Question

8. Calculate the PORTFOLIO Expected Return and standard deviation of a 60/40 Portfolio of Asset A and asset B. ASSET A 60% ASSET B 40% Return in State Return in State R (A) R(B) PORTFOLIO Rport in Sate S R(P)i Deviation R(P)i Pr Portfolio (Deviation Portfolio 2 State S Squared Dev*Pr Pr State P 0.4 0.6 E(R) E(R) Portfolio Portfolio Var Portfolio sd - 9. Compare the Risk-Return of the two stocks ALONE and the joint risk in the portfolio Interpret your results. Stock Alone Portfolio 60A- 40B Asset A Asset B Expected Return Variance Standard Deviation • Is diversification working or not? Why? What type of risk is addressed with portfolio allocation? Define correlation. Given your results, Assets A and B must be correlated close to what degree? (- 1.0.+1)? Why?

Answer 1

P=Probability

R=Return, R(AB) = [0.6×R(A)]+[0.4×R(B)]

PR=P×R

ER=Expected Return=Mean=Sum of PR

D=Deviation=R-ER

D^2=Deviation^2=D×D

PD^2=P×D^2

Var=Variance=Sum of PD^2

SD=Standard Deviation=Var^1/2

No. Diversification is not working.

Р R(A) 12 16 E[R(A)]= 10.4 1 0.6 PR(A) 4.8 9.6 14.4 D(A) -2.4 1.6 D(A)^2 5.76 2.56 Var(A)= SD(A)= PD(A)^ 2 R (B) 2.304 L 10 1.536 15 3.84 E[R(B)1= 1.9595918 B D(B) 3 2 PR(B) 4 9 13 D(B)^2 PD(B)^ 2 9 3.6 4 2.4 Var(B)= | SD(B)= 2.4494897 R (AB) L 11.2 15.6 E[R(AB)]= 60% A & 40% B PR(AB) D(AB) D(AB)^2 4.48 -2.64 6 .9696 9.36 1.76 3.0976 13.84 Var(AB)= SD(AB)= PD(AB)^2 2.78784 1.85856 4.6464 2.155551 60%A & 40%B Expecte 14.4 13 13.84 3.84 4.65 Return Vari ance Standar d Deviatio 1.96 2.45 2.16

Because A has higher return and lower risk whereas B has comparatively lower return with higher risk. Therefore, diversification leads to lower return and higher risk as compared to A alone.

Unsystematic Risk i.e. risk associated only with that particular security is addressed with portfolio allocation whereas Systematic Risk i.e. risk associated with overall market remains unaffected.

Correlation is the mutual relationship between two things i.e. how and upto what extent same factor affects two securities.

In given case, correlation must be nearer to -1 of at least it will be negative and not zero or positive. Because portfolio allocation leads to lower return and higher risk.

If they were positively correlated, dicersification would be advantageous.

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