“Anything that relies on correlation is charlatanism”

24Feb12

This is a wonderful read for multiple reasons. Some of them:

 

– I supposedly read a lot of Crisis related material but did not come across David Li. Either I did not “get it” or his formula was not covered in depth. We have seen a lot of Black Scholes bashing, but not enough of David Li bashing.

– Amazing quotes which explain in simple words how some of these need to be thought through

“Investors like risk, as long as they can price it. What they hate is uncertainty—not knowing how big the risk is. As a result, bond investors and mortgage lenders desperately want to be able to measure, model, and price correlation. Before quantitative models came along, the only time investors were comfortable putting their money in mortgage pools was when there was no risk whatsoever—in other words, when the bonds were guaranteed implicitly by the federal government through Fannie Mae or Freddie Mac.”

Its now not surprising to understand why everyone loves “beta”. It is a single number which measures the risk of a stock. In finance circles, if you understand “beta” and master how it is computed (and the various nuances involved in computing it), you are considered to be “real good in finance”. The interviews with most I-banks (have either sat through or have heard first hand interview experience) revolve around various questions around computing beta (Simple ones: E.g. How long should the price data be taken to compute beta effectively, how do we know the fight frequency – daily or weekly prices, In what kind of instances would the time period taken not be correct etc.)

To understand the mathematics of correlation better, consider something simple, like a kid in an elementary school: Let’s call her Alice. The probability that her parents will get divorced this year is about 5 percent, the risk of her getting head lice is about 5 percent, the chance of her seeing a teacher slip on a banana peel is about 5 percent, and the likelihood of her winning the class spelling bee is about 5 percent. If investors were trading securities based on the chances of those things happening only to Alice, they would all trade at more or less the same price.

But something important happens when we start looking at two kids rather than one—not just Alice but also the girl she sits next to, Britney. If Britney’s parents get divorced, what are the chances that Alice’s parents will get divorced, too? Still about 5 percent: The correlation there is close to zero. But if Britney gets head lice, the chance that Alice will get head lice is much higher, about 50 percent—which means the correlation is probably up in the 0.5 range. If Britney sees a teacher slip on a banana peel, what is the chance that Alice will see it, too? Very high indeed, since they sit next to each other: It could be as much as 95 percent, which means the correlation is close to 1. And if Britney wins the class spelling bee, the chance of Alice winning it is zero, which means the correlation is negative: -1.

If investors were trading securities based on the chances of these things happening to both Alice and Britney, the prices would be all over the place, because the correlations vary so much.

But it’s a very inexact science. Just measuring those initial 5 percent probabilities involves collecting lots of disparate data points and subjecting them to all manner of statistical and error analysis. Trying to assess the conditional probabilities—the chance that Alice will get head lice if Britney gets head lice—is an order of magnitude harder, since those data points are much rarer. As a result of the scarcity of historical data, the errors there are likely to be much greater.

In the world of mortgages, it’s harder still. What is the chance that any given home will decline in value? You can look at the past history of housing prices to give you an idea, but surely the nation’s macroeconomic situation also plays an important role. And what is the chance that if a home in one state falls in value, a similar home in another state will fall in value as well?”

– And this:

“Li wrote a model that used price rather than real-world default data as a shortcut (making an implicit assumption that financial markets in general, and CDS markets in particular, can price default risk correctly).

It was a brilliant simplification of an intractable problem. And Li didn’t just radically dumb down the difficulty of working out correlations; he decided not to even bother trying to map and calculate all the nearly infinite relationships between the various loans that made up a pool. What happens when the number of pool members increases or when you mix negative correlations with positive ones? Never mind all that, he said. The only thing that matters is the final correlation number—one clean, simple, all-sufficient figure that sums up everything.”

– The key:

“”The relationship between two assets can never be captured by a single scalar quantity,” Wilmott says. For instance, consider the share prices of two sneaker manufacturers: When the market for sneakers is growing, both companies do well and the correlation between them is high. But when one company gets a lot of celebrity endorsements and starts stealing market share from the other, the stock prices diverge and the correlation between them turns negative. And when the nation morphs into a land of flip-flop-wearing couch potatoes, both companies decline and the correlation becomes positive again. It’s impossible to sum up such a history in one correlation number, but CDOs were invariably sold on the premise that correlation was more of a constant than a variable.”

 

 

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7 Responses to ““Anything that relies on correlation is charlatanism””

  1. 1 rajapanda

    Seriously !! what a fantastic read.. thanks

  2. 3 Siobhan Meyer

    Hi,

    I came across your page recently and I’m trying to find an email address to contact you on to ask if you would please consider adding a link to my website. I’d really appreciate if you could email me back.

    Thanks and have a great day!

  3. Hi Pradeep,

    Your post brings up an excellent point of how modern finance now equates risk with Beta. Obviously as you mention using Beta as the only measure of risks is problematic on a number of levels. Beta is a good measure of stock price volatility but true investment risk is measured by the possibility of losing money. I think most value investors view risk as being the latter, which I think goes a long way to explain why they have tended to outperform the market over long periods of time.

    Regards,

    Ankur

    • Hi Ankur,

      Agree fully on your points. A lot of those investments which depend on how accurately WACC or Beta is calculated do not see the forest for the trees (They are not even looking at the right trees for that matter!).

      Regards,
      Pradeep

  4. 6 rjt163

    Most of the times, IMO, risk and discount rate have to be based on common sense thinking about the actual risk posed by future cash flows and how volatile the cash flows can be.

    Beta is an important tool for altogether different reasons. You need a quantitative/ statistical measure of risk which can be reasonably justified.

    I believe that’s the reason why its used so extensively by bankers and even investment funds. Say, a PE fund does a deal and has to document it (say for LPs). Now, you can’t go to an LP and justify that I used a discount rate based on riskiness of cash flows and my common sense ! That would sound stupid. So, rather I would say I have computed discount rate just like it is done by everyone else in finance, and wow, there would be far fewer questions asked. Its the same about all equity research reports and other valuation reports – the need to justify is what makes beta so relevant.

    • These are my strong views. Actually, if the only need is to make money over long periods of time, beta is irrelevant. Beta, like a lot of other things, is relevant only for convincing others.

      “Say, a PE fund does a deal and has to document it (say for LPs). Now, you can’t go to an LP and justify that I used a discount rate based on riskiness of cash flows and my common sense ! That would sound stupid.” – According to me, you would look stupid to LPs only when you don’t make money over reasonable periods of time. LPs are bothered the least on how you did the valuation modelling. I mean, you cannot go to the LP and tell, hey, I actually used the perfect beta for Suzlon in 2007 and still the stock went down 90%. I don’t think that will lead to much sympathy.

      “Its the same about all equity research reports and other valuation reports – the need to justify is what makes beta so relevant.” – As you rightly said, it is only relevant for professionals who do “investing” as a job. I am paid X, so if I don’t even compute beta, then how can I deserve whatever I am getting!

      To be frank, I would think very few people even in the traditional finance world sweat a lot of time over beta. I think its used more by academicians. I may be wrong though.


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