Question

You have combined two stocks, A and B, into an equally weighted portfolio (Stable) and it has a variance of 35%. The covariance between A and B is 25%. A is a resource stock and has a variance twice that of B. You have formed another portfolio (Growth) that has an expected return of 17% and a variance of 50%. The expected return on the market is 15% and the risk free rate is 7% Covariance (A,Market) = 22% and Covariance (B,Market) = 15.5% and the variance of the Market is 15%.

What is the variance of B?

What is the variance of A?

What is the correlation of A with B?

What is the correlation of Stable portfolio with the Market?

Is your Stable portfolio efficient?

Answer 1

GIVEN STABLE PROTFOLIO DETAILS

VARIANCE = 35%   ,   WEIGHT OF STOCKS =0.5:0.5

COVARIANCE = 25%

VARIANCE OF STOCK A = 2VARIANCE OF STOCK B , LET VARIANCE OF A IS 2X AND B be x

Variance of portfolio = w1.var(A)+ w1.w2.cov(A,B)+w2.var(B)

0.35 = 0.5(2x) + 0.5(x) + 0.5*0.5*0.25

Evaluating for x;x is 0.15

The variance for stock of B is 15% and variance of stock of A is 30%

Correlation Formula =COV (A,B)/ sq.root of (var.A)*sq.root of (var,B)

=0.25/(0.387*0.547)

Correlation of stock A with B is 1.18

.

C)    

covar(stable,market)=E(((wa*ra+wb*rb-E(wa*ra)-E(wb*rb))*(rm-E(rm)))
=E((wa*ra-E(wa*ra)*(rm-E(rm)))+E((wb*rb-E(wb*rb)*(rm-E(rm)))
=wa*E((A-E(A))*(rm-E(rm)))+wb*E((B-E(B))*(rm-E(rm)))
=wa*Covar(A,M)+wb*Covar(B,M)
=0.5*22%+0.5*15.5%
=18.7500%

Correlation of stable portfolio with market=covar(stable,market)/sqrt(var(stable)*var(market))
=18.7500%/sqrt(35%*15%)
=0.818317088

D)   Is stable portfolio is efficient

its better to invest in stocks which are negatively correlated as to compensate risk of one another, but in stable portfolio, the stocks are positively correlated that mean stock will move up or down together.

The variance of portfolio is 35% which is quite high thus the fluctuations of the securities are quite high over the perios of time.