Thursday, March 14, 2013

What Can Quant Traders Learn from Taleb's "Antifragile"?

It can seem a bit ironic that we should be discussing Nassim Taleb's best-seller "Antifragile" here, since most algorithmic trading strategies involve predictions and won't be met with approval from Taleb. Predictions, as Taleb would say, are "fragile" -- they are prone to various biases (e.g. data snooping bias) and the occasional Black Swan event will wipe out the small cumulative profits from many correct bets. Nevertheless, underneath the heap of diatribes against various luminaries ranging from Robert Merton to Paul Krugman, we can find a few gems. Let me start from the obvious to the subtle:

1) Momentum strategies are more antifragile than mean-reversion strategies.

Taleb didn't say that, but that's the first thought that came to my mind. As I argued in many places, mean reverting strategies have natural profit caps (exit when price has reverted to mean) but no natural stop losses (we should buy more of something if it gets cheaper), so it is very much subject to left tail risk, but cannot take advantage of the unexpected good fortune of the right tail. Very fragile indeed! On the contrary, momentum strategies have natural stop losses (exit when momentum reverses) and no natural profit caps (keep same position as long as momentum persists). Generally, very antifragile! Except: what if during a trading halt (due to the daily overnight gap, or circuit breakers), we can't exit a momentum position in time? Well, you can always buy an option to simulate a stop loss. Taleb would certainly approve of that.

2) High frequency strategies are more antifragile than low frequency strategies.

Taleb also didn't say that, and it has nothing to do with whether it is easier to predict short-term vs. long-term returns. Since HF strategies allow us to accumulate profits much faster than low frequency ones, we need not apply any leverage. So even when we are unlucky enough to be holding a position of the wrong sign when a Black Swan hits, the damage will be small compared to the cumulative profits. So while HF strategies do not exactly benefit from right tail risk, they are at least robust with respect to left tail risk.

3) Parameter estimation errors and vulnerability to them should be explicitly incorporated in a backtest performance measurement.

Suppose your trading model has a few parameters which you estimated/optimized using some historical data set. Based on these optimized parameters, you compute the Sharpe ratio of your model on this same data. No doubt this Sharpe ratio will be very good, due to the in-sample optimization. If you apply this model with those optimized the parameters on out-of-sample data, you would probably get a worse Sharpe ratio which is more predictive. But why stop at just two data sets? We can find N different data sets of the same size, calculate the optimized parameters on each of them, but compute the Sharpe ratios over the N-1 out-of-sample data sets. Finally, you can average over all these Sharpe ratios. If your trading model is fragile, you will find that this Sharpe ratio is quite low. But more important than Sharpe ratios, you should compute the maximum drawdown based on each set of parameters, and also the maximum of all these max drawdowns. If your trading model is fragile, this maximum of maximum drawdowns is likely to be quite scary.

The scheme I described above is called cross-validation and is well-known before Taleb, though his book reminds me of its importance.

4) Notwithstanding 3) above, a true estimate of the max drawdown is impossible because it depends on the estimate of the probability of rare events. As Taleb mentioned, even in case of a normal distribution, if the "true" standard deviation is higher than your estimate by a mere 5%, the probability of a 6-sigma event will be increased by 5 times over your estimate! So really the only way to ensure that our maximum drawdown will not exceed a certain  limit is through Constant Proportion Portfolio Insurance: trading risky assets with Kelly-leverage in a limited liability company, putting money that you never want to lose in a FDIC-insured bank, with regular withdrawals from the LLC to the bank (but not the other way around).

5) Correlations are impossible to estimate/predict. The only thing we can do is to short at +1 and buy at -1.

