Ms. Maple is considering two securities, A and B, and the relevant information i
ID: 2753058 • Letter: M
Question
Ms. Maple is considering two securities, A and B, and the relevant information is given below:
State of the economy
Probability
Return on A(%)
Return on B(%)
Bear
0.4
3
6.5
Bull
0.6
15
6.5
a. Calculate expected return and standard deviation of two securities. b. Suppose Miss Maple invested $2,500 in security A and $3,500 in security
B. Calculate the expected return and standard deviation of her portfolio.
State of the economy
Probability
Return on A(%)
Return on B(%)
Bear
0.4
3
6.5
Bull
0.6
15
6.5
Explanation / Answer
Rate of return if State occurs State of economy Probability Stock-A Stock-B Bear 0.4 0.03 0.065 Bull 0.6 0.15 0.065 Answer-a1 The weights of the stocks in the portfolio are given: Weights Stcck-A 0.416666667 Stock-B 0.583333333 Here the expected return of the stocks are given as: Expected return of the Stock-A = 0.4x0.03 + 0.6x0.15 = 0.102 Expected return of the Stock-B = 0.4x0.065 + 0.6x0.065 = 0.065 Therefore portfolio's expected return = 0.41x0.102 + 0.5833x0.065 = 0.080416667 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 Bear 0.4 0.14 0.102 0.038 0.001444 0.0005776 Bull 0.6 0.05 0.102 -0.052 0.002704 0.0016224 Variance = 0.0022 standard deviation of Stock-A = 0.046904158 So for Stock-B State of economy Probability Stock-B Expected return Deviation Dev squared Prob x Dev Sq Bear 0.4 0.07 0.065 0.005 0.000025 0.00001 Bull 0.6 0.18 0.065 0.115 0.013225 0.007935 Variance = 0.007945 standard deviation of Stock-B = 0.089134729 Now prepare a variance covariance matrix: Stock-A Stock-B Stock-A 0.0022 0.004180789 Stock-B 0.004180789 0.007945 From this matrix we get: Cov(A,B) = 0.004180789 So the Variance of two stock portfolio = (0.4167)^2 x 0.0022+(0.5833)^2 x 0.007945+ 2x0.4167x0.5833x0.046904x0.089134x0.004180789 = 0.003094 And the standard deviation of the portfolio = 5.56%
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.