securities like stocks. The choice of the fraction of funds appor- tioned to risky investments is the first part of the investors asset allocation decision, which de- scribes the distribution of risky investments across broad asset classes-stocks, bonds, real es- tate, foreign assets, and so on. Finally, the security selection decision describes the choice of which particular securities to hold within each asset class. The top- down analysis of portfolio con- struction has much to recommend it. Most institutional investors follow a top-down approach. Capital allocation and asset allocation decisions will be made at a high organizational level, with the choice of the specific securities to hold within each asset class delegated to partic- ular portfolio managers. Individual investors typically follow a less-structured ap- proach to money management, but they also typically give priority to broader allocation issues. For example, an individuals first decision is usually how much     183 II. Portfolio Theory 7. Capital Allocation between the Risky Asset and the Risk−Free Asset The McGraw−Hill Companies, 2001         184 PART II Portfolio Theory     of his or her wealth must be left in a safe bank or money market account. This chap- ter treats the broadest part of the asset allocation decision, capital allocation between risk-free assets versus the risky portion of the portfolio. We will take the composi- tion of the risky portfolio as given and refer to it as "the" risky asset. In Chapter 8 we will examine how the composition of the risky portfolio may best be determined. For now, however, we start our "top-down journey" by asking how an investor de- cides how much to invest in the risky versus the risk-free asset. This capital alloca- tion problem may be solved in two stages. First we determine the risk-return trade-off encountered when choosing between the risky and risk-free assets. Then we show how risk aversion determines the optimal mix of the two assets. This analysis leads us to examine so-called passive strategies, which call for allocation of the port- folio between a (risk-free) money market fund and an index fund of common stocks.         7.1 CAPITAL ALLOCATION ACROSS RISKY AND RISK-FREE PORTFOLIOS   History shows us that long-term bonds have been riskier investments than investments in Treasury bills, and that stock investments have been riskier still. On the other hand, the riskier investments have offered higher average returns. Investors, of course, do not make