2However, due to diversification effects, this simple form of analysis is in-2Variance had been considered as a measure of financial risk as early as 1906 by Fisher (Fisher,1906).
1 Introduction3sufficient: 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 onitsmarginal impacton the risk–return profile of the investor’s entire portfolio. Putdifferently, 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 DystopiaThe original portfolio choice formulation by Markowitz has the investor make allher forecasts, of expected asset returns and covariances between them as we shallsee in Chapter 2, at the start of an investment period, and then lets the investor restuntil the end of the period. In particular, the investor is “prohibited” from tinkeringwith the allocations until the start of the next period. When that time comes, sheacts as though any previous period never existed, or any further period will neverexist: decisions are made strictly one period at a time. For this reason, Markowitz’sformulation is calledsingle-period.It is also called “myopic”, referring to the inability of the investor to see beyondthe immediate future and anticipate future opportunities. Obviously, in practice, in-vestors do not all die after one period, and a huge assortment of stratagems areemployed to “repair” the single-period formulation to varying degrees and make itbetter 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 receivesincome from non-investment sources, changing the investable capital in known (orunknown) ways. Moreover, frictions abound in the process: there are costs to everytrade, and governments are prompt to ask for a commission on any good deed (alsoknown as “taxes”). Planning ahead for these contingencies, in fact for the completefuture set of contingencies weighted by their probabilities, requires a drastically dif-ferent viewpoint than that afforded by single-period approaches. They lead to themultiperiod formulations, first analyzed by Mossin (1968), Samuelson (1969) andMerton (1969) (see §3/p. 37).A special group of investors commands specific requirements: that ofinstitu-tional investors, in particular mutual or hedge fund managers operating in a com-petitive environment. Their main characteristic is that they are not only interestedin maximizing the utility of their client’s final wealth, but also in optimizing thetrajectory that wealth takes to reach its final destination. Consider, for instance, a