xpected return and variance Question Details The expected returns, return varian
ID: 2668950 • Letter: X
Question
xpected return and varianceQuestion Details
The expected returns, return variances, and the correlation between the returns of four securities are as follows.
Security Expected Variance of Correlation
Return Return A B
A 0.17 0.0169 1.0 0.4
B 0.13 0.0361
1. Determine the expected return and variance for a portfolio composed of 25% of
security A and 75% of security B.
your answer:
1. Determine the expected return and variance for a portfolio composed of 25% of security A and 75% of security
B.
Portfolio Expected Return = A*r(a) + B*r(b)
where A, B, are relative weights of securities a, b in portfolio and r(a), r(b) are corresponding expected returns of
securities
So Portfolio Expected Return = 25%*0.17 + 75%*0.13 = 0.0425+0.0975 = 0.14 =14%
Standard Deviation (SD) = sqrt( Variance) = Sqrt(V)
So SD (A) = Sqrt (0.0169) = 0.13
& SD(B) = sqrt(0.0361) = 0.19
Correlation(a,b) = Covariance(a,b) / ( St.Dev.(a)* St.Dev.(b) )
So Covariance(a,b) = Correlation(a,b) *( St.Dev.(a)* St.Dev.(b) ) = 0.4*0.13*0.19 = 0.00988
Variance(a,b) = sq(A)*var(a) + sq(B)*var(b) + 2*A*B*cv(a,b) = sqrt(25%)*0.17 + sqrt(75%)*0.13+2*25%*75%*0.00988
ie Var(a,b) = 0.085+0.1126+0.0037 = 0.2013
My question is why var(a)=0.17 instead of 0.0169, and var(b)=0.13 instead of 0.0361 as the given?
Explanation / Answer
I think you have mistaken. That is not Var(a) = 0.17, it is expected return for security a. Therefore var(a) is 0.0169. And the same case also happen in second security also, It is not Var(b) = 0.13. it is expected retun. Var(b) is 0.0361 is correct.Related Questions
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