Consider the following information: Your portfolio is invested 26 percent each i

Question

Consider the following information:

Your portfolio is invested 26 percent each in A and C, and 48 percent in B. What is the expected return of the portfolio? (Do not round your intermediate calculations.)

9.29%
10.83%
10.32%
7.93%
11.35%

HINT: It is best if you first calculate the return on the portfolio in all 4 states. You will need those numbers in the next part of the problem.

.0322
.0204
.0214
.0071
.0236

NOTE: The standard deviation is the square root of the variance. It tells us on average, how far away the return will be from the expected return.

8.45%
13.91%
14.64%
15.38%
17.97%

Rate of Return if State Occurs State of Economy Probability of
State of Economy Stock A Stock B Stock C Boom .20 .44 .29 .31 Good .30 .18 .16 .14 Poor .11 .09 .10 .07 Bust .39 -.02 -.05 -.10

Explanation / Answer

Rate of return if State occurs State of economy Probability Stock-A Stock-B Stock-C Boom 0.2 0.44 0.29 0.31 Good 0.3 0.18 0.16 0.14 Normal 0.11 0.09 0.1 0.07 Bust 0.39 -0.02 -0.05 -0.1 Answer-a1 The weights of the stocks in the portfolio are given: Weights Stcck-A 0.26 Stock-B 0.48 Stock-C 0.26 Here the expected return of the stocks are given as: Expected return of the Stock-A = 0.2x0.44 + 0.3x0.18 + 0.11x0.09+0+39x-0.02 = 0.144 Expected return of the Stock-B = 0.2x0.29 + 0.3x0.16 + 0.11x0.1+0+39x-0.05 = 0.0975 Expected return of the Stock-C = 0.2x0.31 + 0.3x0.14 + 0.11x0.07+0+39x-0.1 = 0.0727 Therefore portfolio's expected return = 0.26x0.144 + 0.48x0.0975 + 0.26x0.0727 = 10.32% Answer-a2 No we have to calculate the standard deviation of individual stocks. So for Stock-A State of economy Probability Stock-A Expected return Deviation Dev squared Prob x Dev Sq Boom 0.2 0.44 0.1441 0.2959 0.08755681 0.017511362 Good 0.3 0.18 0.1441 0.0359 0.00128881 0.000386643 Normal 0.11 0.09 0.1441 -0.0541 0.00292681 0.000321949 Bust 0.39 -0.02 0.1441 -0.1641 0.02692881 0.010502236 Variance = 0.01821995 standard deviation of Stock-A = 0.134981 So for Stock-B State of economy Probability Stock-B Expected return Deviation Dev squared Prob x Dev Sq Boom 0.2 0.29 0.0975 0.1925 0.03705625 0.00741125 Good 0.3 0.16 0.0975 0.0625 0.00390625 0.001171875 Normal 0.11 0.1 0.0975 0.0025 6.25E-06 6.875E-07 Bust 0.39 -0.05 0.0975 -0.1475 0.02175625 0.008484938 Variance = 0.00858381 standard deviation of Stock-B = 0.092649 So for Stock-C State of economy Probability Stock-C Expected return Deviation Dev squared Prob x Dev Sq Boom 0.2 0.31 0.0727 0.2373 0.05631129 0.011262258 Normal 0.3 0.14 0.0727 0.0673 0.00452929 0.001358787 Bust 0.11 0.07 0.0727 -0.0027 7.29E-06 8.019E-07 0.39 -0.1 0.0727 -0.1727 0.02982529 0.011631863 Variance = 0.01262185 standard deviation of Stock-C = 0.112347 Now prepare a variance covariance matrix: Stock-A Stock-B Stock-C Stock-A 0.01821995 0.012506 0.015165 Stock-B 0.01250587 0.008584 0.010409 Stock-C 0.01516474 0.010409 0.012622 From this matrix we get: Cov(A,B) = 0.01250587 Cov(A,C) = 0.01516474 Cov(B,C) = 0.01040882 So the Variance of three stock portfolio = (0.26)^2 x 0.01821995+(0.48)^2 x 0.008584+(0.26)^2 x 0.012622+ 2x0.26x0.48x0.01250587+2x0.26x0.26x0.1516474 + 2x0.48x0.26x0.01040882 =   0.030285 Answer-a3 Standard deviation = 0.174026 or 17.40%

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.