On Yahoo, you’ll find me writing about Accelerated Correlation.

Accelerated correlation

I heard recently that a $1 change in crude oil would impact our fiscal deficit by 0.80%. The calculation is simple. India imports about 750m barrels of crude per year. A $1 hike in crude is equivalent to $750 million more to be spent buying crude, which at the rupee rate of Rs. 45 is Rs. 3,375 crores. That will push up fiscal deficit of about 400,000 crores by another 1%. Ceteris paribus, or “all else being equal”.

But ceteris is not paribus, if you’ll excuse the bad Latin. All else is, as usual, not equal. The fiscal deficit is impacted by multiple things — oil subsidy, fertilizer subsidy, interest paid by the government on borrowings and so on. In good times, these are reasonably independent of each other. But a rapid crude price increase changes the picture dramatically.

A 1% increase is likely to be subsidized as well. But when crude goes up 10% or 20% there is no room for the subsidy and the price increase has to spill over to actual fuel prices, which that hurts everyone through inflation. High inflation will be countered with high interest rates, which even the government will have to pay on its borrowings. Fertilizer creation involves natural gas, which moves with crude; and so up goes our fertilizer subsidy as well. The impact to the deficit, on an extreme move, is probably much higher than the 0.8% assumed.

And subsequently, our behavior will change — we’ll use lesser oil. We’ll probably have a recession. That changes deficit structures much more dramatically, like the US has seen.

We also assumed exchange rates remain the same. But if crude goes up by 20%, we’ll need to buy more dollars to buy oil; that will drive the rupee down, and the impact is evident on extreme moves. This is sad because we should be selling our reserves to counter the downside, but RBI is very reluctant to sell.

All else is not equal, because all else is impacted by a dramatic change in one “variable”.  As that variable sees extreme changes, you see accelerated correlation with everything else that matters. It’s more like disruptus paribus.

Take home prices in the US. In 2005, it would seem stupid to say home prices in New York was impacted by overbuilding in California. Two different areas with very different demand structures. But the price drop in one area started hurting credit elsewhere since it was the banking system that lent to property. Lack of credit meant that otherwise unrelated areas got hurt and prices started falling, and people sold because prices were falling, which made prices fall some more. Indeed, even today, when the US economy seems to be recovering, housing prices are hitting rock bottom.

Indian stock markets usually perform in the same direction as the west, except for a few months in 2010 we broke away on the upside. We were no longer correlated, they announced, and it turns out we weren’t; just when our markets have crashed 20%, the US markets are up 10%. But should there be another global crisis, you’ll find everything correlated, regardless of whether a Sonia made a Karunanidhi toe the line.

An analyst might have designed an excel sheet, with independent inputs; such as “Price rise in California”, “Price rise in New York” etc.  She might then have evaluated the risk of a “stress” in each of these prices independently. She might have used past data (going back till say 1994) and demonstrated that the “correlation” of price changes in each of these areas was 0.12, a reasonably low number, enough to demonstrate that price drops were likely to be “somewhat independent of each other”.  But when it came to evaluating the system as a whole, any notion of a price drop of more than 30% country-wide would be dismissed as “too much risk”, not supported by the historical correlation. The problem wasn’t the excel sheet — the  correlation in good times was fine; the correlation in bad times becomes intense, and in mathematical terms, goes to 1.

The risk you would see in a small change to your model isn’t the same as what you see in a larger, much more widespread change. Taleb argues that such large changes are a lot more frequent than historical analysis would reveal, and it is futile to even attempt to model them. And if you tried, you could get really absurd, as Satyajit Das noted in Traders, Guns and Money, where a risk manager he knew tried to model a scenario where: A trader with a complex, secret position is hit by a bus when bicycling to work, and is unconscious with his mobile phone shattered. A big counterparty bank announcing bankruptcy, needing instant action from the now-unreachable trader. At the same time, the bank’s power supply and backup fail, so no one can even be alerted or modeling done. And so on, till it reaches “a tragedy of biblical proportions”. You could go overboard with just a fertile imagination.

We must take sweeping statements with necessary pinches of salt. Real estate prices haven’t gone down in India in the last ten years, and never all at the same time. But that doesn’t mean it can’t, or that price crashes in one area won’t hurt others.

We will continue to grow at 9% every year, if everything remains the same. High growth means high inflation, because even the farmers will demand their portion of the growth. The high growth itself means that everything cannot be the same; Correlations accerate.

You could of course go the other way and see correlations that are purely accidental. The stars are aligned in this manner and that usually means the stock markets go up. If I switch off the TV in the first two overs, Tendulkar gets out. Whatever queue I choose becomes the slowest. When I leave my sentences incomplete, I make…

Now, tell them about it: