Security F has an expected return of 10.90 percent and a standard deviation of 4
ID: 2757726 • Letter: S
Question
Security F has an expected return of 10.90 percent and a standard deviation of 43.90 percent per year. Security G has an expected return of 15.90 percent and a standard deviation of 62.90 percent per year. What is the expected return on a portfolio composed of 39 percent of Security F and 61 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.34. 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))Explanation / Answer
Solution :
F
G
R
10.90%
15.90%
SD
43.90%
15.90%
W
39%
61%
a) Rp = Rf*Wf+Rg*Wg
13.95%
(.109*.39)+(.159*.61)
b)
Corr(f,g)=.34
SDp=square root of [(Wf^2)(SDf^2)+(Wg^2)(SDg^2)+2*wf*wg*corr(f,g)*SDf*SDg]
square root of [(.39^2)*(.439^2)+(.61^2)*(.159^2)+(2*.39*.61*.34*.439*.159)] =
22.36%
R=RETURN
SD=STANDARD DEVIATION
W=WEIGHT
Corr(f,g)=correlation coefficient between F and G security
Rp = poertfolio return
F
G
R
10.90%
15.90%
SD
43.90%
15.90%
W
39%
61%
a) Rp = Rf*Wf+Rg*Wg
13.95%
(.109*.39)+(.159*.61)
b)
Corr(f,g)=.34
SDp=square root of [(Wf^2)(SDf^2)+(Wg^2)(SDg^2)+2*wf*wg*corr(f,g)*SDf*SDg]
square root of [(.39^2)*(.439^2)+(.61^2)*(.159^2)+(2*.39*.61*.34*.439*.159)] =
22.36%
R=RETURN
SD=STANDARD DEVIATION
W=WEIGHT
Corr(f,g)=correlation coefficient between F and G security
Rp = poertfolio return