Suppose that a mutual fund manager has a $$15$ million portfolio with a beta of $1\mathrm{.}7.$ Also suppose that the risk free rate is $4\mathrm{.}5\%$ and the market risk premium is $6\%.$

The manager expects to receive an additional $$5$ million, which is to be invested in a number of new stocks to add to the portfolio. After these stocks are added, the manager would like the fund's required rate of return to be $13\mathrm{.}5\%.$

For notation, let $r$ represent the required return, let $r_{RF}$ represent the risk free rate, let $b$ represent the beta of a group of stocks, and $r_m$ represent the market return.

According to the video, which equation most closely describes the security market line $($SML$)?$

$r=r_{RF}+b(r_M+r_{RF})$

$r=r_{RF}-b(r_M-r_{RF})$

$r=r_{RF}+b(r_M-r_{RF})$

$r=r_{RF}+\frac{b}{r_M-r_{RF}}$

Hint: Recall that the manager wants the new required rate of return for the portfolio to remain at $13\mathrm{.}5\%.$

Using the equation you just identified, and plugging in the relevant information, yields a beta of the portfolio, after the new stocks have been added, of approximately $q,.$

True or False: The beta for the portfolio after the stocks have been added is the weighted average of the beta before the stocks where added and the beta of the new stocks that are being added $($weighted as a percentage of

the total funds invested$).$The beta of the portfolio after the stocks have been added $($which you just calculated$),$ along with the new total amount of funds invested, implies that the beta of the stocks added to the portfolio must be: $?$