= 15%       rƒ = 7% F     S = 8/22 E(rP) - rƒ = 8%        P = 22%         which makes sense because the standard deviation of the portfolio is proportional to both the standard deviation of the risky asset and the proportion invested in it. In sum, the rate of return of the complete portfolio will have expected value E(rC) rf y[E(rP) - rf] 7 8y and standard deviation C 22y. The next step is to plot the portfolio characteristics (given the choice for y) in the ex- pected return-standard deviation plane. This is done in Figure 7.2. The risk-free asset, F, ap- pears on the vertical axis because its standard deviation is zero. The risky asset, P, is plotted with a standard deviation, P 22%, and expected return of 15%. If an investor chooses to invest solely in the risky asset, then y 1.0, and the complete portfolio is P. If the chosen position is y 0, then 1 y 1.0, and the complete portfolio is the risk-free portfolio F. What about the more interesting midrange portfolios where y lies between zero and 1? These portfolios will graph on the straight line connecting points F and P. The slope of that line is simply [E(rP) rf]/ P (or rise/run), in this case, 8/22. The conclusion is straightforward. Increasing the fraction of the overall portfolio in- vested in the risky asset increases expected return according to equation 7.1 at a rate of 8%. It also increases portfolio standard deviation according to equation 7.2 at the rate of 22%. The extra return per extra risk is thus 8/22 .36. To derive the exact equation for the straight line between F and P, we rearrange