trade-off:   E(rC) rf y[E(rP) rf]   C rf [E(rP) rf] (7.3) P 8 7 22 C II. Portfolio Theory 7. Capital Allocation between the Risky Asset and the Risk−Free Asset The McGraw−Hill Companies, 2001         CHAPTER 7 Capital Allocation between the Risky Asset and the Risk-Free Asset 189     Thus the expected return of the complete portfolio as a function of its standard deviation is a straight line, with intercept rf and slope as follows: S E(rP) rf 8 P 22   Figure 7.2 graphs the investment opportunity set, which is the set of feasible expected return and standard deviation pairs of all portfolios resulting from different values of y. The graph is a straight line originating at rf and going through the point labeled P. This straight line is called the capital allocation line (CAL). It depicts all the risk- return combinations available to investors. The slope of the CAL, denoted S, equals the increase in the expected return of the complete portfolio per unit of additional standard deviation-in other words, incremental return per incremental risk. For this reason, the slope also is called the reward-to-variability ratio. A portfolio equally divided between the risky asset and the risk-free asset, that is, where y .5, will have an expected rate of return of E(rC) 7 .5 8 11%, implying a risk premium of 4%, and a standard deviation of C .5 22 11%. It will plot on the line FP midway between F and P. The reward-to-variability ratio is S 4/11 .36, precisely the same as that of portfolio P, 8/22.     CONCEPT C H E C K ☞ QUESTION 2 Can the reward-to-variability ratio, S [E(rC) rf]/ C, of any combination of the risky asset and the risk-free asset be different from the ratio for the risky asset taken alone, [E(rP) rf]/ P, which