The table below shows summary statistics for two mutual funds, a bond portfolio

Question

The table below shows summary statistics for two mutual funds, a bond portfolio specializing in long-term debt securities and a stock fund that specializes in equity securities.

Bonds (Debt)

Stocks (Equity)

Expected Return

0.06

0.18

Std Deviation

0.10

0.24

Calculate the variance of each fund and the covariance between the two, and produce the covariance matrix for the two funds, assuming the correlation between the funds is –0.40.

Use the bordered-multiplied covariance matrix method to calculate the variance for a portfolio containing 30% Bonds and 70% Stocks (assume the correlation between the funds is –0.40). Also compute the expected return for this portfolio.

Bonds (Debt)

Stocks (Equity)

Expected Return

0.06

0.18

Std Deviation

0.10

0.24

Explanation / Answer

let D=bonds(Debt) and E=stocks(equity)

var(D)=0.1*0.1=0.01 and Var(E)=0.24*0.24=0.0576

cov(D,E)=r*sd(D)*sd(E)=(-0.4)*0.1*0.24=-0.0096

covriance matrx is givne as

let protfolio is z=w*D+(1-w)*E, here w=0.3 and 1-w=1-0.3=0.7

E(z)=E(w*D+(1-w)*E)=w*E(D)+(1-w)*E(E)=0.3*0.06+0.7*0.18=0.144

expected return=0.144

var(z)=var(w*D+(1-w)*E)=w*w*var(D)+(1-w)*(1-w)*var(E)+2*w*(1-w)*cov(D,E))

=0.3*0.3*0.01+0.7*0.7*0.0576-2*0.3*0.7*0.0192=0.0211

sd(z)=sqrt(0.0211)=0.1451

variance of portfolio is 0.0211 and standard deviation of folio is 0.1451

E(z)=E(w*D+(1-w)*E)=w*E(D)+(1-w)*E(E)=0.3*0.06+0.7*0.18=0.144

expected return=0.144

D E D 0.01 -0.0192 E -0.0192 0.0576

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