主 题: Quantile Momentum
报告人: Prof. G.Bassett (Univ. of Illinois at Chicago)
时 间: 2007-06-13 下午 4:00
地 点: 理科一号楼 1418
Abstract: Momentum strategies buy stocks that have recently done well and sell stocks that have recently done poorly. The excess return of such strategies is well known and has been extensively investigated. The possibility that momentum’s excess returns are due to incidental exposures to risk factors such as size or value have been largely discounted so that momentum stands alone and largely undisputed among anomalies that have been suggested. While momentum returns have tended to be positive overall, it is important to note that there have periods with negative returns, most recently from 2001 to 2003.
Stock momentum is typically measured in terms of recent average monthly return. The most commonly used measure of momentum of stock i at the start of month t, moit, is i’s average return over the previous 2 to12 months, moit=average(rt-2,…,rt-12) (which is essentially the total return over the specified period). The most recent month return is usually excluded because of short term reversals. Empirical work on momentum has focused on alternative specifications of “recent”, for example, averaging periods extending over sub periods from 3 to 48 months previous.
In this paper we investigate momentum returns under the standard definition of “recent”, but using what we call quantile measures of performance. For example, instead of the standard definition consider, moit=max(rt-2,…,rt-12). In this case stocks are ranked not by their average but by their maximum recent returns. Stocks in the long momentum portfolio are those with the largest recent maximum monthly return. Conversely, the short momentum portfolio consists of those stocks whose maximum values over the recent period are the smallest. It is clear that the stocks in momentum portfolios using average returns can be very different from those in portfolios based on the maximum.
Similarly, consider recent performance, moit=min(rt-2,…,rt-12). In this case the long momentum portfolio will consist of stocks whose recent minimum monthly return has been superior. This definition of superior recent performance can be very different than superior based on the average or the monthly maximum.
More generally, recent performance can be measured in terms of the θth quantile of recent monthly returns, moit=Q(θ:rt-2,…,rt-12). Based on 11 previous returns, rt-2,…,rt-12, θ in (0,1/11) identifies the smallest recent monthly return, θ in (1/11, 2/11) identifies the second smallest monthly return, and so on. For each θ, the associated ranking of moit over all stocks provides an alternative measure of superior and inferior performance on which to construct momentum portfolios.
We present the returns to long and short momentum portfolios based on these alternative definitions of quantile momentum. We find that the alternative definitions can give very different returns from one another, as well as from the standard method based on the average. We also consider the correlations between the alternative strategies, with an eye on combining momentum strategies.
We also consider from a theoretical perspective the incidental β exposures that exist with the alternative definitions. A well known feature of momentum portfolios is that they carry incidental β exposures depending on whether the market has been rising or falling. In rising markets high β stocks tend to do better than low β stocks so that long-short momentum portfolios based on the standard momentum definition have positive β values. Conversely, in falling markets momentum will tend to have β<0. A practical matter for portfolio managers using momentum strategies is the extent to which momentum can be improved by neutralizing the incidental β exposures.
In a rising market over the previous 2 to 12 months it will be high β stocks that will have tended to do better so that long momentum portfolios based on the average definition will have βs larger than one. Compare this with the long momentum portfolio based on minimum monthly superior performance. Since it is extremely unlikely that each of the previous 2 to 12 months have positive market returns, a stock’s worst month is most likely to occur when the market falls. In this case stocks with the best minimum return will likely be those with βs less than one. We investigate how the various definitions of momentum are likely to affect the incidental β exposures in long and short momentum portfolios.