Question

A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a rate of 7%. The probability distribution of the risky funds is as follows:

	Expected Return			Standard Deviation
Stock fund (S)		16	%		38	%
Bond fund (B)		12			21

The correlation between the fund returns is 0.12.

  

Solve numerically for the proportions of each asset and for the expected return and standard deviation of the optimal risky portfolio. (Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.)

A) portfolio invested in the stock

B) portfolio invested in the bond

C) expected return

d) standard deviation

Answer 1

[E(r)–r] 06-[E(re)-r;]Cournyre) W = [E(r)–r]04 +[E(re)-r-]-[E(r) –r: +E(re)-r-]Courre)

Where WD is weight of bond,

E(rD) = expected return on bond = 12%

E(rE) = expected return on stock = 16%

rF = risk free rate = 7%

σE = standard deviation of stock = 38%

σD = standard deviation of Bond = 21%

Cov(rD,rE) = covariance between stock and bond = σE*σD*corr(rD,rE) = 0.38*0.21*.12 = 0.009576

So, WD = [((0.12-0.07)*(0.38^2)) - ((0.16-0.07)*(0.009576))]/[((0.12-0.07)*(0.38^2)) + (0.16-0.07)*(0.21^2)) - ((0.12 - 0.07 + 0.16-0.07)*(0.009576))] = 0.5669 or 56.69%

So,

A) portfolio invested in the stock = 1-WD = 1-0.5669 = 0.4331 or 43.31%

B) portfolio invested in the bond = 0.5669 or 59.69%

C) expected return = E(rD)*WD + E(rE)*WE = 12*0.5669 + 16*0.4331 = 13.73%

D) standard deviation = SQRT[((WD*σD)^2) + ((WE*σE)^2) + 2*WD*σD*WE*σE*Corr(rD,rE)]

So, standard deviation = SQRT((0.5669*0.21)^2 + (0.4331*0.38)^2 + 2*0.5669*0.38*0.4331*0.21*0.12) = 21.44%