Investment Procedures

Investment Procedures

Investment Procedures

Investment Procedures

Almost certainly, the discussion has been at such a high level ofgenerality that it provides little concrete guidance for real investors. After some more similar, general, and abstract discussion of relatedtopics, such as capital asset pricing and risk, we hope to provide somehelp in translating these general concepts into usable investmentprocedures.In order to define Markowitz's efficient set of portfolios, it is necessary to know for each security its expected return, its variance, andits covariance with each other security. If the efficient set were tobe selected from a list of only 1,000 securities, the volume of necessaryinputs and the computational costs would be intolerably large. Itwould be necessary to have 1,000 statistics for expected return, 1,000variances, and 499,500 covariances.* It is not realistic to expect security analysts to provide this volume of inputs. If 20 analysts wereresponsible for the 1,000 stocks, each analyst would be responsiblefor providing almost 25,000 covariances. The volume of work wouldbe intolerable and, furthermore, it seems to be quite difficult to havean intuitive feeling about the significance of a covariance.

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Because of this practical difficulty, the Markowitz portfolio modelwas exclusively of academic interest until William Sharpe suggesteda simplification which made it usable.1 Since almost all securities aresignificantly correlated with the market as a whole, Sharpe suggested that a satisfactory simplification would be to abandon the covariances of each security with each other security and to substitute information on the relationship of each security to the market. In his terms, it ispossible to consider the return for each security to be represented by the following equation:whereRtis the return on securityi, atandb,Lare parameters,ciis arandom variable with an expected value of zero, and / is the level ofsome index, typically a common stock price index. In words, the returnon any stock depends on some constant (a) plus some coefficient(b) times the value of a comprehensive stock index (say, the S & P "500")plus a random component. Sharpe's simplication reduces the number of estimates that the analyst must produce from 501,500 to 3,002 fora list of 1,000 securities.*

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There have been other efforts at simplification derived fromSharpe's ideas. Cohen and Poaguesuggested that several indexesrather than a single index be used, with the return for each securitybeing related to the index most appropriate for itperhaps some indexof production which is a component of the aggregate Index of Industrial Production of the Federal Reserve Board. Their empirical resultssuggest that the cost of using simplificationseither Sharpe's ortheirsis small. That is, the portfolios which are efficient as a resultof their simplified processes are very similar to the efficient portfoliosthat result from Markowitz's more complex process. Furthermore, if results are evaluated in terms of the two criteria, expected return andrisk, the efficient portfolios from the simple process are insignificantlyworse than the efficient portfolios from the complex process.

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