Consider the following capital market: a risk-free asset yielding 0.75% per year

Question

Consider the following capital market: a risk-free asset yielding 0.75% per year and a mutual fund consisting of 70% stocks and 30% bonds. The expected return on stocks is 10.75% per year and the expected return on bonds is 3.25% per year. The standard deviation of stock returns is 30.00% and the standard deviation of bond returns 8.75%. The stock, bond and risk-free returns are all uncorrelated.

1. What is the expected return on the mutual fund?

8.50%

2. What is the standard deviation of returns for the mutual fund?

21.16%

Now, assume the correlation between stock and bond returns is 0.45 and the correlations between stock and risk-free returns and between the bond and risk-free returns are 0 (by construction, correlations with the risk-free asset are always zero).

3. What is the standard deviation of returns for the mutual fund? Is it higher or lower than the standard deviation found in part 2? Why?

Explanation / Answer

3. What is the standard deviation of returns for the mutual fund? Is it higher or lower than the standard deviation found in part 2? Why?

Standard deviation = (Variance)1/2

Variance=We^2*Se^2 + Wd^2*Sd^2 + 2*WeWdSeSd*Correlation coefficient

here

We = weight of equity in mutual fund

Se = Standard deviation of Equity

Wd = weight of debt in mutual fund

Sd = Standard deviation of debt

Variance=We^2*Se^2 + Wd^2*Sd^2 + 2*WeWdSeSd*Correlation coefficient

= .49*900 +..09*76.57 + 2*.7*.3*30*8.75*.45

= 447.89+49.61=497.50

so standard deviation =497.5^(1/2) = 22.30%

it is higher than the standard deviation of part 2

because

due to positive correlation between stock and bond , risk part is increased so standard deviation is higher in this case.

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