## Beta and the Risk Premium

Consider a portfolio made up of Asset A and a risk-free asset. We can calculate some different possible portfolio expected returns and betas by varying the percentages invested in these two assets. For example, if 25 percent of the portfolio is invested in Asset A, then the expected return is:

E(RP) = .25 X E(RA) + (1 - .25) X Rf = .25 X 20% + .75 X 8% = 11%

Similarly, the beta on the portfolio, pP, would be:

Notice that, because the weights have to add up to 1, the percentage invested in the risk-free asset is equal to 1 minus the percentage invested in Asset A.

One thing that you might wonder about is whether or not it is possible for the percentage invested in Asset A to exceed 100 percent. The answer is yes. This can happen if the investor borrows at the risk-free rate. For example, suppose an investor has \$100 and borrows an additional \$50 at 8 percent, the risk-free rate. The total investment in Asset A would be \$150, or 150 percent of the investor's wealth. The expected return in this case would be:

The beta on the portfolio would be:

We can calculate some other possibilities, as follows:

 Percentage of Portfolio in Asset A Portfolio Expected Return Portfolio Beta 0% 8%
0 0