frontier, and the choice of a particular port- folio from along that frontier. The determination of the optimal combination of securities proceeds in the same manner as the analysis of the optimal combination of asset classes. Why, then, do we (and the investment community) distinguish between asset allocation and security selection? Three factors are at work. First, as a result of greater need and ability to save (for col- lege educations, recreation, longer life in retirement, health care needs, etc.), the demand for sophisticated investment management has increased enormously. Second, the widening spectrum of financial markets and financial instruments has put sophisticated investment beyond the capacity of many amateur investors. Finally, there are strong economies of scale in investment analysis. The end result is that the size of a competitive investment company has grown with the industry, and efficiency in organization has become an important issue. A large investment company is likely to invest both in domestic and international mar- kets and in a broad set of asset classes, each of which requires specialized expertise. Hence the management of each asset-class portfolio needs to be decentralized, and it becomes im- possible to simultaneously optimize the entire organizations risky portfolio in one stage, although this would be prescribed as optimal on theoretical grounds. II. Portfolio Theory 8. Optimal Risky Portfolio The McGraw−Hill Companies, 2001           236 PART II Portfolio Theory     The practice is therefore to optimize the security selection of each asset-class portfolio independently. At the same time, top management continually updates the asset alloca- tion of the organization, adjusting the investment budget allotted to each asset-class port- folio. When changed frequently in response to intensive forecasting activity, these reallocations are called market timing. The shortcoming of this two-step approach to portfolio construction, versus the theory-based one-step optimization, is the failure to ex- ploit the covariance of the individual securities in one asset-class portfolio with the indi- vidual securities in the other asset classes. Only the covariance matrix of the securities within each asset-class portfolio can be used. However, this loss might be small because of the depth of diversification of each portfolio and the extra layer of diversification at the asset allocation level.       8.6 OPTIMAL PORTFOLIOS WITH RESTRICTIONS ON THE RISK-FREE ASSET   The availability of a risk-free asset greatly simplifies the portfolio decision. When all in- vestors can borrow and lend at that risk-free rate, we are led to a unique optimal risky port- folio that is appropriate for all investors given a