Given the above information on two investments A and B, calculate the following
ID: 2710215 • Letter: G
Question
Given the above information on two investments A and B, calculate the following statistics: The correlation coefficient between A and B is 0.169. (Note that since the correlation is given, you do not have to do the long calculation for covariance, just use .) AB AB A B
A. Expected Return for A
B. Standard Deviation for A
C. Expected Return for B
D. Standard Deviation for B
E. The expected return on a portfolio consisting of 60% A and 40% B.
F. The standard deviation of a portfolio consisting of 60% A and 40% B.
G. The covariance between A and B
Show all work.
Investment State I Return (p=0.3) State II Return (p = 0.5) State III Return (p=0.2) A 5% 11% 9% B 6% 8% -3%Explanation / Answer
Answer A
Expected Return for A = 8.8%
Answer B
Standard Deviation for A = 2.72%
Answer C
Expected Return for B = 5.20%
Answer D
Standard Deviation for B = 4.19%
Answer E
Expected return of a portfolio consisting of 60% A and 40% B = 7.36%
Answer F
Standard Deviation of a portfolio consisting of 60% A and 40% B = 2.53%
Answer G
Covariance between A and B = 1.93
Stock A
Probability
Returns
Expected return = Probability * return
0.30
5%
1.5%
0.50
11%
5.5%
0.20
9%
1.8%
Total
8.8%
Expected return = 8.8%
Variance = 0.30 * (5 – 8.8)^2 + 0.5 * (11-8.8)^2 + 0.2 * (9-8.8)^2
= 0.30 * (-3.8)^2 + 0.5 * 2.2^2 + 0.2 * 1.8^2
= 0.30 * 14.44 + 0.5 * 4.84 + 0.20 * 3.24
= 4.332 + 2.42 + 0.648
= 7.4
Standard Deviation = Square Root (7.4) = 2.72029% or 2.72% (rounded off)
Stock B
Probability
Returns
Expected return = Probability * return
0.30
6%
1.8%
0.50
8%
4%
0.20
-3%
-0.6%
Total
5.20%
Expected Return = 5.20%
Variance = 0.30 * (6-5.2)^2 + 0.5 * (8-5.2)^2 + 0.2 * (-3-5.2)^2
= 0.3 * 0.8^2+ 0.5 * 2.8^2 + 0.2 *(-8.2)^2
= 0.3 * 0.64 + 0.5 * 7.84 + 0.20 * 67.24
= 0.192 + 3.92 + 13.448
= 17.56
Standard Deviation = Square Root (17.56) = 4.190465 or 4.19% (rounded off)
Portfolio of 60% A and 40% B
Expected Return = 0.6 * 8.8% + 0.4 * 5.2% = 5.28% + 2.08% = 7.36%
Correlation coefficient = 0.169
Covariance between A and B = correlation coefficient * standard deviation A * standard deviation B
= 0.169 *2.72 * 4.19 = 1.9260592 or 1.93 (rounded off)
Portfolio Variance = wA^2 * std deviationA^2 + wA^2*std.deviationA^2 + 2*wA*wB*covariance(a,b)
= 0.6^2 * 2.72^2 + 0.4^2 * 4.19^2 + 2 * .0.6 * 0.4 * 1.9260592
= 0.36 * 7.4 + 0.16 * 17.56 + 0.924508416
= 2.664 + 2.8096 + 0.924508416
= 6.398108416
Standard Deviation of Portfolio = Square Root (6.398108416) = 2.52944 or 2.53 (rounded off)
Probability
Returns
Expected return = Probability * return
0.30
5%
1.5%
0.50
11%
5.5%
0.20
9%
1.8%
Total
8.8%
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.