Step $3$: Practice: Portfolio Beta

Now it's time for you to practice what you've learned.

Suppose that a mutual fund manager has a $$12$ million portfolio with a beta of $1\mathrm{.}5.$ Also suppose that the risk free rate is $3\%$ and the market risk premium is $2\%.$

The manager expects to receive an additional $$8$ 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 $5\mathrm{.}5\%.$

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.

If the required rate of return is to remain at $5\mathrm{.}5\%,$ the beta of the portfolio, after the new stocks have been added, must be $1\mathrm{.}25>.$

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 $0\mathrm{.}875.$