Ms. Maple is considering two securities, A and B, and the relevant information i
ID: 2739994 • 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
Part A: Calculate expected return and standard deviation of two securities.
Part B: Suppose Miss Maple invested $2,500 in security A and $3,500 in security B. Calculate the expected return and standard deviation of her portfolio.
PLEASE SHOW FORMULAS AND CALCULATIONS . THANK YOU.
State of the economy
Probability
Return on A(%)
Return on B(%)
Bear
0.4
3
6.5
Bull
0.6
15
6.5
Explanation / Answer
Part A: Calculation of expected return and standard deviation of two securities.
Expected return of the security A
Return on A = Return on Bear x Probability of Bear + Return on Bull x Probability of Bull
= 3% x 0.4 + 15% x 0.6 = 10.2%
Return on B = Return on Bear x Probability of Bear + Return on Bull x Probability of Bull
= 6.5% x 0.4 + 6.5% x 0.6 = 6.5%
Standard Deviation (S.D.) of A
Probable return Xi
Provability p(Xi)
Deviation (xi - x)
Deviation squared (Xi - X)2
Product (Xi - X)2P(Xi)
0.4
3%
-7.20%
51.84
20.736
0.6
15%
4.800%
23.04
13.824
Total
34.56
X= return = 10.20%
Variance = 34.56%
Standard Deviation = = 5.878%
Standard Deviation (S.D.) of B
Provability p(Xi)
Probable return Xi
Deviation (xi - x)
Deviation squared (Xi - X)2
Product (Xi - X)2P(Xi)
0.4
6.50%
0.00%
0.00
0
0.6
6.50%
0.000%
0.00
0
Total
0
X = return = 6.5%
Variance = 00.00%
Standard Deviation = = 0%
Part B: Calculation of the expected return and standard deviation of her portfolio.
Return of Pertfolio=
(Amount invested in A x Return of A) + (Amount invested in B x return of B)
($ 2,500 x 10.2%) + ($3500 x 6.5%) = $ 482.5
Return of portfolio= (482.5/$6000) = 8.0417%
Standard deviation of portfolio:
S.D. of two asset portfolio=
W1=weight of A
W2=Weight of B
Co variance of A and B= 0
=Square route of (weight of A square x Variance+ Weight of B square X variance + 2 x weight of A x Weight of B x Cov (A and B))
Probable return Xi
Provability p(Xi)
Deviation (xi - x)
Deviation squared (Xi - X)2
Product (Xi - X)2P(Xi)
0.4
3%
-7.20%
51.84
20.736
0.6
15%
4.800%
23.04
13.824
Total
34.56
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