Tail Risk: Who’s Afraid of King Kong?
How quickly we forget.
After a bullish 2018 for the markets, all of a sudden, tail risk is back on everyone’s minds.
Which means it’s a good time to talk with mathematician and risk management expert Raphael Douady. Douady has authored a number of scholarly articles on tail risk and collaborated with Nassim Nicholas Taleb, of Black Swan fame, among others. He will be speaking at the “Value Investing and Risk Analytics in the Age of Technology” conference on Saturday, 28 April 2018, at Stony Brook University in Stony Brook, New York.
What follows is a lightly edited transcript of our conversation.
CFA Institute: Let’s begin with one of your sayings, “Sometimes the markets fear a mouse, but at other times they are not afraid of a King Kong!” What do you mean by that?
Raphael Douady: The point I’m making here is that you can have inherent instability within the market when the smallest disturbance can turn everything upside down. Whereas sometimes you have such a stability that even if you have a King Kong, nothing will happen.
The best example in nature is the case of a forest. Let’s say it is very wet. Even if a fire ignites, it will remain contained. If the forest is dry, like California’s last summer, a single cigarette or even the sun or an accidental thunderbolt can burn down the whole forest.
Speculative situations, when a bubble starts building up, are similar to a game of musical chairs. The least likely signal may mean that the game is over and the whole market blows up. This pattern is consistent in every financial crisis.
At the same time people do suffer from FOMO — fear of missing out — especially since every bull market scales a wall of worry. With the benefit of hindsight, one can look silly sitting in cash on the sidelines, paranoid about a random cigarette’s potential to cause a devastating firestorm.
Exactly, you cannot really anticipate when a random event will occur. The frequency of each event occurring is inversely proportional to its size. There are a lot of small events and far fewer major events.
When the market is prone to blow up on a small event, you can be sure that within a short period of time it will blow up, because small events come randomly but frequently.
An example actually, and it is terrible to mention it, is 2000–2001:
- In March 2000, the end of the dot‑com bubble was triggered at some point, for no reason, by a story about DELL and the Japanese economy. It was so simple and barely mentioned in the news. Suddenly, the whole dot‑com bubble blew up. Everybody knew it was a bubble. Everybody agreed that it was obvious. Still, people were investing like crazy, hoping someone would be even crazier . . .
- Just 18 months later, and this is very much often the case, after a crisis bursts the situation is very stable. And then tragically . . . 9/11. In our living memory, can you think of a bigger geopolitical event than 9/11? Despite its conspicuous significance, 9/11 is a small glitch in the history of the market compared to what happened a year before, in March 2000. Relatively speaking, it is just a small price drop.
This demonstrates how the market can react to a mouse when it is in an unstable situation. On the contrary, a different market can almost ignore a King Kong.
To gauge this Jekyll and Hyde duality, is it wise to use volatility or standard deviation of past returns as a proxy for risk?
Volatility is partial information. I would not discard it completely. That would be a mistake . . . The problem is, as the saying goes, “Better no information than partial information,” because it gives a false sense of security.
That is typically the case when people talk about volatility targeting. The reason is volatility goes up and down very fast. In particular, it has shocks on the upside, but then tends to slow down to a more regular pace. Look at the period we just had: The market was crazy in January. Then there’s a strong correction at the beginning of February. Since then, the market has been rather volatile. It went up and down. It remained volatile since, whereas just before there was almost no volatility. A typical pattern: an enormous trend with no volatility, followed by a very volatile, trendless period.
There are periods of high volatility and periods of low volatility. If you just monitor the volatility, you get some sort of regularization of the size of the tail. It gives an element of risk control, tough partial.
Huge volatility spikes precisely occur upon large black swan events. When you have these outsized events, you don’t have time to act. You don’t buckle up when the accident is coming! Instead, put in place something that can potentially anticipate that. Even though you’re in beautiful weather, the storm is coming, or is likely to come. You can never eliminate uncertainty. You cannot be sure exactly when an event will strike, but you can be sure that it will occur at some point.
One must permanently be prepared. You don’t want to have all the sails out when the storm hits. Even if you have, let’s say, a 10% or 20% chance the storm is coming, and still have 80% or 90% chance it’s not coming, you may wish to take some of your sails down. Don’t invest massively even though volatility is very low. Monitoring volatility only is an enormous mistake. Not monitoring volatility at all would also certainly be a mistake.
The devious nature of tail risk means that, when it’s the furthest thing from everyone’s mind, investors may “bleed to death,” paying up for seemingly unnecessary insurance. When tail risk is front of mind, the insurer will bankrupt you by selling you a policy because it’s so expensive. What should an investor do?
This is a difficult question, of course, because of the cost of insurance . . . When you have a car or a house, you don’t discuss it. You buy insurance all the time.
