An investor can design a risky portfolio based on two stocks, A and B. Stock A h

Question

An investor can design a risky portfolio based on two stocks, A and B. Stock A has an expected return of 20% and a standard deviation of return of 7%. Stock B has an expected return of 9% and a standard deviation of return of 2%. The correlation coefficient between the returns of A and B is 0.5 The risk-free rate of return is 3%. The standard deviation of return on the optimal risky portfolio is. Note: Express your answers in strictly numerical terms. For example, if the answer is 5%. write 0.05"

Explanation / Answer

Standard Deviation of Return on the optimal risky portfolio

Given,

E(rA) =20% ,E(rB) =9%

Standard deviation SD(A) =7% ,SD(B)=2%

Coefficient corelation between A and B Cov(rA,rB) = 0.5 ,Risk Free Return Rf =3%

Weightage of A in Portfolio W(A) ={[ E(rA)-Rf ] * SD(A)^2 -[ E(rB)-Rf ] *Cov(rA,rB) } /

[ E(rA)-Rf ] * SD(A)^2+[ E(rB)- Rf ] * SD(B)^2 -[ E(rA)-Rf + E(rB)-Rf]* Cov(rA,rB)

={[20-3]*7^2 - [9-3]*0.5} / [20-3]*7^2 +[9-3]*2^2 - [ 20-3+9-3]*0.5

={17*49 - 6*0.5} / 17*49 + 6*4 -23*0.5

=(833-3)/(833+24-11.5) =830/845.5 =0.9817

Weightage of B in Portfolio W(B) =1-W(A) =1-0.9817 =0.0183

Standard Deviation of Return on the optimal risky portfolio

SD(P) = [W(A)SD(A)]^2 +[W(B)SD(B)]^2+2W(A)W(B)Cov(rA,rB)

=[0.9817*7]^2+[0.0183*2]^2+2*0.9817*0.0183*0.5 =47.223+0.00149+0.0179=47.242% =0.4724

Standard Deviation of Return on the optimal risky portfolio SD(P) = 0.4724

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