Consider the following situation: State of Economy Probability of State of Econo
ID: 2744857 • 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
Part - a. Which has the most systematic risk
Stock A: E(Ra) = 0.2(0.25) + 0.8(-0.3) = -0.19 -19%
-0.19 = 0.03 + 0.07
Beta = -3.142857143
SD = [0.2(0.25 + 0.19)^2] + [0.8(-0.3 + 0.19)^2]
SD = 0.03872 + 0.00968 = 0.0484
SD = (0.0484)^1/2 = 22%
Stock B:E(Rb) = 0.2(0.1) + 0.8(0.05) = 0.06 6%
0.06 = 0.03 + 0.07
beta = 0.4285714286
SD = [0.2(0.1 – 0.06)^2] + [0.8(0.05 – 0.06)^2]
SD = 0.00032 + 0.0000072 = 0.0003272(0.0003272)^1/2
SD= 0.0180886705 = 1.8%
Stock C:E(Rc) = 0.2(0.05) + 0.8(0.1) = 0.09 9%
0.09 = 0.03 + 0.07
beta = 0.8571428671
SD = [0.2(0.05 – 0.09)] + [0.8(0.1 – 0.09)]SD
SD= -0.008 + 0.008 = 0%
Answer for part A: STOCK C has the most systematic risk as it has the largest beta.
Part B: Which stock has the most unsystematic risk.
Answer for part B: STOCK A has the most systematic risk as it has the largest SD (standard deviation).Steps already shown in pervious part
Part C Standard deviation of portfolio:
Boom: 0.42(0.25) + 0.18(0.1) + 0.4(0.05)
0.105 + 0.018 + 0.02 = 0.143
Recesion: 0.42(-0.3) + 0.18(0.05) + 0.4(0.1)
-0.126 + 0.009 + 0.04 = -0.077
0.2(0.143) + 0.8(-0.077)
0.0286 + -0.616
-0.033 = -3.3%
The standard deviation for the portfolio = 8.80%
Part - D: If inflation is 2.5% Real return = (-0.033-0.025)/(1.025) = -0.0566 = -5.66%
State Prob Return (R - ER) (R - ER)^2 (R - ER)^2 * P Boom 0.2 0.143 0.176 0.030976 0.0061952 Recession 0.8 -0.077 -0.044 0.001936 0.0015488 Expected Return -3.30% Standard deviation 8.80%