The Variance Of The Unexpected Market Returns Essay

Because and are iid, the variance of the unexpected market returns is: and the covariance between the unexpected stock and market returns is: Therefore, combining (B.1) and (B.2) gives the expression for the noise beta of stock i: The approximation is likely to be good in non-concentrated markets, like the U.S. stock markets. In the particular case in which all stocks are of equal size (i.e., ), then we are in the presence of the base case of minimum market concentration ( and ). In this particular situation, (B.3) is reduced to , corresponding to the framework of Ball (1977). In this case, equation (15) is reduced to , implying that the unconditional beta will be driven towards one as the predictability of the market returns goes to zero: . What happens to the noise beta when stocks are of various sizes? To answer this question, it is helpful to derive the noise beta of a typical portfolio. From (B.3), the noise beta of the equally weighted portfolio of stocks is given by: while the noise beta of a value-weight portfolio is: It also comes from (B.3) to (B.5) that even if the stocks are of various sizes, the noise betas of the stocks and portfolios will also be close to one when the level of market concentration is low. Indeed, when the degree of market concentration tends to perfect competition, all terms in RHS of equations (B.3) to (B.5) will be close to one. For instance, as of December 2015, there were about 7,209 U.S. stocks listed in CRSP database, for a totalShow MoreRelatedHedge Funds : Hedge Fund1628 Words   |  7 Pagesadequacy. In 2000, Fung and Hsieh used a mean-variance approach to study hedge fund exposures in some major market events. They analysed hedge fund performance during turbulent market times. 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