Markets buying insurance all the time can be prohibitive. If the focus is on the long‑term performance, that becomes something that you really have to monitor.
Here’s my opinion: First of all, having a cheap, faraway, permanent insurance makes sense. That’s exactly the solid method: never be completely naked, always have something that covers you at some point.
That doesn’t mean that it will really insure you against everything, but it will cap your losses. Actually it will still keep you exposed to a certain amount of loss, but not as much as if you were buying an all-weather indemnity which is completely cost prohibitive.
It may be feasible to finance purchases of puts by selling some at-the‑money call options. That requires balancing the net cost by monitoring the premiums of these two options.
The second useful technique is to build tools to measure market instability. Such tools won’t precisely anticipate when the market is going to blow up, but at least they let you get a sense of how dry the proverbial wood is. Then you can say, “Okay, in some situations, I want to spend a bit more money and have a better protection. And in some other situations, I can live with a weaker protection, because, yes, something may happen, but the probability is lower.”
You can play on that. I’m not saying never being completely naked, but at least you will find the appropriate strike price. Obviously the closer this strike price to the money is, the more expensive insurance will be — however if you feel that it is very important to have good insurance, you would want to pay for it.
Some other moments, on the contrary, the shock may still occur, but you can relax a bit and be more aggressive. For example, how many firemen do you put on high alert to watch out for the forest fire? In the summer, you need more firemen than in the winter. The fire still may occur in winter, but it will be far less frequent and fewer firemen are required watching.
Now that makes sense, but what about Harry Markowitz’s modern portfolio theory (MPT)?
That is very, very dangerous. MPT adds risk precisely at a moment prone to higher volatility. It makes you sail with all the sails open, only by observing the weather yesterday and maybe not even today. It doesn’t anticipate the possible weather tomorrow.
The problem is that a typical Markowitz portfolio makes money only in calm periods. When there is an event in the market, it drops about twice as much as simple buy and hold. Tail risk makes MPT very, very dangerous.
Diversification is supposed to help during tough times. Do you have a view on that?
With diversification, same story. When the tail risk strikes, you are completely undiversified because what is uncorrelated in normal times becomes correlated in a crisis.
You have to focus on what is uncorrelated and even sometimes negatively correlated in extreme moments. Risk management via diversification means that, in portfolio construction, you can completely disregard what happened in normal times. The only question is how things happen in the extreme.
This is what will drive any reasonable risk figure. Portfolio risk will essentially be a function of how things are correlated in the extreme. This is a golden rule that people tend to forget.
Are you essentially kicking out the central plank of investment theory?
I’m completely kicking portfolios built on correlations.
Because correlations are inherently unstable, and they converge to 100% in a crisis?
It’s even worse than that. Suppose there are two regimes: one normal regime with certain regime of correlations, and another extreme regime with another regime of correlations.
I’m not saying that necessarily correlations are higher. Sometimes, they can be opposed, etc. Let me take the example of managed futures or CTAs [commodity trading advisors], who can be negatively correlated to the market in some situations. We saw that in 2008: When the market drops, CTAs will make money. If you wanted to be safe in 2008, you’d better have been invested in CTAs.
Now, you build your portfolio. You have one regime, let’s say, representing 90% of the time. The other regime is 10%. However, 10% is a significant amount of time. It’s not completely rare, it’s just much less frequent than the other. It’s like you have a weekday regime and a weekend regime. Put another way: there are more days in the week than Sunday. Then in a minority of the time you get a Sunday regime.
The extreme regime has a different set of correlations. Suppose you optimize your portfolio only for a Monday to Saturday regime. You build your portfolio for this benign set of correlations. It will absolutely not be optimized for the scary Sunday regime. What happens is that you get a portfolio that understates volatility. Let’s assume that the volatility of assets in your portfolio is around 20%. Diversifying on a portfolio-wide level will, typically, reduce the volatility to a mere 10%. Volatility has seemingly halved, thanks to diversification. Perfect.
On Sundays, nevertheless, the extreme volatility remains unreduced. What does that imply? That you built a portfolio that has a much fatter tail than your initial assets. Initially, assets have fat tails, that is, a ratio between normal and extreme events, which you already ignored. The portfolio you have built now has even fatter tails, while the ratio of the extreme volatility to the normal volatility has been multiplied by two.
The mechanism by which you have optimized your portfolio, instead of creating a safe portfolio, has created the most unsafe portfolio that you can imagine.
You basically assured yourself a nice game of Russian roulette?
Exactly. This is why Markowitz optimization is not only a bad idea, it’s dangerous. It’s not only that it doesn’t work. It works against you. Now, there is something that’s well‑known in medicine. There is a principle in medicine, if you ask any doctor with experience — they will tell you, “I don’t know of a medication that is neutral. It does not exist. If a medication doesn’t have proven benefits, you can be assured it is harmful.”
