Question

Consider the following information about three stocks:

  

				Rate of Return If State Occurs
State of	Probability of
Economy	State of Economy			Stock A			Stock B			Stock C
Boom		.20			.38			.50			.50
Normal		.55			.16			.14			.12
Bust		.25			.00			?.30			?.50

  

a-1	If your portfolio is invested 30 percent each in A and B and 40 percent in C, what is the portfolio expected return? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Portfolio expected return

%

a-2	What is the variance? (Do not round intermediate calculations and round your answer to 5 decimal places, e.g., 32.16161.)

  

Variance

  

a-3	What is the standard deviation? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Standard deviation

%

b.	If the expected T-bill rate is 3.60 percent, what is the expected risk premium on the portfolio? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Expected risk premium

%

  

c-1	If the expected inflation rate is 3.20 percent, what are the approximate and exact expected real returns on the portfolio? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

Approximate expected real return	%
Exact expected real return	%

c-2	What are the approximate and exact expected real risk premiums on the portfolio? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

Approximate expected real risk premium	%
Exact expected real risk premium	%

Answer 1

a.

Boom Scenario

Expected return of portfolio in Boom scenario = (30% × 38%) + (30% × 50%) + (40% × 50%)

  = 11.40% + 15.00% + 20.00%

= 46.50%

Expected return of portfolio in Boom scenario is 46.50%.

Normal Scenario

Expected return of portfolio in Normal scenario = (30% × 16%) + (30% × 14%) + (40% × 12%)

   = 4.80% + 4.20% + 4.80%

     = 13.80%

Expected return of portfolio in Normal scenario is 13.80%.

Bust Scenario

Expected return of portfolio in Bust scenario = (30% × 0%) + (30% × -30%) + (40% × -50%)

   = 0% - 9.00% - 20%

= -29%

Expected return of portfolio in Bust scenario is -29%.

Now,

Expected return and standard deviation of portfolio is calculated in excel and screen shot provided below:

Expected return of portfolio is 9.64%, variance of portfolio is 6.55% and standard deviation is 25.58%.

b.

T bill rate = 3.60%

Expected risk premium = 9.64% - 3.60%

= 6.04%

Expected risk premium of portfolio is 6.04%.

c-1.

Inflation rate = 3.20%

Approximate real return = 9.64% - 3.20%

= 6.44%

Approximate real return is 6.44%.

again,

Exact real return = (1 + 9.64%) / (1 + 3.20%) - 1

= 1.0624 - 1

= 6.24%

Exact real return is 6.24%.

c-2.

T bill rate = 3.60%

inflation rate = 3.20%

Approximate expected real risk premium = 6.04% - 3.20%

= 2.84%

Approximate expected real risk premium of portfolio is 2.84%.

Exact expected real risk premium = (1 + 6.04%) / (1 + 3.20%) - 1

= 1.0275 - 1

= 2.75%

Exact expected real risk premium is 2.75%.