TRU Investment Group advises clients on how to create a diversified

investment portfolio. One of their clients is interested in a portfolio consisting

of investment in the Mango Fund and a treasury bond fund. The expected

percent return of an investment in the Mongo Fund is $7\mathrm{.}80\%$ with a standard

deviation of $18\mathrm{.}90\%.$ The expected percent return of an investment in a

treasury bond fund is $5\mathrm{.}50\%$ and the standard deviation is $4\mathrm{.}60\%.$ The

covariance of an investment in the Mango Fund with an investment in a

treasury bond fund is $-12\mathrm{.}4.$

a$)$ Which of the funds would be considered the more risky? Why?

b$)$ If TRU Investment Group recommends that the client invest $75\%$ in the

Mango Fund and $25\%$ in the treasury bond fund, what is the expected

percent return and standard deviation for such a portfolio? What would be

the expected return and standard deviation, in dollars, for a client

investing $$10,000$ in such a portfolio?

c$)$ If TRU Investment Group recommends that the client invest $25\%$ in the

Mango Fund and $75\%$ in the treasury bond fund, what is the expected

return and standard deviation for such a portfolio? What would be the

expected return and standard deviation, in dollars, for a client investing

$$10,000$ in such a portfolio?

d$)$ Which of the portfolios in parts $($b$)$ and $($c$)$ would you recommend for an

aggressive investor? Which would you recommend for a conservative

investor? Why?