$1\mathrm{.}4$ A pension fund manager is considering two mutual funds. The first is an all equity share fund and the second is a long$-$term government and corporate bond fund. The likely return of the equity share fund and the bond fund depend on the state of the economy by the end of the year as follows: State of the economy Probability All equity share fund Bond fund

Severe recession

$0\mathrm{.}10$

$-37\%$

$-9\%$

Mild recession

$0\mathrm{.}20$

$-11\%$

$15\%$

Normal growth

$0\mathrm{.}35$

$14\%$

$8\%$

Boom

$0\mathrm{.}35$

$30\%$

$-5\%$

a$)$ Calculate the values of mean return and variance of all equity share fund. $(4$ marks$)$

b$)$ Calculate the value of the covariance between the equity and bond funds. $(2$ marks$)$

c$)$ Explain what has caused the covariance to be lower than the variance. $(2$ marks$)$

d$)$ If the mean return and variance for the bond fund amount to $3\mathrm{.}15\%$ and $74\mathrm{.}3275\%$ respectively, calculate and comment on the corelation coefficient between the two fund returns. $(4$ marks$)$