Suppose $r_{RF}=5\%,r_M=10\%,$ and $r_A=12\%$

a$.$ Calculate Stock A$\text{'}$s beta.

b$.$ If Stock A$\text{'}$s beta were $2\mathrm{.}0,$ then what would be A$\text{'}$s new required rate of return?

As an equity analyst you are concerned with what will happen to the required return to Universal Toddler Industries's stock as market conditions change. Suppose $r_{RF}=5\%,r_M=12\%,$ and $b_{\text{u}\text{x}\text{i}}=1\mathrm{.}4.$

a$.$ Under current conditions, what is ruti, the required rate of return on UTI stock?

b$.$ Now suppose $r_{RF}(1)$ increases to $6\%$ or $(2)$ decreases to $4\%.$ The slope of the SML remains constant. How would this affect $r_M$ and $r_{\text{U}\text{T}\text{I}}?$

c$.$ Now assume $r_{RF}$ remains at $5\%$ but $r_M(1)$ increases to $14\%$ or $(2)$ falls to $11\%.$ The slope of the SML does not remain constant. How would these changes affect rumr?

Your retirement fund consists of a $$5,000$ investment in each of $15$ different common stocks. The portfolio's beta is $1\mathrm{.}20.$ Suppose you sell one of the stocks with a beta of $0\mathrm{.}8$ for $$5,000$ and use the proceeds to buy another stock whose beta is $1\mathrm{.}6.$ Calculate your portfolio's new beta.

Suppose you manage a $$4$ million fund that consists of four stocks with the following investments:

$\backslash$table$[[$Stock$,$Investment,Beta$],[$A$,$$$400,000,1\mathrm{.}50],[$B$,600,000,-0\mathrm{.}50],[$C$,1,000,000,1\mathrm{.}25],[$D$,2,000,000,0\mathrm{.}75]]$