Taleb hates Markowitz portfolio optimization, and one of the reasons is that it relies on estimates of covariances of asset returns. As he said, a pair of assets that may have -0.2 correlation over a long period can have +0.8 correlation over another long period. This is especially true in times of financial stress. I quite agree on this point: I believe that manually assigning correlations with values of  +/-0.75, +/-0.5, +/-0.25, 0 to entries of the correlation matrix based on "intuition" (fundamental knowledge) can generate as good out-of-sample performance as any meticulously estimated numbers.The more fascinating question is whether there is indeed mean-reversion of correlations. And if so, what instruments can we use to profit from it? Perhaps this article will help.

6) Backtest can only be used to reject a strategy, not to predict its success.

This echoes the point made by commenter Michael Harris in a previous article. Since historical data will never be long enough to capture all the possible Black Swan events that can occur in the future, we can never know if a strategy will fail miserably. However, if a strategy already failed in a backtest, we can be pretty sure that it will fail again in the future.

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The online "Quantitative Momentum Strategies” workshop that I mentioned in the previous article is now fully booked. Based on popular demand, I will offer a "Mean Reversion Strategies" workshop in May. Once again, it will be conducted in real-time through Skype, and the number of attendees will be similarly limited to 4. See here for more information.






34 comments:

Anonymous said...

I would like to counter point one: one can use long options to "play" the mean reversion and hence reduce risk significantly. Also, more often then not once the mean has been reached it is being overshot so as to create more upside than just the mean.

Ernie Chan said...

Anon,
That is a good point.

However, the time decay of options tend to make long-term mean-reversion strategies less profitable, while transaction costs due to bid-ask spreads tend to make short-term mean-reversal strategies implemented by options unprofitable.

Ernie

Anonymous said...

Hi Ernie

I disagree with point 1. The true defining feature of an antifragile strategy is positive skewness. More upside than downside as Taleb puts it. This can be achieved with either MR or MOM strategies.

mathtrading said...

Hi Ernie,

Good observations.
In regards to High Frequency strategies, you could consider them more antifragile than lower frequency strategies also because with the former it should be quicker to understand if they stop working/start deteriorating.

Similarly, you could argue that Mean Reversion strategies are more antifragile than Momentum ones in a sense because typically they have a higher win % than Momentum strategies (and so again - theoretically speaking- it should be easier to detect anomalous performance).


I guess overall what you want is a system that is as robust as possible against different types of biases.

Andrea

Anonymous said...

Interesting post Ernie!

I'd argue that mean reversion strategies to the short side are less risky than to the long side(if a blackswan was to occur) due to the fact that the market falls substantially faster than it rises therefore the momentum/velocity to a short seller is beneficial if there call is correct but extremely detrimental to the one who is long at that point in time.

I have to disagree with Talebs notion that markets are unpredictable in the short term and I'm sure you would also agree with that. The man is a genius without a doubt but I just find it ironic that his hedgefund is called empirica (after empiricism) yet he rejects the empirically hypothesis in the markets and hunts for these black swans.

Anonymous said...

Hi Ernie

Is this antifragile thing just a reinvention of robustness? I would also claim that robust cover a broader scope than antifragile. Also you said:

"Correlations are impossible to estimate/predict. The only thing we can do is to short at +1 and buy at -1."

What do you mean here? Short what and buy what? Correlation does not tell you the direction afaik.

Thanks for another good post.

Ernie Chan said...

Hi Anon,
Please give an example of how you can construct a MR strategy that has more upside than downside in face of a Black Swan event. I maintain it is impossible, so you just need to give me one counter-example to refute me.
Ernie

Ernie Chan said...

Hi Andrea,
Yes, MR strategies have higher winning ratios, and indeed easier to detect when they stop working.

However, the problem is not whether they work most of the time. It is what happened during that one time when they didn't work (e.g. on the day of flash crash). Or more importantly, how they will behave in face of a future unknown catastrophe that we can't yet imagine.

Ernie

Ernie Chan said...

Hi Anon,
I quite agree that a MR strategy that shorts only will be less fragile.

Taleb's fund mainly bought OTM options. So he is practising what he preaches.

Ernie

Ernie Chan said...

