Characteristics of pricing errors in stocks implied by autocovariance and ‘drag’

Abstract

In this article, we estimate the lower bounds on the volatility and autocorrelation of pricing errors in stocks and infer the market-wide component in the pricing errors, by combining information from the autocovariance and ‘drag’ in stock returns. For the smaller US stocks, we estimate lower bounds of 8−10% for the volatility and 0.3−0.5 for the autocorrelation of the pricing errors, at monthly horizon. We infer that approximately 50% of the pricing errors of the smaller stocks originate from the market-wide component, whereas for larger stocks, virtually all of the pricing errors are market-wide. In practice, this evidence means that market-wide bubbles and busts are far more important than idiosyncratic sources of pricing errors, like thin trading, low liquidity or little analyst following.

Keywords:

• drag
• noisy prices
• bubble
• bust
• pricing error

JEL Classification:

• G11
• G12
• G14

Notes

¹ In this literature, Ito-type quadratic approximations are accepted for monthly returns. The table below shows that this works well for 1/(1 + x): even with a SD of x equal to 0.20, the percentage error in the mean is only 0.60% when using a quadratic approximation, down from 4.4% for the linear approximation. (The distribution underlying the computations is normal.) For smaller SD, the bias is only a few basis points (at SD = 0.10) or a fraction of a basis point (at SD = 0.05.)

² This is to eliminate tiny, illiquid and penny stocks which are reasonably more likely to contain data errors. Penny stocks are often fallen angels (Chan and Chen, 1991) which are highly speculative and illiquid. Tiny companies likewise have limited liquidity, can be subject to high price pressure or price manipulation and often represent too little value to warrant attention.