Security F has an expected return of 11.00 percent and a standard deviation of 4
ID: 2646171 • Letter: S
Question
Security F has an expected return of 11.00 percent and a standard deviation of 44.00 percent per year. Security G has an expected return of 16.00 percent and a standard deviation of 63.00 percent per year.
What is the expected return on a portfolio composed of 40 percent of Security F and 60 percent of Security G? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
If the correlation between the returns of Security F and Security G is .35, what is the standard deviation of the portfolio described in part (a)? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
Security F has an expected return of 11.00 percent and a standard deviation of 44.00 percent per year. Security G has an expected return of 16.00 percent and a standard deviation of 63.00 percent per year.
Explanation / Answer
Answer:
(a) Expected Return of portfolio
Formula:
E(R) = WF*RF + WG* RG
WF = Weight of Security F = 40%
RF = Return of Security F = 11%
WG = Weight of stock 2 = Security G = 60%
RG = Return of Security G = 16%
Expected Return of portfolio = (40% * 11 %)+(60% * 16%) = 14%
(b)
Portfolio Standard Deviation = [ w2F*?2(RF) + w2G*?2(RG) + 2*(wF)*(wG)*Cov(RF, RG)] ^(1/2)
w2F = (0.40)^2 = 0.16
?2(RF) = (0.44)^2 = 0.1936
w2G = (0.60)^2 = 0.36
?2(RG) = (0.63)^2 = 0.3969
Cov(RF, RG) = Correlation Coefficient (F &G) * ?(RF) * ?(RG)
= 0.35 * 0.44 * 0.63 = 0.09702
Portfolio Standard Deviation
= [ (0.16*0.1936) + (0.36*0.3969) + (2*0.40*0.60*0.09702)]^(1/2)
=(0.030976 + 0.142884 + 0.0465696 )^ (1/2)
= (0.2204296) ^ (1/2)
= 0.4695
= 46.95%