Timing a Strategy Using Mean-Reversion (A Critique)
Warning: geekiness ahead.
I’ve seen some work coming out of the quant-blogosphere recently related to “timing” a strategy using mean-reversion, or in other words, increasing exposure to a strategy after it performs poorly and reducing exposure after it performs well.
On paper this often tests out to be a good idea (especially in today’s very mean-reversion driven market) but I’m wary of it for two reasons: (a) evolving markets, and (b) changing the nature of the strategy. Allow me to pontificate…
First, a super-simple illustration:
[Growth of $10,000, logarithmically-scaled]
The graph above shows the (frictionless) results of two strategies “trading” the S&P 500 index from 2000 to present compared to buy & hold (in blue). The first (red) goes long at today’s close if the S&P 500 closes down today and short if it closes up.
The second (green) is “timing” the first strategy. Before each trade, we look at the first strategy’s returns for the previous 21-days (1-month) and compare it to all similar periods over the previous 1-year. If the most recent 21-day return is in the top 1/3, we do NOT take a position (because the strategy has been performing “too well”). Otherwise, we take the full position.
Note: This is a proof of concept; I am not suggesting anyone actually trade these strategies, only making a point. As we’ve talked about a number of times before (read more and more), daily mean-reversion is a recent phenomenon (and likely to change with a portfolio-crushing lack of notice), extremely volatile, and difficult to capitalize on alone taking trading frictions into account.
The performance improvement by “timing” the strategy becomes clearer when we look at the numbers:
On paper, a major improvement – improved risk-adjusted returns, significantly lower drawdowns, and a third less exposure to the market – what’s not to like?
Two Issues…
First, markets evolve (example) and without the benefit of hindsight this might be a dangerous approach.
Here we knew that the strategy would continue to perform in the future, but in the real-world (as I harp incessantly) fundamental characteristics of the market like daily mean-reversion are not static – they are constantly changing. By rewarding a strategy that was failing, we would inherently increase (or at the very least, not decrease) exposure as the market was evolving and the strategy was falling off a cliff.
Like our abnormal market filter (included in the State of the Market report, and YK and Scotty strategies), this is the “devil I don’t know” paradox. Historically our strategies have performed better without the abnormal market filter, and in a perfectly curve-fitted world, we would have no reason to use it. But as a developer I have to respect the devil that I don’t know (yet) and sometimes put logic (and the safety of the portfolio) ahead of the numbers.
Second, looked at from another perspective, we aren’t so much “timing” the strategy as changing the nature of how the strategy is trading.
That’s a little hard to wrap the noggin’ around with daily MR, so imagine the same approach applied to a trend-following strategy like 50/200-day MA crossovers.
If the strategy had performed well over the last 21-days, that’s not indicative that the strategy is working. That’s just indicative of a market that’s been bullish over the last 21-days. By then not trading the strategy (because it had performed so well) we didn’t successfully “time” the strategy, we modified the strategy to not trade when the market was overbought in the intermediate-term. We changed the nature of the strategy itself.
There’s not necessarily anything wrong with that, but it’s not our stated purpose.
Final Thought…
I’m not forever closing my doors to the concept of mean-reversion in strategies, but any approach would have to respond to the two critiques above (particularly the first).
Happy Trading,
ms
P.S. I hope that all translated well from the thoughts swimming around in my head…this was a difficult one to put into pixels (I’m a thinker, not a writer).
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Filed under: Follow-Through, Trading Strategies | 18 Comments
great post, and very thought provoking. here is a counterpoint:
Being willing to trade mean reversion in the market but not at the strategy level, is not entirely logical. After all the market is a composite of different people’s strategies, thus you are effectively trading a composite strategy equity curve when you are trading the market. Trading a distinct strategy equity curve is no different. You approach it the exact same way in concept.
It is simple to satisfy both mean reversion and confidence simultaneously. Either set a minimum limit of confidence before “turning off the strategy” in this case as long as confidence in follow through was above 50% or 60% in the SOTM you would increase allocation slightly during mean reversion. OR you could simply trade mean reversion as long as the slope of the equity curve was higher over the last 6 months or 1 year etc. Ideally, you could do both. Regardless, you could filter to reduce some exposure when things are doing “too well” and add some additional exposure when things have underperformed.
At the very least, the concept of reducing exposure—ie taking profits when a strategy is performing too well, is a good way of reducing drawdowns as well. After all the biggest blowups in hedge fund history occured when too many people chased the same trading strategies because they were doing so well. This was also the root of the crash in 1987. Eventually, the other devil known as chasing performance caused their own demise.
RE to DV: I agree w/ your counterpoint to a point.
I agree that it is like doubling down on a mean-reversion strategy (at the individual-strategy level, not this strategy-mean-reversion we’re talking about in this post). But even at the individual strategy level there has to be an uncle point (like I do with the abnormal market filter) where we say, okay, this isn’t working and I’m not going to follow it off the cliff. I’ll state the obvious here – RH didn’t have that mechanism in place in July…enough said.
But the way I’ve seen this strategy-MR postured multiple times is I’m going to play the strategy when it’s weak, and my point is that that’s a bad idea (sans hindsight) because sometimes weakness leads to long-term failure. If a “bracketed” approach like you’re suggesting works historically, then that would resolve my concern #1 (though I’d have to ponder concern #2 a bit).
michael
(not edited)
This reminds me of an excellent strategy ‘Keep betting more on losing horse’…There has to be reasons besides ‘losing’ for betting on that particular horse…past market similarities, short term failure against long term success, or succesful hereditary, modified genes, inside information. If there are no other reasons, it is simply betting on losing horse.
