Consider the following information about three stocks: Rate of Return If State O

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 .22 .30 .42 .58 Normal .46 .23 .21 .19 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 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 4.30 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 3.90 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 %

Explanation / Answer

(a-1) Portfolio expected return = Sum of (weightage * return * probability) of Stock A, B and C

=[(0.30*0.22 + 0.46 *0.23 + 0.01 *0.32) *0.25] + [(0.42 *0.22 +0.21 *0.46 * -0.22*0.32)*0.25% ] +

[(0.58 *0.22 +0.19*0.46 + -0.50 *0.32) * 0.50]

= (6.6% + 10.58 +0.32%) 0.25 + (9.24% +9.66% -7.04%)0.25 + (12.76% +8.74%-16%) *0.50

= 17.5% *0.25 + 11.86% *0.25 + 5.5% *0.5

= 4.38% ( Stock A) + 2.97% (Stock B) + 2.75%(Stock C)

= 10.1%

(a-2) Variance of Stock A, B andC

Variance A = (0.22 * [30% -4.38%]2) + (0.46 * (23% - 4.38%)2 + (0.32 * (1% - 4.38%)2

= 0.22 * 25.62%2 + 0.46 * 18.62%2 + 0.32 *-3.38%2

   =0.22 * 0.066 + 0.46 *0.035 + 0.32*0.0011

= 0.0145 + 0.0161 + 0.000352

= 3.10%

B = ( 0.22 *(42% - 2.97%)2 + 0.46( 21% - 2.97%)2 + (0.32 * (-22% - 2.97%)2

= 0.22 * 39.03%2 + 0.46 *18.03%2 + 0.32 * -24.97%

   = 0.22*0.1523 + 0.46 *0.0325 + 0.32*0.0624

= 0.0335 + 0.015+0.02

= 6.85%

C = 0.22 * (58% - 2.75%)2 + (0.46 * (19% - 2.75%)2 + (0.32 * (-50% - 2.75%)2

     = 0.22 *55.25%2 + 0.46 * 16.25%2 + 0.32 *52.75%2

   = 0.22 * 0.305 + 0.46 *0.0264 + 0.32 *0.2783

= 0.0671 + 0.0121 + 0.0891

= 16.83%

(a-3) Standard deviation = variance1/2

   Stock A = 3.10%1/2

= 17.61%

   Stock B = 6.85%1/2

= 26.17%

Stock C = 16.83%1/2

   = 41.02%

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