A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and co

Question

2 years ago

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A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and co

rporate bond fund, and the third is a T-bill money market fund that yields a sure rate of 5.5%. The probability distributions of the risky funds are:
Suppose now that your portfolio must yield an expected return of 12% and be efficient, that is, on the best feasible CAL.

Mathematics

1 answer:

Firdavs [7] · Answer 1 · 2023-04-07T13:10:29+03:00

This problem is about pension fund management. It is to be noted that the best Feasible Capital Allocation Line (CAL) is: 0.3162.

<h3>What is Capital Allocation Line (CAL)?</h3>

A graph's capital allocation line depicts all conceivable combinations of risky and risk-free assets, allowing investors to estimate future returns depending on risk.

<h3>What is the calculation for the above solution?</h3>

It is to be noted that the optimal risky portfolio's stock percentage is determined by:

Weight of Stock = ((Return on Stock - Risk Free Rate) * Variance of bond) - ((Return on Bond - Risk Free Rate) * Co-Variance of bond & Stock)/ ((Return on Stock - Risk Free Rate) * Variance of bond + (Return on Bond - Risk Free Rate) * Variance of Stock - ((Return on Bond - Risk Free Rate + Return on Stock - Risk Free Rate + ) * Co-Variance of bond & Stock)

→ The weight of stock

= ((15% - 5.5%) * 529) - ((9% - 5.5%) * 110.40)/ ((15% - 5.5%) * 529) + (9% - 5.5%) * 1,024 - ((15% - 5.5% + 9% - 5.5%) * 110.40)

= [(50.255) * (3.864) /(50.255) + (46.08) - (14.352)]

Weight of Stock = 0.646628

Weight of Bonds = 1 - 0.646628

Weight of Bonds= 0.353372

Expected return of portfolio = 0.646628 * 15% + 0.353372 * 9%

= 12.88%

Standard Deviation of Portfolio (SDP)= (0.6466282² * 1,024 + 0.3533722² * 529 + 2 * 0.646628* 0.353372* 110.40)⁰·⁵

SDP = (544.67)⁰·⁵

SDP = 23.34%

Hence,