The Treasury bill rate is $4\%,$ and the expected return on the market portfolio is $12\%.$ Using the capital asset pricing model:

a$.$ Draw a graph similar to Figure $8\mathrm{.}6$ showing how the expected return varies with beta.

b$.$ What is the risk premium on the market?

c$.$ What is the required return on an investment with a beta of $1\mathrm{.}5?$

d$.$ If an investment with a beta of $\mathrm{.}8$ offers an expected return of $9\mathrm{.}8\%,$ does it have a positive NPV$?$

e$.$ If the market expects a return of $11\mathrm{.}2\%$ from stock X$,$ what is its beta?