Almost certainly, the discussion has been at such a high level of generality that it provides little concrete guidance for real investors. After some more similar, general, and abstract discussion of related topics, such as capital asset pricing and risk, we hope to provide some help in translating these general concepts into usable investment procedures. In order to define Markowitz’s efficient set of portfolios, it is necessary to know for each security its expected return, its variance, and its covariance with each other security. If the efficient set were to be selected from a list of only 1,000 securities, the volume of necessary inputs and the computational costs would be intolerably large. It would be necessary to have 1,000 statistics for expected return, 1,000 variances, and 499,500 covariances.* It is not realistic to expect security analysts to provide this volume of inputs. If 20 analysts were responsible for the 1,000 stocks, each analyst would be responsible for providing almost 25,000 covariances. The volume of work would be intolerable and, furthermore, it seems to be quite difficult to have an intuitive feeling about the significance of a covariance.
Because of this practical difficulty, the Markowitz portfolio model was exclusively of academic interest until William Sharpe suggested a simplification which made it usable.1 Since almost all securities are significantly 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 is possible to consider the return for each security to be represented by the following equation: where Rtis the return on security i, atand b,Lare parameters, ciis a random variable with an expected value of zero, and / is the level of some index, typically a common stock price index. In words, the return on 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 for a list of 1,000 securities.*
There have been other efforts at simplification derived from Sharpe’s ideas. Cohen and Poague suggested that several indexes rather than a single index be used, with the return for each security being related to the index most appropriate for it—perhaps some index of production which is a component of the aggregate Index of Industrial Production of the Federal Reserve Board. Their empirical results suggest that the cost of using simplifications—either Sharpe’s or theirs—is small. That is, the portfolios which are efficient as a result of their simplified processes are very similar to the efficient portfolios that result from Markowitz’s more complex process. Furthermore, if results are evaluated in terms of the two criteria, expected return and risk, the efficient portfolios from the simple process are insignificantly worse than the efficient portfolios from the complex process.
Lecture Series on Basic Electrical Technology by Prof. L.Umanand, Principal Research Scientist, Power Electronics Group, CEDT, IISC Bangalore
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