$1.$ Using the following selected stock: Crocs. Consider a beta of $1\mathrm{.}93$ for the stock. Assume a risk$-$free rate of $5\%.$ Assume the S&P $500$ portfolio $($market$)$ has a return of $12\%$ and a standard deviation of $25\%.$

a$.$ Use the CAPM to estimate the required return for the selected stock.

b$.$ You want a portfolio beta of $\mathrm{.}8.$ How much will you invest in the market portfolio and how much in the selected stock?