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 4.5%. The probability distribution of the risky funds is as follows: Standard Deviation 35% 29 Expected Return Stock fund (S) Bond fund (B) 15% 6 The correlation between the fund returns is 0.15 Do not solve numerica for the proportions of each asset and for the expected return and standard deviation of the optimal s your final answers to 2 decimal places. Omit the "%" sign in your response.) ot ? o. undin er mediate calculations and r n Portfolio invested in the stock Portfolio invested in the bond Expected returm Standard deviatio

Explanation / Answer

Step 1: Develop Covariance-Matrix

We can develop the covariance with the use of information provided in the question as below:

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Step 2: Calculate Optimal Risky Portfolio Proportions

The value of optimal risky portfolio proportions is calculated as below:

Portfolio Invested in Bonds = [(Expected Return on Bonds - Risk Free Rate)*Standard Deviation of Stocks^2] - [(Expected Return on Stocks - Risk Free Rate)*Standard Deviation of Bonds*Standard Deviation of Stocks*Correlation Coefficient]/[(Expected Return on Bonds - Risk Free Rate)*Standard Deviation of Stocks^2] + [(Expected Return on Stocks - Risk Free Rate)*Standard Deviation of Bonds^2] - [(Expected Return on Stocks - Risk Free Rate + Expected Return on Stocks - Risk Free Rate)*Standard Deviation of Bonds*Standard Deviation of Stocks*Correlation Coefficient]

Portfolio Invested in Stocks = 1-Portfolio Invested in Bonds

Substituting values in the above formula, we get,

Portfolio Invested in Bonds = (((6% - 4.5%)*(35%)^2) - ((15% - 4.5%)*29%*35%*.15))/(((6% - 4.5%)*(35%)^2) + ((15% - 4.5%)*(29%)^2) - ((6% - 4.5% + 15% - 4.5%)*35%*29%*.15)) = 2.70%

Portfolio Invested in Stocks = 1 - 2.70% = 97.30%

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Step 3: Calculate Expected Return and Standard Deviation

The value of expected return and standard deviation is arrived as below:

Expected Return = Portfolio Invested in Bonds*Expected Return on Bonds + Portfolio Invested in Stocks*Expected Return on Stocks = 2.70%*6% + 97.30%*15% = 14.76%

Standard Deviation = (Portfolio Invested in Bonds)^2*(Standard Deviation of Bonds)^2 + (Portfolio Invested in Stocks)^2*(Standard Deviation of Stocks)^2 + 2*Portfolio Invested in Bonds*Portfolio Invested in Stocks*Standard Deviation of Bonds*Standard Deviation of Stocks*Correlation Coefficient)^1/2 = ((2.70%)^2*(29%)^2 + (97.30%)^2*(35%)^2 + 2.70%*97.30%*29%*35%*.15)^(1/2) = 34.12%

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Tabular Representation:

Bonds Stocks Bonds 841 (29*29) 152 (29*35*.15) Stocks 152 (35*29*.15) 1,225 (35*35)

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