What Goes Up Must Come Down?

LinearRegression-S&P500INDEX-0%Percentile

Relationship between one year’s returns and the next. Essentially, there’s not much of a relationship except in cases of extreme losses, which are often followed by a better year.

Investor Analytics just published the fifth in a series of articles in a new column I have in Risk Magazine’s Hedge Fund Review, which you can find here. The topic for this article is both simple and profound: since 2013 was a great year for stocks, chances are that 2014 will be bad so that the stock market maintains its long-term average. The phenomenon is call “reversion to the mean” and is the underlying logic behind thinking that a sports player is “due” (a fallacy) and for the notion that a tall parent is more likely to have a shorter child (a truth).

We looked at the returns of the S&P 500 over the past 86 years and constructed rolling 1-year windows to generate over 20,000 data points to examine in our hunt for signs that if you have a “good year” that the next year has an increased likelihood of being a “bad year”. It turns out that it’s just not so. You can read the article for the details, but it’s very clear that having a good year really doesn’t change the odds of the next year being good or bad. The average return of the next year is slightly lower than usual, but the range of returns is tremendously wide. Specifically, the overall average for the S&P500 is 7.5%, with a volatility of 20%. That means that for any given year, at the 95% confidence interval, the stock market gives a return somewhere between -25% and +40%. But following a year like 2013 (up 30%), the market returns on average 4.7% with a volatility of 17.5% which translates to a 95% confidence interval between -24% and 33.6%. See the big difference? Neither do I.

The plot in this post shows the overall relationship between two subsequent years: the first year on the horizontal axis, the second on the vertical. The large blob in the middle represents about 98% of the data, which essentially shows that one year tells you next to nothing about the next year.

The graphs we published showed a striking lack of relationship between one year’s returns and the next, except in the most extreme cases. Our conclusion is simple: your risk is not really changed from last year, and this year is has just a good chance of being good as it does of being bad. It’s up to you to make the most of it.

When Hedging Doesn’t Work

Sometimes hedges just don’t work.  I don’t mean that sometimes they don’t limit your risk enough.  I mean that sometimes they actually backfire and add risk.  That’s what happened this past weekend with several of my friends during the East Coast’s Hurricane Irene.  Here’s how it happened:

Before the Hurricane

Leading up to the arrival of Hurricane Irene in the Northeast of the US this past Saturday night, officials were sounding the alarm bells in New York City and surrounding areas.  New York City has some very low lying areas that can easily flood during storm surges, which were predicted to be particularly bad unless the hurricane changed course.  The city itself has very little experience with hurricanes since they don’t usually come this far North, but all indications were that this was going to be bad.  Mayor Bloomberg ordered mandatory evacuations of low-lying areas and the entire city’s public transportation system shut down to move the trains and buses to higher elevation.  In New Jersey, where I live, we knew that most of our rivers would overflow like they usually do during bad storms.  Predictions were for over 12 inches of rain in about as many hours.  Flood-prone towns in New Jersey and the entire New Jersey shoreline were evacuated.  Most residents of New York city stayed in the city.

Several of my friends in New York and New Jersey decided to ride the hurricane out in their vacation homes in the Catskill Mountains, about 2 to 3 hours north of New York City.  At the time, this made all the sense in the world.

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Who Defaults First: Greece or the US?

When I saw the BBC headline I thought to myself: “get with it, the US is not going to default.  This is just a game of political chicken.”  For the past several months, whenever this topic has come up, I’ve been thinking that this is an example of great showmanship by the Republicans who are going to teach President Obama a very painful and expensive lesson in using leverage when you have it.  I even read this CNN article earlier today, which summed up my take on the whole thing rather nicely.  And then I started to consider the possibility of the US Congress and the White House failing to reach an agreement.

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Gauss’s Fat Tails

The term “fat tails” is thrown around with what I consider reckless abandon.  Most times I find that people use it without having an appreciation for what it really means and then they make the wrong conclusion.  So, I’m going to take a stab at explaining what I think a correct interpretation is.  The first and most prevalent wrong conclusion is that all quants and financial models underestimate the risk of extreme events.  Wrong – there are plenty of ways to reasonably and accurately model tails.  The second is that all models use the Normal Distribution.  Wrong – there’s a host of distributions that can be and are used.  A corollary to that wrong assumption is that VaR (Value-at-Risk), in particular, always uses the Normal Distribution, which is also wrong.  VaR makes no assumptions about what distribution is used, but I’ll have an entirely different set of posts about VaR.  This post will be part one of what may be a series of posts on the topic of fat tails in particular, and this one will be limited to discuss actual data and comparing it to the most commonly used distribution, the Normal curve.

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