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The Science of Defundamentalisation

Published in Automated Trader Magazine Issue 30 Q3 2013

Short-term return reversal is a long-established phenomenon in financial markets. Yet despite this longevity, the challenge of isolating fundamental return drivers from their non-fundamental counterparts in a reversal model still persists. Automated Trader talks to Zhi Da, Associate Professor of Finance at the University of Notre Dame and author of a recent paper on the subject, about a novel approach to this conundrum.

AT: What prompted this particular line of research?

Zhi: Researchers in finance love to solve puzzles and short-term return reversal is considered one of the oldest puzzles of these. The fact that past returns can predict future returns is somehow fascinating and has therefore been a subject of academic debate since the 1960s, which intensified after a period of detailed research in the 1990s. One of the most interesting facets to the phenomenon is that it has been shown to be extremely robust and not just an artifact of data mining, which makes teasing out its underlying causes especially fascinating. This, plus the possibility of enhancing the traditional reversal strategy, was the motivation for our research and the publication of its associated paper "A Closer Look at the Short-term Return Reversal".

AT: Your paper cites three fundamental components [1] of stock return, but in order to measure the second of these (cash flow news due to changing expectations about fundamental future cash flows) you use analysts' earnings estimates revisions, which has not been done before. What prompted this choice?

Zhi: Academic finance literature already contains very rigorous studies of return decomposition. A classic example of this is the work of Campbell and Shiller in the 1980s and early 1990s. In their papers they demonstrated algebraically that it was possible to decompose return into a cash flow component and a discount rate component. The cash flow component basically summarises changes in investors' expectations about future cash flow. However, this is not just about the cash flow expectations for the next period, but for multiple periods all the way out to infinity. So in essence it is concerned with revising expectations about a sequence of cash flows.

While this is straightforward enough in theory, estimating it in practice is problematic, so this has been the subject of extensive research over the past 20 years. Initially research focused on predictive regressions, whereby they set up vector auto-regressive regressions in an attempt to arrive at a representative predictor of future dividends returns. The same basic approach would then also be used to calculate expected earnings revisions.

However, over the last seven or eight years researchers have started to appreciate that there are numerous issues associated with using this statistical approach. Apart from complexity and inaccuracy, the approach is essentially very indirect. By contrast, we reasoned that the primary objective was simply to measure investors' changing expectations of future cash flow - and equity analysts are essentially providing these expectations directly. Therefore why not just use these, rather than jumping through numerous statistical hoops and probably obtaining a noisy result anyway?

A further advantage is that these analysts are not just providing one cash flow forecast, but also estimates for future periods out to the very long term. All that is then required is the calculation of some differences in order to measure changes in earnings expectation over time, without the need for estimation and statistical modelling.

One potential problem is that individual analysts may have a particular bias, but since one is concerned with changes in forecast rather than their absolute level, a persistent bias in either direction doesn't actually matter. The only real caveat is whether or not an analyst's bias is persistent.

AT: How do you handle things such as outliers in changes of analysts' forecasts?

Zhi: In actual fact this is not a major issue if you are trying to implement the strategy at a portfolio level, because extreme outliers on both sides effectively cancel each other out. If people are investing in a sufficiently diversified portfolio, then these outliers become less of a concern. However, at an individual firm level I don't think there is any scientific way of dealing with these outliers. What people tend to do in these circumstances is apply some form of Winsorising [2], so if the change number looks too extreme then it will be adjusted to say 95% tau.

AT: What is your process for calculating the final number actually used for expectation changes in future stock cash earnings?

Zhi: We obtain some measure of cash flow expectations for one and two years, and so on out to infinity. However, in practice there are only three forecasts commonly available for the majority of stocks that receive coverage. These are earning forecasts for the current fiscal year (referred to as A1t in the paper), the next fiscal year (A2 t), and a long-term growth forecast (LTG t). This last is the forecast growth rate in earnings over the next three to five years. After A2 t we use the long-term growth forecast to extrapolate future earnings. However, sometimes when you look at long-term growth forecasts you see numbers such as 40%, and you logically wouldn't expect the company to keep growing at that rate forever. There therefore needs to be a steady-state stage and a typical assumption for this is that in the long run all firms will be growing at a rate that is close to GDP growth (typically in the 4% to 7% range). Alternatively one can use a sector-specific measure, such as the average historical growth rate in earnings within each sector.

Our approach is to extrapolate LTG t to the long run steady-state growth value from year five out to year 15. Beyond year 15 we assume that everything will be growing at the steady-state rate. In this fashion we calculate a set of earning forecasts from the current fiscal year out to infinity. Then in the next period we do the same calculation to produce a new set of forecasts. We then calculate the difference between the two sets of forecasts, which gives us the change in overall cash flow expectation along the complete spectrum that has taken place over the intervening period.

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