A V Rajwade: Measuring financial risks

Some recent events raise questions about the risk measurement methodologies in use in much of the banking world.

As the crisis in global credit markets, which started with increasing defaults in the sub-prime mortgage market in the United States, continues to grab headlines, the standard risk measurement systems are coming into question. In retrospect, I was right in titling my analysis as "When risk becomes uncertainty" (BS August 27, September 3 and September 10). I was, however, wrong in surmising at that time that the crisis had affected European banks more than their US counterparts; the loss numbers for American banks are even larger. Merrill Lynch ($8 bn) and Citigroup (up to $11 bn) seem to be the two largest so far.

To recapitulate, risk management literature gives a particular meaning to "risk", to distinguish it from the uncertainty of outcomes in general: risk is the kind of uncertain outcomes whose probability distribution is known and, therefore, permits the quantification of the risk, with a given degree of confidence. The entire discipline of financial economics, two of whose stellar contributions are the portfolio theory and the option pricing model (Black Scholes), is based on this assumption. Indeed, risk measurement methodologies based on these principles are also at the heart of modern banking regulation, namely Basle II. The recent events raise questions about the risk measurement methodologies in use in much of the banking world: if sophisticated players like Merrill Lynch and Citigroup, who employ highly qualified "rocket scientists" to continuously improve their models, have reported large, unforeseen losses, surely something is wanting?

At the heart of the accepted methodology is the assumption that relative changes in the price of assets, measured on a continuously compounded basis, are normally distributed. Is the assumption valid? Some weaknesses are well-known and accepted. Please see the graphs accompanying this article, showing the normal distribution curve as also the distribution of the actual price changes in the dollar/rupee exchange rate and the clean price of the 10-year G-Sec, in the Indian market. It will be readily seen that the actual price changes do broadly follow the pattern of a normal distribution. But the fact is that they do not meet the tests statisticians have devised for the assumption of normality. For one thing, the distributions suffer from what is technically known "kurtosis" "" i.e. taller peaks in the centre, and fatter tails. The latter weakness is of particular relevance to risk measurement: it implies that extreme price movements at both ends of the graph are much more frequent than predicted by the normal distribution. There is of course enough empirical evidence of this, in equity (the crashes in 1987 and 2000), currency (dollar: yen rate in October 1998, and the New Zealand dollar: yen rate more recently) and credit derivatives markets (more recently; a Goldman fund manager described the price change as a "25 sigma event".) Normal distributions do not rule out such extreme price changes, but it is a fact that they seem to occur more frequently than the assumption of normality would lead us to expect.

The second major weakness is that normal distributions require each new observation to be independent of the previous one "" for instance, the height of the next adult you would be measuring, has nothing to do with the height of the previous person you measured. Independence implies that each observation "" say, the daily change in dollar: rupee exchange rate "" is random. Every participant in financial markets would confirm that this assumption is not valid "" as a rule, volatile price changes often follow each other, even as a quiet day leads to another quiet day.

It is these two major departures from the characteristics of a normal distribution which prompt mathematicians like Benoit Mandelbrot ("The (mis) behaviour of markets") and market philosophers like Nassim Taleb (the author of "Fooled by Randomness", "The Black Swan", and a recent article in the Financial Times, October 24, "The pseudo-science hurting markets") to criticise, sometimes in very critical and contemptuous terms, the methodology for risk measurement widely accepted today in the banking world, as also by the regulators. Having read and studied their writings as a student of financial markets, I feel that such criticisms also raise some questions:

They do not suggest a better methodology for measuring risk, or argue that risk cannot, and therefore should not, be measured at all. In the latter case, how will capital be prescribed?

They ignore the fact that regulators, and even developers of the models like Robert Merton, are aware of the weaknesses "" and hence endlessly emphasise back testing, stress testing, etc. "" but still find them useful for prescribing capital ratios.

One financial market which has successfully used similar techniques for a long time is the life insurance market. Again, the models work extremely well in the physical world where the entire engineering of bridges, sky-scrapers, and aircraft is based on their ability to withstand extreme stress, with a given degree of confidence. And, the safety of these engineering marvels testifies to the utility of the models.

But it is a fact that they sometimes do fail in measuring risk in financial markets, surely to the discomfort of the regulators. To my mind, this is because of two basic differences between the physical and the financial worlds:

The physical world conforms to the laws of physics. On the other hand, financial market participants are too often influenced by human emotions like greed, fear and the herd instinct. The assumption of rational human behaviour, underlying much of economic theory, is, sadly, a myth.

Even more important, the risk-reward relationship between the trader and his employer are highly skewed: if the risk results in profit, the trader gets a bonus; if there is a loss, the worst he faces is a sack. Does this tempt the trader to knowingly take undue risks?

But, paraphrasing Churchill on democracy, the current models may be the worst way of measuring risk, except for all the others!