Question

Consider the following information about three stocks: Rate of Return If State Occurs State of Probability of State of Economy 22 Economy Stock A Stock B Stock C Boom 30 23 42 21 58 19 Normal 46 Bust 32 01 .22 50 a-1. If your portfolio is invested 25 percent each in A and B and 50 percent in C, what is he portfolio expected return? (Do not round Intermedlate calculations and enter your answer as a percent rounded to 2 declmal places, e.g., 32.16.) a-2. What is the variance? (Do not round Intermedlate calculations and round your answer to 5 decimal pleces, e.g., .16161.) a-3. What is the standard deviation? (Do not round Intermedlate calculations end enter your answer as a percent rounded to 2 declmal places, e.g., 32.16.) If the expected T-bill rate is 4.30 percent, what is the expected risk premium on the portfolio? (Do not round Intermedlete calculations and enter your answer as e percent rounded to 2 decimal places, e.g.,32.16.) c-1. If the expected inflation rate is 3.90 percent, what are the approximate and exact expected real returns on the portfolio? (Do not round lintermedlate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) c-2. What are the approximate and exact expected real risk premiums on the portfolio? (Do not round Intermedlate calculations and enter your answers as o percent rounded to 2 decimal places, e.g.. 32.16.) b. Portfolio expected returm a-1. a-2. Varianoe a-3. Standard deviation 96 Expected risk premium c-1. Approximate expected real return b. 96 96 Exact expected real return % c-2. Approximate expected real risk premium Exact expected real risk premium

Answer 1

a. Portfolio expected return

Expected return of Stock A = $\sum$ Probability * Return

= (0.22*0.3) + (0.46*0.23) + (0.32*0.01)

= 0.175 or 17.5%

Expected return of Stock B = (0.22*0.42) + (0.46*0.21) + (0.32*-0.22)

=0.1186 or 11.86%

Expected return of Stock B = (0.22*0.58) + (0.46*0.19) + (0.32*-0.50)

=0.055 or 5.5%

Portfolio Expected Return = $\sum$ Weight * Return

= (0.25*17.5) + (0.25*11.86) + (0.5*5.5)

= 10.09%

b. Variance

Economy	Probability	Stock A	Stock B	Stock C	Portfolio Return	Return Deviation	Squared Return Deviation	Squared Return Deviation * Probability
Boom	0.22	0.3	0.42	0.58	0.47	0.075	0.005625	0.0012375
Normal	0.46	0.23	0.21	0.19	0.205	-0.19	0.0361	0.016606
Bust	0.32	0.1	-0.22	-0.5	-0.28	-0.675	0.455625	0.1458
					0.395			0.1636435

Variance = 0.1636435 * 100

= 16.36435

c. Standard Deviation

Standard Deviation = Variance ^ 1/2

= 16.36435 ^ 1/2

= 8.18

d, Expected risk premium

Expected risk premium = Expected rate of return - Risk Free Rate

Expected rate of return (from part a) = 10.09%

Risk Free Rate = T- bill rate = 4.30%

Expected risk premium = (10.09 - 4.3)% = 5.79%