The commonsense approach of “It can’t hurt” is the wrong approach. Any doctor who really has been around will tell you that if you don’t see a positive effect from the medication, don’t take it, stop, because it will have a negative effect.
It’s the same thing with investments: Other than cash, none have zero correlation. An asset either is potentially correlated to your portfolio, or it is a hedge. That is, if it doesn’t explicitly reduce your risk, you can be sure it will increase it.
I get it. Talking of the doctors, infamous Long-Term Capital Management (LTCM) famously employed not MDs but many PhDs in economics along with Nobel Prize-winners Myron Scholes and Robert C. Merton who sought to master tail risk. Why did it blow up so spectacularly?
I was in touch with LTCM team early on when they created the fund. What happened is that [John W.] Meriwether had hired a bench of very brilliant mathematicians, PhDs, etc. The bench of talent was very deep. . . . He was fascinated by those people.
Let me explain using an analogy with Formula One:
- Who are the best car drivers, the people who master a car like nobody else, who really are in control in extreme situations? Formula One drivers are extraordinary. We are vastly inferior in comparison, even though we know how to drive a car. These guys can monitor a car at speeds over 200 miles per hour.
- What state-of-the-art cars are the most stable — you can do anything with it, and it will stick to the ground? Formula One. Best engineering, huge sophisticated tires, etc.
- What streets are completely regular — not a single pebble, absolutely flat, not a single wrinkle, etc.? Formula One circuits.
Where do we have the most collisions? Formula One.
What is the catch here? The catch is that nobody in a city, with your driver’s license or mine, is crazy enough to drive a car 200 miles an hour. If you have very clever people, they will do things not a single non‑insane people will do.
They do things that are completely crazy. They seem to master it. But what happens when you hedge and hedge and hedge all sorts of risk is that harmful events arrive with no warnings, because all warnings have been erased.
Let’s talk about Black-Scholes‑Merton. The idea of hedging risk is very often half hedging. It works in mathematics, but they are hiding the dust under the carpet. That’s exactly what happened with LTCM. They thought they were hedged.
What happens when you hedge risk? The things that you become exposed to become more and more nonlinear, more and more fast‑paced
You will hedge the first, the second, the third derivative. In the end, you get something that seems very controlled. It looks completely flat.
Then, when the wall is approaching, there is no sign that you are going to hit it because you’ve erased everything. You feel great, and then boom! You explode.
They are completely unaware of the problem.
It goes back to October 1987. I don’t think anyone has really learned the lesson of the 1987 crash. Portfolio insurance presents a very, very important lesson. You think that you have created convexity — you can limit the downside and asymmetrically benefit from the upside — and it looks to you like you created this favorable payoff. But when it becomes systemic and everyone follows the same playbook, it’s a different question.
The mechanism by which you create convexity precisely at the same time creates these complex internal dynamics for the market as a whole. These put a system in place so that if the market starts dropping, you will create a huge cascade of selling orders.
You accelerate the mechanism by which the whole market protects itself by selling when the stop levels are hit. In fact, the market is in a tragedy of the commons situation. Individual protection leads to extreme fragility of the system as a whole.
Because it’s dynamic.
Because of dynamics, exactly. The fact that everybody tries to optimize creates hidden concavity. It induces the whole system, which could have been, not specifically anti‑fragile, but simply neutral, to become fragile.
Fascinating. Where can we hide from the tail risk then? Crisis alpha products?
In the crisis, surprisingly enough, people started blaming hedge funds. I would do the opposite. It’s not that I want to be particularly nice to hedge funds. I’m just looking at things as a dynamicist, and the only stabilizing power here is the vulture attitude. That is the people who say, “Well, at that price, it’s so low, that I’m buying.” The presence of vultures is, in fact, very healthy for the market, surprisingly enough.
You buy when the blood is in the streets and the hyenas are prowling.
Absolutely. No one likes to see a lion eating a poor antelope. Then you say, “Well, let’s take care of this.” Remove all of the lions, and then you get completely invaded by antelopes.
And antelopes all starve to death because they ran out of grass.
Exactly. It’s all metaphors. Sometimes the people who look like the bad guys, in fact, can save the system.
To finish up, what can people expect to hear about at the panel at Stony Brook on 28 April?
Precisely, all the questions that we’ve been just discussing will likely be addressed. Perhaps not all of them, maybe in a different manner, maybe some different questions. Certainly, we’ll hear people with different views, but all of them with strong valuable experience.
If you liked this post, don’t forget to subscribe to the Enterprising Investor.
All posts are the opinion of the author. As such, they should not be construed as investment advice, nor do the opinions expressed necessarily reflect the views of CFA Institute or the author’s employer.
Image credit: ©Getty Images/ CSA-Archive