# A mental model for thinking about tail risk

Earlier today, yields for 10-year bonds in Greece shot up 200 basis points as investors contemplate the risk associated with a potential government transition. European Commission head Jean-Claude Juncker has waded into the domestic political debate warning Greeks against voting for “extreme forces” and instead going for “known faces”. These are signs that we are in a major crisis in Greece. And so I want to flesh out some related thoughts on tail risk and why I have been saying risk reduction is an appropriate strategy right now.

When I think about tail risk, I think about market events being approximated by a Gaussian bell curve with a normal distribution when the actual distribution of market events has many more data points at the two extremes of the distribution. And the model I have in my head for how this works is related to why Burton Malkiel’s “Random Walk” framework can be dangerous. Malkiel has been in the press recently and I think this Bloomberg article from Tuesday encapsulates the debate that emanates from his view:

The author of “A Random Walk Down Wall Street” has walked all the way to Silicon Valley.

Burton Malkiel has been giving much the same investing advice for four decades: Keep fees low and don’t believe advisers and fund managers who promise to beat the market. Lately, he’s championed global diversification, and especially emerging market stocks. Lots of people have listened to the Princeton University professor — “A Random Walk” is on its 11th edition and has sold more than 1.5 million copies.

Now Malkiel, 82, is bringing his message to a younger crowd. He’s the chief investment officer of Wealthfront, one of the online investing start-ups trying to win millennial investors away from traditional brokers and advisers.

Making stock picks and market predictions still isn’t Malkiel’s style. But he has a lot to say about the future of the investing business, the risks that investors face today and where in the world they can find long-term opportunities.

We’re into the season of the “year ahead” predictions. How useful do you think those are?There isn’t anybody who can tell you what’s the best asset class for 2015. Nobody. I’ve never known anybody who can time the market. I’ve never known anybody who knows anybody who can consistently time the market.

Yet, at the same time, if you see risks in the market, doesn’t it behoove you to rebalance your portfolio to minimize those risks? What Malkiel is saying is that most people won’t be able to see those risks and time their rebalance effectively enough to beat the market. And so investors are better off sticking with the herd and minimizing fees in order to maximize returns. This makes a lot of sense. But at the same time, I am left unconvinced because there are investors who outperform the market by taking a value investing strategy that is in essence a market timing view which rebalances asset allocation based on what is expensive and what is inexpensive at any one given time. And the mental model I have explains why this strategy can succeed.

Let’s start with 17th century philosophers Descartes and Espinoza. James Montier, who is now at fund manager GMO, wrote a piece in 2005 that explained that we need to suspend disbelief to process information, something Spinoza was able to prove in contradiction to Descartes framework of how we took in new information. The problem is that strongly-held beliefs get in the way of that processing. Effectively, we have decided we know all there is to know about something and refuse thence forth to suspend disbelief of new information enough to process it. Instead, when presented with data that does not fit the strongly-held view, we relieve the cognitive dissonance by re-interpreting the new data in a way that fits with our strong priors and get rewarded emotionally for doing so. I wrote about how this occurs in the political sphere back in May 2009 to make my case that people were being too pessimistic about the economy. So you end up getting what is called “the backfire effect”, where, ironically, the dissonant information actually entrenches belief in the opposite.

In markets, this means that the Malkiel random walk framework is flawed because price movements can never be truly independent of prior price movements. The herding, momentum, confirmation bias and other psychological effects that are all emanate from the way we process information guarantees that price movements are not random. They appear to be random, but they appear less random at market extremes.

When you do polls, you use a normal distribution to build confidence intervals and you want confidence that the poll is within a certain range, taking out the extreme outliers. Pollsters often use 95% confidence intervals because that is a pretty robust prediction confidence interval. On a normal distribution a 95% confidence interval is associated with what’s called 1.96 sigma or a point on the normal distribution that is 1.96 standard deviations away from the mean. For me, this is the point at which outlier events happen, not just for polling events but in markets. And that’s where the tail risk lies.

Now, if events are not truly random, the normal distribution will underestimate the probability of these tail events, such that by the time you get to 1.96 sigma, the reflexivity embedded in the information processing aspects I started out with becomes enormous. The price movements themselves have created a self-reinforcing dynamic simply based on the way we all process information. And unless you step back from this and look at the probability distribution, it’s easy to think the trend can continue indefinitely.

In a lot of markets, we are approaching that 1.96 sigma area. And it’s here where volatility begins. Here’s how I described what happens at these tipping points in May, based on some observations by physicist Mark Buchanan: “many events in nature and the financial markets have event patterns defined more by power law probability distributions than by standard Gaussian bell curve distributions. This is what produces so-called fat tails. The way [Buchanan] describes it in the book is that fingers of instability build that individually could end in a market dislocation. If you think of a forest of trees, then the instability could lead to a forest fire. In markets, it leads to a market hiccup or melt-up. Now, when enough fingers of instability build up in nature, what happens is a catastrophe of unpredictable size and scope, an earthquake of 5.0 or 6.0 or 7.0 on the Richter scale or a forest fire of 100 acres or 1000 acres or 10,000 acres. The key here is that the fingers of instability come together to form a potentially catastrophic outcome that cannot be predicted in time or size but that varies in an exponential magnitude that is not consistent with a Gaussian distribution.”

This basically means anything could happen when you get to second sigma points on the distribution. The normal distribution is lying to you at that point. You think you know what could happen but the range of outcomes is so extreme that events your models are telling you are extremely rare become much more likely.

So when we see things like oil prices dropping over 40% and Greek yields spiralling up to panic levels, it is a sign that tail risk is elevated and that irrespective of what asset classes you are operating in, now is not the time to increase risk. It is the time to reduce it and hedge. I have made the case for a number of months now that although the US remains an economy with positive growth dynamics, the nexus of excess in shale oil, leveraged loans and high yield presents a potential locus where contagion can spread and create a financial crisis. I am not saying we are going to have a financial crisis, I am saying that we are at a point where the normal distribution of potential outcomes vastly underestimates the potential for adverse market conditions. And what we do know from previous crises is that debt is an agent which creates contagion. Debt distress means that liquidity becomes a large factor in how markets work through dislocations. And when debtors are distressed, they are forced for liquidity concern to sell good assets in unrelated markets, creating contagion and precipitating stress in those markets that would otherwise be absent.

So we don’t know where this is headed. The fact that what is occurring both in the oil market and with Greece are events that are highly political makes gauging the outcomes hard. But I hope I have made a good case for understanding how important thinking about tail risk is.

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