The Hindu Business Line : Forget the extreme, hedge for normal price events

THE sharp fall in the S&P CNX Nifty on January 4 pales when compared to the 13 per cent decline on May 17, 2004. This is but yet another evidence that the distribution of asset price returns carries fat tails, or that extreme events happen more often than you would imagine. The question is: Should mutual fund managers employ risk management models to protect the downside during such extreme market declines?

This article argues that hedging such extreme events may be sub-optimal. The reason is that asset price movements exhibit price jumps, if not a pure random walk. So, extreme changes in asset prices are difficult to forecast. Of course, portfolio managers can employ jump-diffusion or other highly esoteric models to replicate the non-normal movement in asset prices. Perhaps then, the ability to control portfolio risk against extreme events may improve. But that may not be enough considering the high hedging costs and the low probability of successfully predicting extreme events. Mutual fund managers may be, perhaps, better off hedging normal asset price variations.

Extreme events: Sharp decline in asset prices are not outliers. That is why anticipating extreme events become important for risk management. An argument can, perhaps, be based on the fractal theory, which centres on the concept of self-similarity. Financial assets have been shown to adhere to fractal theory. This means that price patterns are scale-invariant. That is, intra-day asset price movements are similar to patterns graphed on a weekly, monthly and yearly basis. If extreme events cannot be predicting intra-day, how can they be predicted for a longer horizon?

Some portfolio managers employ extreme value theory to control portfolio risk against events such as the May 17 decline. Others use non-normal distributions such as the Edgeworth-Sargan density to account for the fat tails. It is moot whether mutual funds in India would want to adopt such sophisticated risk management models. And even if portfolio managers equip themselves with such models, there is another task to be performed.

Long-horizon hedges: At present, exchange-traded equity derivatives are available for only three consecutive months. In most cases, options and futures are not actively traded beyond the near month. The market needs to provide long-term hedge products such as Long-term Equity AnticiPation Securities (LEAPS) traded on the Chicago Board of Trade (CBOT). LEAPS has a two/three-year life from the date of listing. The CBOT also has Equity FLEX options, where investors can custom-tailor their requirement. Of course, such kind of sophistication may take a while to be adopted in India.

Till then, the market could offer long-dated options for hedgers. The problem is, however, of costs. At present, equity options market suffers from inefficient pricing. Consider this. The implied volatility of index and equity options is far higher than the volatility in the underlying. Such a phenomenon persists for at-the-money options as well. Even adjusting for the assumption of lognormal distribution of asset prices that most "normal" option valuation models make, the difference between historical volatility and implied volatility is large. If such inefficiencies are transported to long-dated options, the absolute premiums will be very high. This will make hedge unattractive for professional money managers.

OTC products: Mutual funds could of course look at OTC products such as equity-default swap. This swap works in the same way as a credit-default swap except that trigger event will be a sharp decline in asset prices due to market risk. Swaps are costly and illiquid. Considering that forecasting extreme events is difficult, equity-default swaps could drag actual returns when the portfolio is hedged and such event does not happen.

Portfolio managers are, however, better equipped to forecast "normal" changes in asset prices. This event can be hedged effectively. Extreme events have to be left unhedged. Of course, this strategy presupposes that unit-holders do not have fixed investment horizon. Empirical evidence suggests that asset prices mean-revert after extreme events. This suggests that the unit-holders can extend their investment horizon to enable portfolio managers to recover losses incurred during extreme events.

(Feedback can be sent to bvenky@thehindu.co.in)

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