P5-13: Portfolio return and standard deviation. Jamie Wong is considering buildi
ID: 2629675 • Letter: P
Question
P5-13: Portfolio return and standard deviation. Jamie Wong is considering building an investment portfolio containing two stocks, L and M. Stock L will represent 40% of the dollar value of the portfolio, and stock M will account for the other 60%. The expected returns over the next 6 years, 2010-2015, for each of these stocks are shown in the following table:
Expected return
Year
Stock L
Stock M
2010
14%
20%
2011
14
18
2012
16
16
2013
17
14
2014
17
12
2015
19
10
a. Calculate the expected portfolio return, r p , for each of the 6 years.
Expected return
Year
Stock L
Stock M
2010
14%
20%
2011
14
18
2012
16
16
2013
17
14
2014
17
12
2015
19
10
Explanation / Answer
E(L) = 0.14 + 0.14 + 0.16 + 0.17 + 0.17 + 0.19 = 0.97
E(M) = 0.20 + 0.18 + 0.16 + 0.14 + 0.12 + 0.10 = 0.90
a.) Expected value = [0.4*0.97 + 0.6*0.9]/6 = 0.928/6 = 0.15467 = 15.467%
b.) Variance = [0.4*(0.97-0.928)^2 + 0.6*(0.9-0.928)^2]/6= 2.284 x 10^-4
So standard deviation = sqrt(var) = sqrt(2.284 x 10^-4) = 0.015113 = 1.5113%
c.) Let correlation coefficient = r
s.d of L = 0.0434
s.d of M = 0.0837
0.015113^2 = (0.4)^2(0.0434)62 + (0.6)^2*(0.0837)^2 + 2*(0.4)(0.6)(0.0434)(0.0837)*r
So r = - 0.964
Since r is close to -1, stocks L and M have strong correlation.
d.) Benefits include reduction in portfolio risk as r is negative
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