Thin-trading effects in beta: Bias v. estimation error.

Market model; Thin trading;

EVALUATING THE WISDOM OF CROWDS

ABSTRAC

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status: publishe

Flawless fundamental indexing.

Perold (2007) shows that, given a diffuse prior that is being updated in light of a noisy market price, the posterior distribution says that value-weighting and equal-weighting one's portfolio makes no difference. We argue that the diffuse prior is hard to reconcile with reality and that a plausible prior predicts that value weighting does create a `drag' on returns, as the proponents of Fundamental Indexing have held all along.fundamental indexing; drag; noisy price; flawed; not;

An Anatomy of Fundamental Indexing

Adherents of Fundamental Indexing (FI) suggest that it is more profitable to base portfolio weights on indirectly size-related indicators like accounting data rather than directly on market caps. In noisy markets `a la Roll (1984), it is argued, underpriced stocks overperform but are underweighted and vice versa, implying a ‘drag’ which FI claims to avoid. Mixed into the debate is the question whether mispricing is partly identifiable or not, i.e. whether a policy of actively increasing the small-cap weights and vv helps. Carhart style regressions are unable to explain the extra return, but that conclusion is not robust across variant models, and there are substantial doubts about the constantness of factor sensitivities. Cross-sectional regression of weight shifts show that the weight shifts are much larger than necessary to avoid drag and that the cross-sectional patterns are also quite variable over time. In short, not only there are style shifts, but they are also unstable. To estimate the benefits from drag avoidance, purged of style shifts without having to rely on generalized FF regressions, our procedure is to sort stocks on size into vigintiles, and compare within each vigintile the performance of FI-weighted returns to equally-weighted (EW) returns, which should be immune to drag too without much style shift. We find that within-vigintile EW portfolios are style neutral w.r.t. market and value, and do not meaningfully outperform VW portfolios. Thus, avoiding drag is not why FI does well: drag is empirically unimportant. Most or all of the prima facie benefits must be from time-varying style shifts.status: publishe

An Anatomy of Fundamental Indexing

Proponents of Fundamental Indexing (FI) suggest that it is more protable to base portfolio weights on indirectly size-related indicators like accounting data rather than directly on market caps. In noisy markets a la Roll (1984), it is argued, underpriced stocks (which typically overperform) get underweighted and vice versa. This negative interaction implies a `drag', which FI claims to avoid. The key question is to what extent the extra return that FI pays really reflects drag avoided rather than style shifts. By way of background check we first look at the proposed changes in the weights across size classes and over time. FI-based weights are biased towards smaller firms; but this size bias is also (i) too large to be just a Bayesian reaction to noisy valuations, and (ii) very unstable over time and across size classes. This means that conventional regression analysis's plagued by unstable exposures. We find direct evidence of this in our own regressions. In addition, the choice of factors and time periods drastically changes the alphas. Regressions, in short, are not helpful To estimate the pure benefits from drag avoidance, purged of style shifts without having to rely on style regressions, we study an investment strategy that should be immune to drag, but without much style shift: we sort stocks into twenty size buckets (vigintiles), and form a portfolio where a stock's weight equals the average value-weight of all stocks in its vigintile. We nd no meaningful extra return, whether at the total-portfolio level or per vigintile. Thus, avoiding drag is not why FI does well: drag is empirically unimportant. Most or all of the prima facie benefits must be from time-varying style shifts.no isbnstatus: publishe