2 however due to diversification effects this simple

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2 However, due to diversification effects, this simple form of analysis is in- 2 Variance had been considered as a measure of financial risk as early as 1906 by Fisher (Fisher, 1906).
1 Introduction 3 sufficient: the decision to hold a security should not only depend on a simple com- parison of its expected risk and return profile to that of other securities, but also on its marginal impact on the risk–return profile of the investor’s entire portfolio. Put differently, the decision to hold a security cannot be made in isolation, but is con- tingent upon the other securities that the investor already holds (or wants to hold). Earlier treatments of security analysis, including such classics as Graham and Dodd (1934) and Williams (1938), lack this perspective. Myopia Dystopia The original portfolio choice formulation by Markowitz has the investor make all her forecasts, of expected asset returns and covariances between them as we shall see in Chapter 2, at the start of an investment period, and then lets the investor rest until the end of the period. In particular, the investor is “prohibited” from tinkering with the allocations until the start of the next period. When that time comes, she acts as though any previous period never existed, or any further period will never exist: decisions are made strictly one period at a time. For this reason, Markowitz’s formulation is called single-period . It is also called “myopic”, referring to the inability of the investor to see beyond the immediate future and anticipate future opportunities. Obviously, in practice, in- vestors do not all die after one period, and a huge assortment of stratagems are employed to “repair” the single-period formulation to varying degrees and make it better reflect reality; Chapter 2 covers the most common ones. However, even these fixes are insufficient since they do not reflect the fact that in- vestment is, fundamentally, an extended process. The asset universe provides chang- ing opportunities, some of which can be anticipated in advance. Perhaps the in- vestor could want to consume a portion of her wealth along the way, or receives income from non-investment sources, changing the investable capital in known (or unknown) ways. Moreover, frictions abound in the process: there are costs to every trade, and governments are prompt to ask for a commission on any good deed (also known as “taxes”). Planning ahead for these contingencies, in fact for the complete future set of contingencies weighted by their probabilities, requires a drastically dif- ferent viewpoint than that afforded by single-period approaches. They lead to the multiperiod formulations, first analyzed by Mossin (1968), Samuelson (1969) and Merton (1969) (see §3/p. 37). A special group of investors commands specific requirements: that of institu- tional investors , in particular mutual or hedge fund managers operating in a com- petitive environment. Their main characteristic is that they are not only interested in maximizing the utility of their client’s final wealth, but also in optimizing the trajectory that wealth takes to reach its final destination. Consider, for instance, a

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