A pension fund manager is considering three mutual funds. The first is a stock f

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 6%. The probability distribution of the risky funds is as follows:

You require that your portfolio yield an expected return of 13%, and that it be efficient, on the best feasible CAL.

What is the standard deviation of your portfolio? (Round your answer to 2 decimal places. Omit the "%" sign in your response.)

What is the proportion invested in the T-bill fund and each of the two risky funds? (Round your answers to 2 decimal places.Omit the "%" sign in your response.)

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 6%. The probability distribution of the risky funds is as follows:

Explanation / Answer

Answer:

we find that the proportion in the stock fund is

{(0.21-0.06)(0.18)2-(0.12-0.06)(0.28)(0.18)(0.09)}/{(0.21-0.06)(0.18)2+(0.12-0.06)0.282+(0.21-0.06+0.12-0.06)(0.28)(0.18)(0.09)}

= (0.00486-0.00027216)/(0.00486+0.004704+0.00095256) = 0.01051656;

the proportion in the bond fund, therefore, is 1-0.01051656 or 0.9894834

Using these numbers, we see that the expected return of the tangent portfolio is (0.01051656)(21) + (0.9894834)(12) = 12.09%;

the variance of the portfolio is 0.01052 (282) + (0.98942)(182) + 2(0.09)(0.0105)(0.9894)(28)(18 ) = 318.1824

The standard deviation, therefore, is the square root or 17.83%.

If we require that our portfolio yield an expected return of 13%, then we can find the corresponding standard deviation from the optimal CAL.

The equation for this CAL is: E(rC) = rf+{[E(rP)-rf]/P}C; i.e.

0.13 = 0.06 + [(0.1209-0.06)/0.1783)]C. Solving, we find C =

b. To find the proportion invested in the T-bill fund, remember that the mean of the complete portfolio is an average of the T-bill rate and the optimal combination of stocks and bonds (P). Let y be the proportion invested in the portfolio P.

The mean of any portfolio along the optimal CAL is E(rC) = (1 – y) × rf + y × E(rP) = rf + y × [E(rP) – rf] = .06 + y× (.1209 – .06); setting

E(rC) = 13% we find: y = .79225 and (1 y) = .2077 (the proportion invested in the T-bill fund).

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.