The table below shows descriptive statistics for two mutual funds, a bond portfo

Question

The table below shows descriptive 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

5%

15%

Standard Deviation

6%

18%

Calculate the expected return and variance of the portfolio consisting of wD proportion of the debt fund and wE proportion of the equity fund, assuming the correlation between the two funds is –0.30.

Calculate the expected return, variance, and standard deviation of the portfolio consisting of 40% debt and 60% equity, assuming the correlation between the two funds is –0.30.

Calculate the expected return and standard deviation of the portfolio for values of wD ranging from 0.00 to 1.00 in increments of 0.10, and values of correlation equal to –1, 0, +1, and –0.30.

Bonds (Debt)

Stocks (Equity)

Expected Return

5%

15%

Standard Deviation

6%

18%

Explanation / Answer

let portfilio is z=wD+(1-w)E, D=Bonds(debt) and E=stock(equity)

E(z)=E(wD+(1-w)E)=wE(D)+(1-w)E(E)

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

(first part) z=0.4*D+0.6*E

E(z)=E(0.4*D+0.6*E)=0.4*E(D)+0.6*E(E)=0.4*5+0.6*15=11

expected return=11%

var(z)=var(0.4*D+0.6*E)=0.16*var(z)+0.36*var(E)+2*0.4*0.6*cov(D,E)=

=0.16*var(z)+0.36*var(E)+2*0.4*0.6*r*sd(D)*sd(E)=0.16*6*6+0.36*18*18+2*0.4*0.6*(-0.3)*6*18=106.85

sd(z)=sqrt(var(z))=sqrt(106.85)=10.34

(second part) following protfolio is generated using the information given

z=portfolio and r=correlation coefficient

expected return w 1-w E(z)=wD+(1-w)E) r cov(D,E) var(z) sd(z) 0.1 0.9 14 1 9.72 282.24 16.8 0.2 0.8 13 0 0 208.8 14.44991 0.3 0.7 12 -1 -22.68 116.64 10.8 0.4 0.6 11 -0.3 -7.776 106.848 10.33673

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