What this means is, in fact you are MR one strategy based on non-MR another strategy or set of strategies. This also means if you do profit/lose based on MR a strategy it may not be entirely becasue of MRing that strategy but combined effect of performances of other strategies. Michael has repeatedly demonstrated that combining strategies (50/200, 5-10-20, abnormal market filter used as backdrop) does impact risk-adjusted returns, drawdowns, and exposure to the market. In effect you are not betting on losing horse but ‘circumstances’ under which losing horse can win.
JP
The obvious alternative is to increase exposure to a strategy when it is doing well and reduce exposure to it when it is doing poorly. Have you ever looked at that? It seems to be more in tune with your evolving market perspective. It also protects against the devil you don’t know — as long as one reduces exposure fast enough as the strategy fails.
RE to Russ: agreed, that is (at a very, very abstract simple level) the concept behind our adaptive YK model. I think the reason you don’t see that more often is that on paper it often doesn’t appear to work well because of the two points in the post above. michael
P.S. One would also have to be careful not to let a winning streak increase one’s exposure to the point that a sudden reversal of fortune wipes one out.
for what its worth: in the past i had throttled a strategy by means of tracking the equity curve a bit, and it did help smooth the returns out quite a bit.. i haven’t been using it lately.
the technique i used was:
if (upper_bollinger(equity – sma(equity, 20), 200, 2))
stop_trading;
i.,e if the difference in equity vs. the 20 day ma exceeded the 200 day, 2 std deviation upper bollinger band, then the returns are a bit abnormal and stop trading.
One could curve fit the periods a bit, but i found the returns were reasonably stable.
Don’t you think each strategy has a different behaviour?
It can be mean-reverting or trending. I do believe most of them are momentum-based but I do prefer to statistically prove that rather than saying they are all momentum-based.
For instance a runs test is generally used to determine if there is any statistically significant dependency in a sequence of trades in order to determine which equity curve trading method is more suitable.
What do you think?
Paolo
RE to Paolo: if you read my post, I’m not saying they’re momentum-based. I’m saying that on paper many strategies do respond well to being “timed” with mean-reversion. But I’m also saying that timing strategies using MR has some serious potential dangers that need to be respected.
I’m saying that each strategy is a different story….so they won’t all respond well to being “timed” with mean-reversion.
I was then wondering what are your thoughts about using such statistical tests first rather than worry about “potential” dangers that must be proved in the first place (I prefer to test if “potential” means somenthing)
looking forward to hearing back your comments
paolo
RE to Paolo: sure, I agree with that 100%…I think it goes without saying that some strategies are not going to respond well to being timed (at the strategy-level) with mean-reversion. michael
hi Michael,
as with many of your statements, i find the idea of abnormal market filter “not working as well in backtests, but saves your a** in real time”.
Is that in general because it reduces the risk of ruin (i.,e improves the kelly ratio) ?
or because it helps in maintain the investor psychology during the drawdown (i.,e removes “chasing the hot hand” behavior )?
would love to hear your thoughts on this topic. After you initial abnormal market filter posts, i tried it on every one of my backtests, and found it gave worse results.
Your note on how it caused a big drawdown in RH portfolio vs. having the filter on in YK gave me pause.
i have not paid attention to kelly ratio (or other similar metrics) in comparing strategies, and now i am thinking maybe i should..
thanks for your insights !
i meant to say:
find the idea of abnormal market filter “not working as well in backtests, but saves your a** in real time” HIGHLY INSIGHTFUL AND THOUGHT PROVOKING.
RE to bgpl: I would say part of the answer is “investor psychology” but the bigger purpose is as a defense against what the backtest isn’t telling us.
Backtests are great tools, but they are inherently curve-fitted and based on a given set of history (the “normal”), which is why I think in most of my tests, the AMF doesn’t significantly improvement performance. But that’s also why when the market acts out of sorts, models break down.
Measuring when the market is abnormal is a tricky business (and I’m not 100% sure of the best way to do it), but the abnormal market filter is a first pass. We’re simply taking the model out of the market when the market becomes very stretched to the up or downside. Perhaps the model will continue to perform well in this environment, but I’d rather be in the safety of cash than sorry.
michael
One thing that I haven’t heard mentioned is that altering a system by trading the MR of it’s performance may significantly impact returns on the UPSIDE.
Look at many of the standard short-term MR systems (RSI2, consecutive days up/down, short-term MA crossovers) over the end of 2008.
Had those systems been turned off due to excessive performance, one would have sacrificed double digit percentage gains.
What I would like to see you test Michael is something like turning a system off, or reducing position size, when the %profitable over n-days deviates significantly from historical results. Also, a similar concept would be to use the average trade, rather than %profitable.
As the %profitable and/or average trade returns to the lower boundary of what would be “normal,” the system would turn on again and resume trading.
Great post Michael.
David Varadi: “After all the biggest blowups in hedge fund history occured when too many people chased the same trading strategies because they were doing so well.”
Disgree. Most/all the biggest blowups in hedge fund history had one of two causes: too much leverage or fraud.
A “Shades of Grey” approach to an Equity Curve Filter (Anti-Martingale) avoids blow ups (i.e. that 95% or worse scenario if 10,000+ Monte Carlo simulations are run).
To avoid too many whipsaws on a good diversified strategy (implemented on 30+ symbols) my testing shows to use intermediate to long term filters (i.e. last 50-100-200 trades).
For position sizing, short term mean reversion – using a a deviation from short term trend (i.e. last 10 trades) improves baseline results roughly 10-20% based on the type of Strategy & Time-Frame.
Important that “overweight” & “underweight” of base position sizing be scaled so that average position size = 100% (so you can compare “apples to apples”