Question

highlight the answers please. need answers only, ASAP

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 sure rate of 5.3%. The probability distributions of the risky funds are: d, and the three Standard deviation Stock Fund (S) Bond fund (3) Expected Return 141 The correlation between the fund returns is 0.0459 between the tund returns is 0.0459. What is the expected return and standard deviation for the minimum-variance portfolio of the two risky funds? (Do not round Intermediate calculations. Round your answers to 2 decimal places.) Expected return Standard deviation

Answer 1

Solution:

Expected return = 9.95%

Standard deviation = 34% ​​​​​​

Calculations:-

Given that $E (R_{s})$ = 14%, $E (R_{B})$ = 7%, $\sigma_{S}$ = 43%, $\sigma_{B}$ = 37% and $\rho = 0.0459$

We generate the covariance matrix using the formula: $Cov (r_{S}, r_{B}) = \rho\sigma_{S}\sigma_{B}$

	Bonds	Stocks
Bonds	1369	73.0269
Stocks	73.0269	1849

The minimum variance portfolio is found by applying the formula

$w_{Min}(S) = \frac{\sigma _{B}^{2}- Cov(B, S)}{\sigma _{S}^{2}+\sigma _{B}^{2}- 2 Cov (B, S)}$

$w_{Min}(S) = \frac{1369- 73.0269}{1849+1369- 2(73.0269)}$​

$w_{Min}(S) =$0.4219

$w_{Min}(B) = 1 - w_{Min}(S) = 1 - 0.4219 = 0.5781$

The minimum variance portfolio mean and standard deviation are

$E (r_{Min})=w_{Min}(S)E(R_{S}) + w_{Min}(B)E(R_{B})$

$E (r_{Min})=(0.4219)(14) + (0.5781) (7)$

$E (r_{Min})$ = 9.95%

$\sigma_{Min} = (w_{S}^2 \sigma_{S}^2+w_{B}^2 \sigma_{B}^2 + 2 w_{S}w_{B}Cov (S, B))^{1/2}$

$\sigma_{Min} = ((0.4219)^2 (43)^2+(0.5781)^2 (37)^2 + 2 (0.4219) (0.5791)(73.0269))^{1/2}$

$\sigma_{Min}$ = 34.00%