from the efficient set. As before, we ratchet up the CAL by selecting different portfolios until we reach Portfolio P, which is the tangency point of a line from F to the efficient frontier. Portfolio P maximizes the reward-to-variability ratio, the slope of the line from F to portfolios on the efficient frontier. At this point our portfolio manager is done. Portfolio P is the optimal risky portfolio for the managers clients. This is a good time to ponder our results and their implementation. The most striking conclusion is that a portfolio manager will offer the same risky port- folio, P, to all clients regardless of their degree of risk aversion.14 The degree of risk aver- sion of the client comes into play only in the selection of the desired point along the CAL. Thus the only difference between clients choices is that the more risk-averse client will invest more in the risk-free asset and less in the optimal risky portfolio than will a less risk- averse client. However, both will use Portfolio P as their optimal risky investment vehicle. This result is called a separation property; it tells us that the portfolio choice problem may be separated into two independent tasks. The first task, determination of the optimal risky portfolio, is purely technical. Given the managers input list, the best risky portfolio is the same for all clients, regardless of risk aversion. The second task, however, allocation of the complete portfolio to T-bills versus the risky portfolio, depends on personal prefer- ence. Here the client is the decision maker. The crucial point is that the optimal portfolio P that the manager offers is the same for all clients. This result makes professional management more efficient and hence less costly. One management firm can serve any number of clients with relatively small incremental administrative costs.       14 Clients who impose special restrictions (constraints) on the manager, such as dividend yield, will obtain another optimal port- folio. Any constraint that is added to an optimization problem leads, in general, to a different and less desirable optimum com- pared to an unconstrained program. II. Portfolio Theory 8. Optimal Risky Portfolio The McGraw−Hill