Theory shows that it is preferable to apply leverage to a less risky portfolio than to concentrate a portfolio in riskier assets for the purpose of raising expected return. This theoretical result, however, relies upon assumptions that may be only partially valid, if at all. In this chapter, we relax the assumptions that produce this theoretical result to match real‐world conditions, and we reexamine the efficacy of leverage and concentration. We find that what is inarguable theoretically does not always hold empirically when we introduce more plausible assumptions.

The notion that investors are better served by applying leverage to a less risky portfolio rather than concentrating a portfolio in riskier assets in order to raise expected return has an impressive theoretical lineage. As we discussed in Chapter 2, Markowitz (1952) introduced portfolio theory, which shows how to combine risky assets into efficient portfolios that yield the highest expected return for a given level of risk. He called a continuum of such portfolios the efficient frontier. Tobin (1958) showed that the investment process can be separated into two distinct steps: the construction of an efficient portfolio as described by Markowitz, and the decision to combine this efficient portfolio with a risk‐free investment. This two‐step process is called the separation theorem**.** Tobin showed that there is a unique portfolio along the efficient ...

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