# Asset Allocation With Stocks Bonds And Bills

In the previous chapter we examined the simplest asset allocation decision, that involving the choice of how much of the portfolio to leave in risk-free money market securities versus in a risky portfolio. Now we have taken a further step, specifying the risky portfolio as comprised of a stock and bond fund. We still need to show how investors can decide on the proportion of their risky portfolios to allocate to the stock versus the bond market. This, too, is an asset allocation decision. As the nearby box emphasizes, most investment professionals recognize that "the really critical decision is how to divvy up your money among stocks, bonds and supersafe investments such as Treasury bills."

In the last section, we derived the properties of portfolios formed by mixing two risky assets. Given this background, we now reintroduce the choice of the third, risk-free, portfolio. This will allow us to complete the basic problem of asset allocation across the three key asset classes: stocks, bonds, and risk-free money market securities. Once you

5 Given a level of risk aversion, one can determine the portfolio that provides the highest level of utility. Recall from Chapter 7 that we were able to describe the utility provided by a portfolio as a function of its expected return, E(rp), and its variance, -ap, according to the relationship U = E(rp) — .005A^2p. The portfolio mean and variance are determined by the portfolio weights in the two funds, wE and wD, according to equations 8.1 and 8.2. Using those equations and some calculus, we find the optimal investment proportions in the two funds:

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PART II Portfolio Theory

Figure 8.6 The opportunity set of the debt and equity funds and two feasible CALs.

Figure 8.6 The opportunity set of the debt and equity funds and two feasible CALs.

understand this case, it will be easy to see how portfolios of many risky securities might best be constructed.