, = Sqrt((20% x (-19% - 25%)^2 + 80% x (-19% - (-30%))^2)) = 22.00%
a. Most Systematic Risk - Stock C. Systematic Risk is measure by beta of the stock.
Use CAPM, E(R) = Rf + Beta * (Rm - Rf) => Beta = [E(R) - Rf] / (Rm - Rf)
Stock C has the highest positive value.
c. Standard Deviation = square root ((22% x 0.42)^2 + (2% x 0.18)^2 + (2% x 0.4)^2) = 9.28%
d. Real Return = Nominal Return - Inflation = -3% - 2.5% = - 5.5%
Nominal Return = (0.42 x -19%) + (0.18 x 6%) + (0.4 x 9%) = -3%
A B C 20% 25% 10% 5% 80% -30% 5% 10% E(R) -19.00% 6.00% 9.00% Std. Dev. 22.00% 2.00% 2.00%