a.) A pension fund manager is considering three mutual funds. The first is a sto

Question

a.) 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 5%. The probability distribution of the risky funds is as follows:

You require that your portfolio yield an expected return of 12%, 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.)

b.)

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 8%. The probability distribution of the risky funds is as follows:

The correlation between the fund returns is 0.12.

What are the investment proportions in the minimum-variance portfolio of the two risky funds. (Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.

What is the expected value and standard deviation of its rate of return? (Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.)

Explanation / Answer

SECOND CASE PROBLEM:

Expected Returns on a Portfolio= the weighted average of the likely profits of the assets in the portfolio, weighted by the likely profits of each asset class. Expected Rate of Return; E(R), is calculated by using the following formula:

Summation of (Pi * Ri) for i from 1 to n

Where; Pi= Probability Weightage or Proportion % of Asset allocation in overall portfolio

Ri= Expected rate of Return on each asset type

(B)

a-1.

Under Minimum Variance Portfolio, the attempt of the Fund Manager is to minimize the portfolio risk:

Portfolio Variance for given [Stock, Bond] Portfolio= (Weight 1)^2* Variance 1 + (Weight 2)^2* Variance 2 * 2* (Weight 1)*(Weight 2)*CoVariance(1,2) .......................... [I]

Variance= (Standard Deviation)2

Correlation (1,2)= [CoVariance (1,2)] / (SD1*SD2) ......... SD stands for Standard Deviation of each asset in a portfolio

Thus, 0.12= [CoVariance (1,2)] / (38*18); Thus CoVariance(1,2)= 0.12*(38*18)= 82.08

Applying above values in the formula [I] above:

Thus, (0.12)2= (Weight 1)2*(38)2 + (Weight 2)2*(18)2 + 2* (Weight 1)*(Weight 2)*82.08

0.0144= (Weight 1)2*1444 + (Weight 2)2*324 + 2* (Weight 1)*(Weight 2)*82.08; SOLVE for this Equation to obtain values of Wieghts i.e. Investment proportions for Stock and Bond in the portfolio;

ALTERNATIVELY, use the below formula to obtain the same answers:

Weight of Bond = [(SDs)2 - (SDs)*(SDb)*(Corr(s,b))] / [(SDs)2 + (SDb)2 - 2*(SDs)*(SDb)*Corr(s,b)]

= [(38)2 - (38*18*0.12)] / [(38)2 + (18)2 - 2*(38)*(18)*0.12]

= 0.849162 . ......................................... [ANSWER]

Thus, Weight of Stock in Portfolio= 1-0.849162= 0.150838 ....................................... [ANSWER]

Thus, Amount of Portfolio invested in Stock= 15.0838% of total portfolio corpus

and Amount of Portfolio invested in Bond= 84.9162% of total portfolio corpus

a-2.

Expected Rate of Return on Portfolio; E(R)= (0.150838)*(Expected Return on Stock Fund) + (0.849162)*(Expected Return on Bond Fund)= (0.150838)*(0.17) + (0.849162)*(0.13)= 0.136034 = 13.6034% per year

............................................ [ANSWER]

Standard Deviation of Portfolio= (Variance of Stock-Bond Portfolio)1/2

Variance of Stock-Bond Portfolio= Variance of Stock + Variance of Bond + 2*CoVariance(Stock, Bond)

= (SDs)2 + (SDb)2 + 2*(82.08)= 382 + 182 + 164.16

= 1444 + 324 + 164.16= 1932.16

Standard Deviation of Portfolio= (1932.16)1/2

= 43.95634% ...........................................................[ANSWER]

FIRST CASE PROBLEM:

A. a.) Standard Deviation of three-asset portfolio = (Portfolio Variance)1/2

Portfolio Variance with three-asset classes= (Ws)2.(SDs)2 + (Wb)2.(SDb)2 + (Wt)2.(SDt)2 + 2.(Ws).(Wb).(SDs).(SDb).Correlation(s,b) + 2.(Ws).(Wt).(SDs).(SDt).Correlation(s,t) + 2.(Wb).(Wt).(SDb).(SDt).Correlation(b,t)

SD= Standard Deviation and W= Weight

Expected Return on a Portfolio, E(R)= (Ws).(ERs) + (ERb).(Wb) + (ERt).(Wt)

ER figures information for each of the three individual asset classes is missing in this problem. Hence, cannot be solved further..

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