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Opinion

At Yahoo: Accelerated Correlation

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…

  • ayondutta says:

    >I like the way you ended. That's some chutzpah, beyond the usual finance article.

    Ironic that some analyst never give up their inclinations to model even the 'unmodelable'. After discovering a black swan it's like searching for a blue elephant and a green cow.

    But all of this correlation study actually reminds me of the Heisenberg's Uncertainity Principle. Though it was a two variable concept, i.e., mass and momentum, it may be extended to multi-variable scenario.

    On a similar note, studies have revealed that volatility in markets is largely caused by trading itself. (Verified this in John Hull's book about a research paper by K.R. French and R. Roll)

  • Anonymous says:

    >"High growth means high inflation, because even the farmers will demand their portion of the growth" – The food price inflation in India is chiefly because the price signals hardly reach the farmers. If the farmers start getting good prices & participating in a market(opening up of retail, may be), the increased production should offset the price increase in due course. The same if the govt allows imports of agri produces. This notion that high growth always leads to high inflation and food inflation is rather naive & a man-in-the street economic view.

  • Anonymous says:

    >You follow inflation with much passion, I wonder if you track RBI's open market trading operations.

    http://articles.economictimes.indiatimes.com/2011-02-22/news/28621451_1_central-bank-bonds-open-market

    http://www.lewrockwell.com/murphy/murphy113.html

    This is how RBI increases money supply & inflicts inflation on the unsuspecting masses of India.

    Please stop perpetuating this absurd view that "higher growth causes inflation" – Higher economic growth means more goods/services produced. How can more goods produced cause the prices of goods to rise? True economic growth can only reduce prices of goods & thus reduce inflation. Like in technology products. Prices should go down.

    What we have in India is more of growth in monetary turnover(Rupee value of all transactions) & some economic growth. We will never know how much India's supposed growth really is economic & how much of it is RBI driven.

  • Anonymous says:

    >Mr. Deepak Shenoy explains important concepts in very lucid manner.
    I am glad to have discovered such a great blog.

    Can I get links to other good blog/bloggers/books in finance space?

  • Deepak Shenoy says:

    >Ayon: Thanks, you make some very good points!

    Anon1 and 2: you also make good points, and I'll clarify.

    1) RBI OM operations are the same as buying dollars and releasing rupees into the market. We don't get detailed reports on the dollar buying but it seems to have reduced in the last year, and the OMO is just a counterbalancing element on the balance sheet. Yes, money supply has increased and that too contributes to inflation.

    2) First, why inflation will go up when there is eco growth. We all know that productivity increases should increase supply and therefore prices should slow down, but productivity lags demand. In the lag period, prices rise. The rising prices are sticky on the way down, depending on how commoditized the element is (that is – rice prices will moderate, but not, for instance, restaurant prices). Therefore inflation will perk up in reality, although theory seems to suggest otherwise. The amount of productivity gains India has had, in the recorded inflation elements, is small compared to the growth in demand. In fact, as sustained primary level inflation continues, it spills over to teh more sticky secondary prices, and makes overall prices higher. (Secondary is 65% of our WPI)

    Some demand growth is also due to the nature of products that are now in demand. With growth comes a higher demand for stuff that was otherwise not so much in demand. People graduate from eating more staples to cereals, milk, meat and so on, all through the price chain. That change in demand also adds to price growth, which is again sticky on the way down.

    3) Thirdly, technology price changes are about obsolescence as much as productivity growth. If a new product makes an old one obsolete, then you will see economic growth in that, and depending on how you measure prices, there will be deflation or disinflation (like in cars). But you can't do that with MOSt of the Indian economy – eggs are eggs, you can't make them obsolete. Same with services or housing. So productivity gains are lower in comparison with demand increases.

    4) It's also about how inflation is recorded. India doesn't even really record services and rent which are significant parts of our economy, just WPI is used. That means inflation will increase (or decrease) more dramatically than inflation in the spender's account if the growth is not uniform – i.e. as cost of services grows you may not see inflation, but when that growth spills over to product purchases, it starts to show. High sustained growth will eventually reflect in recorded inflation, unless you do stupid things like the US does (removing energy and food, hedonic adjustments and so on).

    Overall, this leads me to believe that with very high nominal growth we will see high inflation. Your theory is okay at small levels (perhaps <5%) but when we grow the economy 20% year on year, the correlation with inflation accelerates. It's all in the extremes mate.