Complicated paper (don’t panic, keep reading) highlighted this week from Jacob Boudoukh, Ronen Israel and Matthew Richardson all associated with AQR Capital which I spotted in the latest edition of No-Life-Bi-Monthly AKA The Financial Analysts Journal.
Complicated because it’s taking on one of the biggest myths in financial forecasting. The authors therefore probably felt the need to exhaustively prove their point; and here is that very simple but very profound point. Analysis of long-run trends in stock markets, especially if that analysis makes prediction about mean reversion, is profoundly flawed (that’s academic-speak for ‘wrong’).The problem? if you want to analyze a stock market over, say, a 60-year period and talk about trends you’ve actually got a very small sample. How so?
Let’s say you want to see if a high P/E leads to poor performance in the following 5-years. Over your 60-year period you’ve only got 12-periods to analyze (60/5). Analysts know this isn’t enough data to speak with authority on so they generate more data by moving dates to create overlapping periods. So, rather than 12-periods, if you shift your start day for observation by just one day, presto! you’ve now got 24-periods; and so on.
By generating this extra data in creating these overlapping periods and using an error adjustment factor appropriate for larger data sets [Newey-West standard error distributions in most cases, don’t ask!] it appears you’re getting better and better readings and therefore more reliable predictions; but you’re so not!
Why not? By creating the extra data you’re not fundamentally changing the periods you observe. A five-year period and a five year plus one day period at either end is still, pretty much, the same five-year period. What looks like two data points therefore isn’t really anything of the sort.
To whom does this matter? Well, most all of us who’ve ever listened to some talking head opine about whether or not a stock-market is ‘..cheap (or dear) relative to history based on analysis..’. The bottom line here is (many) forecasts based on historical observation are, statistically speaking, pretty irrelevant due to a the small sample.
Somewhat un-intuitive; but true nonetheless. For the courageous the paper in full can be accessed via the following link Long-Horizon Predictability
Happy Sunday.