There are two assets: a mutual fund tracking the S&P $500$ index and gold. If inflation

stays low $($during the next year$)$ the fund will have a rate of return of $r_M=0\mathrm{.}45.$ If

inflation increases, then the rate of return will be $r_M=-0\mathrm{.}05.$ Assume that the above

two events are equally likely to happen.

Gold is currently selling at $$250$ per ounce. If inflation increases, then the rate of return

on gold will be $r_g=0\mathrm{.}04,$ while if inflation remains low the rate of return on gold will be

$r_g=-0\mathrm{.}06.$

Compute the expected values, the variances and the correlation of the rates of return of

the two assets over the next year.