Hi Anon,
Taleb defines robustness as "insensitive to Black Swans", while antifragility is "benefiting from Black Swans" (such as winning a lottery ticket).

Indeed, how do we buy/short correlation? The paper that I linked to tells us how. By buying index options (straddles), while shorting a basket of options on the index components, we are long correlation between the index components. If the correlations go up, the volatility of the index will go up relative to the volatility of the components, and so will the index option price relative to the price of options of the components, and our positions will make money.

Ernie

Anonymous said...

"I quite agree that a MR strategy that shorts only will be less fragile"

I could not disagree more.

With a short you have a number of factors that are horrific. For starters, you have the upward drift. Second, It is much easier to create a robust long only strategy, at least based upon everything that I have done. Lastly, when short your equity and notional exposure are moving in opposite directions.

Sure you can re-balance, but you can do the same thing when long. Think about what happened to the

Being caught short thinking "mean reversion" when equity is going down, notional exposure is going up, and the upside is unbounded is perhaps the most painful form of psychological torture that the market can dish out.

At least a long side strategy requires you to be active to get into this same position - with a short it just "happens" and you can watch as you are reduced to oblivion. I would bet that shorting the SP has caused more untimely exits from this world than going long - macabre as such thoughts are.

Mean reversion trading is a misnomer. Calling it mean reversion gives false confidence and is only an analogy - mistaking this analogy for reality is the source of many "mean reversion" risk problems.

Ernie Chan said...

Anon,
I quite agree that if one insist on holding on to a short position in a MR strategy, it can be more dangerous than holding on to a long position.

However, prices tend to spike up less than spike down. So the risk of blowing up within one trading session is lower with shorts. We always have the option of exiting the short position at a loss at the end of the session. But if one is levered, we may be wiped out by a big spike down.

Ernie

Anonymous said...

"Taleb defines robustness as "insensitive to Black Swans", while antifragility is "benefiting from Black Swans" (such as winning a lottery ticket)."

Winning a lottery ticket is NOT a black swan.

Market crashes are only black swans to longs. They benefit shorts.

Black swan depends on perspective and thus Taleb tries to make it an absolute by defining a new non-existent term that does not make sense.

"This man is brave but that man is antibrave?"

"This lady is lovely but that one is antilovely?"

Let's get serious and stop promoting absurdity. As soon as this blog mentions Taleb and antifragility it loses half of its credibility mayby for a few dollars of fees from Amazon from that referer link in the beginning.


Ethan Masa said...

Hi Ernie,
very good article! Finally a quant dare to speak back to Mr Taleb! Last time he was on CNBC says he only own stocks options!
He is right in his three books on trading related issues.However, he mentioned once about Jim Simons and never discussed much about it.
I would rather run a pool of algo trading than owning stock options at current level.
Nevertheless, Taleb is still one of best mind out there!

Ernie Chan said...

Anon,
Black Swans are defined by Taleb as extremely rare events, but whether they are beneficial to you or not depends on your strategy. As you said, if you were short, and Lehman collapsed, this Black Swan was very beneficial to you. However, your strategy would still be fragile, because if instead of a Lehman collapse, it got acquired at a good price, you would be hurt. The only way your strategy would be antifragile is if you were long options, so that you would have benefited in either directions, and would only lose the premium if nothing happened.

Buying a lottery ticket is antigragile, because the upside is huge, but the downside is minimal.

I see that you are the anti-Taleb. However, I would not refrain from discussing trading and risk management ideas or philosophies here just because half the readers might disagree with them.

Ernie

Ernie Chan said...

Hi Ethan,
Taleb mentioned in this book that he thinks most financial options are either too expensive, or at least fairly priced. The book is more about finding options in non-financial endeavours.

Ernie

Tom said...

What I dislike about Markowitz portfolio optimization is that it makes asset allocations preferences based on past performance. So nothing is to say the portfolio will perform completely opposite over the next time period.

