Momentum v. mean-reversion

Short term update: Bloomberg columnist Ritholtz shares this article, and Barron's compelling columnist Ben Levisohn compliments this article as "wonky and worthwhile".  Complimented as "a great deep dive" by Lindzon, president of StockTwits.  For all other sample citations, please see here.

Which is a better trading strategy, momentum or mean-reversion?  Try this mathematical thought experiment for yourself.  Look at the four anonymized stocks below, each trading from the mid-1980s.  Each stock chart starts indexed at $100.  What do you see in each of these stocks?  Are there some hints in each of them, which indicate that one of the two trading strategies is better?  Are stocks A and C better buys, versus stock D?

Now let’s look at applying a trading strategy to these companies.  Say a momentum strategy, where we focus on if the stock moves up (relative to its trend) for two years straight, one then invests in that stock until the first relative down-year of that company.  What types of returns would you make from this (“don’t fight the uptrend”) strategy?

Next let’s look at a mean-reversion strategy, where we focus on if the stock moves down (relative to its trend) two years straight, one then invests in that stock until the first relative up-year of that company.  Which of these strategies is easier to use (i.e., momentum, or “buy the dip”)?  And what sort of returns would you estimate getting from these simple trading rules described here?

By answering such math questions, we learn a lot about the risks and rewards, of these fundamentally exclusive trading ideas.  These are the same ideas that are mathematically embedded into modern ARIMA econometric models.  Pause for a moment and try to determine by looking at the four stock returns above, which sort of trading signal and profit would be generated:

I.    <$100
II.   $100-$200
III.  >$200

What we see below is that both of these technical rules produce the same results!  About $75 profit (or answer I above), off of the $100 initial price.  So in other words the implementation of one successful strategy (after all we profited $75) mathematically means we would not be able to profit on the other strategy.  Aren’t we therefore -by nature- still leaving money on the table?

Inspecting the above stock chart more closely, we might also notice that both trading signals only worked about 7 or 8 of the years, per company (or a quarter of the time per strategy).  This also implies the other half of the time neither trading style exclusively applied, even though some risk should have been taken as the stocks were still in an overall uptrend.  We also notice that even with fairly equal returns from stocks A and C, have differing results within the same strategies!  Worse yet, we notice the risks involved in either strategy, since none of the strategy returns shown above just moved in an up-only direction.  Both can suffer losses from mistiming within the strategy.

Putting this altogether, we see all of the mixed prospects of using one of these trading strategies.  The results in this case of both strategies equaling $175, after 30 years, falls short of the results of typically amassing $400 if we instead just kept a buy-and-hold strategy the entire time (see the top-most chart.)  Also the $75 profit is is likely less than any optimistic market participant would have guessed ex-ante, while first seeing the chart (e.g., the I, II, III choices above).

Also notice that the interpretation of both momentum and mean-reversion are the same, in a short-term view, in that one is waiting for a a slight trend in order to still make the same decision (in this case to buy stocks).  This means that both strategies are in fact the same to some degree (and offer the same returns as noted above!), differing only in the hope of the investor about where stocks should head.  We say "hope" because again at the end of waiting for the same signal, the future direction of the stock is still random. 

Still not convinced buy-and-hold would be the best approach to these stocks above?  Think there is a better rule-based algorithm you could apply to better tune your approach to each of these four stocks?  Unfortunately, think again.  The stock chart above is bogus, and in fact each series is just a random number generator.  See the de-trended chart below.

While starting at $100 each variable A, through D, annually fluctuates between -$20, to +$20.  Whatever happens in any given year has no influence on what then happens the following year.  And here is the key probability insight for this article is: ogling at a recent random trend to provide a signal also has no value.  We added a +$10 upward drift each year, on top of the random annual move of -$20, to +$20.  Of course the reality of economic compounding should have been an early tip-off that the top-most chart isn’t perfectly right.

One is essentially being fooled.  Not by me, but by randomness, and that can happen in more ways then we might think.  Articulating ideas from stock chart patterns, which can speak to someone if they hope them to.  But signals mislead with false-positives in this article, just as they often do in real-life (here, here, here, here).  In this case we also see that we could unfortunately have been fooled into thinking that the underlying trend of the "companies" A and C, were different from D.  In fact they were, and are all the same.  One was only fooled here by the compounded random oscillations impacting one's assessment of the core underlying trend; and sure you can delude yourself into thinking you can wait such things out (the chart above was only a 30 year reference!)
 
Also recall that just a month ago that all chart-devoted technicians adamantly accepted that markets were "consolidating" into a multi-month top, with nowhere to go but down.  Instead volatility fell and we are now yet again at all-time highs, including the once-bubbled Nasdaq.  And just as quick, the same folks have gone back to update and rely on the "real-world" market charts to pick up new “signs” of what this all might mean.  It means nothing.  More importantly, it is just random where it will ever matter to you.

A legendary portfolio manager, who self-terminated his portfolio management career after a nice run, said of those who try timing the market:

Far more money has been lost by investors preparing for corrections, or trying to anticipate corrections, than has been lost in corrections themselves.

Peter Lynch’s wisdom in this regard works for individuals who consider the mutually-exclusive success of momentum or mean-reversion strategies, and falsely believe that either is the best way to gain an upper-hand over the market.