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However, the CWM uses the information in both the lagged economic variables and the fund’s portfolio weights. The Conditional Weight Measure is the average of the conditional covariances between future returns and portfolio weight changes, summed across the securities held. 11) as follows: wj (Z, S)[rj − E(rj |Z)] . 7) j The symbol wj (Z, S) denotes the portfolio weight at the beginning of the period. The weights may depend on the public information, denoted by Z. The weights of a manager with superior information, 5 See Grinblatt and Titman (1993) for a discussion.
Dynamic trading is akin to the use of options or other derivatives in its ability to generate nonlinear payoffs. For example, in many option pricing models a derivative can be replicated by dynamic trading in the underlying assets. There are two cases to consider, when addressing the problem of nonlinear payoffs in a managed portfolio. In the first case, it may be possible to replicate the nonlinearity in the funds’ returns by trading other assets whose returns are measured at the same frequency as the funds’ returns.
1997) when there is correlation across the funds. Carhart et al. (2002) show that the effects of survival selection on persistence in performance depends on the birth and death process and can be quite complex. 3 Early Evidence Sharpe (1966) studies the performance of 34 equity style mutual funds, using annual returns for 1954–1963, computing both the Sharpe and Treynor ratios to measure performance. 4%. Measured net of expenses the funds perform below the Dow Jones 30 stock index. 677, and only 11 of the 34 funds have Sharpe ratios above that of the index.