I suppose one way of getting around this is to randomly sample returns etc from each asset and then perform the optimization.

Ernie Chan said...

Tom,
If you randomly assign returns, then why bother to use optimization at all? Why not just assign equal weights to all assets?
Ernie

Jane said...

Ernie,

Point #6, "Backtest can only be used to reject a strategy, not to predict its success" is very thought provoking. If I assume this statement to be correct, then my next assumption is, once I find the strategy that fits my definition of success, I have no more backtesting/optimization. Is that a correct assumption?

If so, then my energies need to turn to risk management? Is this correct?

Assuming all the above is correct I finally get to my question. If my strategy is MR, I need to manage my left tail risk. Can you please comment on the various ways you manage your MR left tail risk.

Jane

Ernie Chan said...

Jane,
I would not spend much time optimizing a strategy, except if you have developed better insights into the rationale of the success of the strategy and want to incorporate those insights.

I have listed a 2 risk management methos for MR strategies here:

1) Stop loss or buying options.
2) Constant proportion portfolio insurance.

Ernie

Christopher said...

MR strategies only by buying at low point during panic market, like warren buffett did

Ernie Chan said...

Christopher,
If we are not Warren Buffet, how do we determine where the low point is?
Ernie

Anonymous said...

Hi Ernie,

I have a question regarding market orders at IB.

Assume there are 100 shares bid at 20 and 100 shares bid at 19.90.

If I submit a sell market order of 200 shares, will I sell only 100 shares at 20 or will the order also go down to 19.90 an sell the next 100 shares?

Ernie Chan said...

Hi Anon,
A market order is guaranteed to be filled in its entirety, so you will be filled at both $20 and $19.9 for 100 shares each.
Ernie

Anonymous said...

Thanks for your reply Ernie.

Would you say that a market-to-limit order then is to prefer in order to not risk pushing down the stocks several levels?

As I understand it, a market-to-limit order executes at $20 and then creates a limit order at 20 for the remaining lot.

Of course the drawback is that you are not guaranteed to get 200 shares executed.

Ernie Chan said...

Anon,
Yes, your goal will be accomplished with a MTL order in IB.
Certainly, no fills can be guaranteed with a limit order.
Ernie

Anonymous said...

Hello Ernie

Are there historical data of options whre you can test your ideas like the the one you put before?

Ernie Chan said...

Hi Anon,
Yes, tickdata.com sells historical options data. But I won't promise that they will be cheap!
Ernie

Alex said...

Ernie,

I'm a long time reader of your blog. My comment/question is a bit off topic for this article, but I'm not sure if older, more appropriate articles will get your attention. My question: I've read repeatedly, in your blog and others, that ETFs are more MR than stocks ( also more predictable ). Can you describe a simple experiment to prove or lend weight to this claim? If I'm able, I'll be happy to conduct the experiment and let you know the results.

Thanks again for an informative and thoughtful blog.

Alex

Ernie Chan said...

Alex,
I am only talking about ETF spreads vs stock spreads. You can run cadf or Johansen tests on all such spreads and confirm whether there are more cointegrating ETFs than stocks.

However, even this test is not conclusive: a pair of cointegrating stock pair has a much higher risk of not cointegrating in the future than a pair of cointegrating ETF pair. This assertion can also be verified by a more elaborate blackest.
Ernie

ian wu said...

Why haven't anyone mentioned breakout trade?

Shouldn't breakout trade be the only one benefit from Blackswan?

Ernie Chan said...

Ian,
The breakout trade is an example of momentum strategy, as such it does benefit from Black Swans as I mentioned.
Ernie

Administrator said...

Hi Ernie, I followed the link to Lime Strategy Studios but there's not much of anything there to describe the platform. Can you say more or provide links to any other docs on it? I too am on a neverending quest for the right testing/trading platform

Ernie Chan said...

Hi Admin,
I am not sure that there is much documentation online. But you can always contact sales@limebrokerage.com for demos.
Ernie