Consider the following information: Rate of Return if State Occurs State of Prob

Question

Consider the following information: Rate of Return if State Occurs State of Probability of Economy State of Economy Stock A Stock B Stock C Boom .15 .35 .45 .27 Good .55 .16 .10 .08 Poor .25 .01 .06 .04 Bust .05 .12 .20 .09 a. Your portfolio is invested 30 percent each in A and C, and 40 percent in B. What is the expected return of the portfolio? (Do not round intermediate calculations and round your answer to 2 decimal places. (e.g., 32.16)) Expected return % b-1. What is the variance of this portfolio? (Do not round intermediate calculations and round your answer to 5 decimal places. (e.g., 32.16161)) Variance b-2. What is the standard deviation? (Do not round intermediate calculations and round your answer to 2 decimal places. (e.g., 32.16)) Standard deviation %

Explanation / Answer

a.Expected return in boom = 0.35*0.3 + 0.45*0.3 +0.27*0.4 = 0.348

Expected return in Good = 0.16*0.3 + 0.10*0.3 + 0.08*0.4 = 0.11

Expected return in Poor = -0.01*0.3 + -0.06*0.3 + -0.04*0.4 = -0.037

Expected return in Bust = -0.12*0.3 -0.2*0.3-0.09*0.4 = -0.132

So expected return = 0.348*0.15 + 0.11*0.55 -0.037*0.25 -0.132*0.05 = 0.09685 = 9.685% = 9.69%

The variance and std. deviation is as shown below:

(B) variance = 0.01665

(C) Std. deviation = 12.91%

Economy Prob P Return R R - E ( R ) [R - E ( R )]^2 [R - E ( R )]^2 * P Boom 0.15 0.348 0.25115 0.063076323 0.009461448 Good 0.55 0.11 0.01315 0.000172923 9.51074E-05 Poor 0.25 -0.037 -0.13385 0.017915823 0.004478956 Bust 0.05 -0.132 -0.22885 0.052372323 0.002618616 Expected return E ( R ) 0.09685 Variance 0.016654128 Standard deviation 12.91%

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