Link between daily volatility and prices

MARKET INSIGHT

It's taken for granted that volatility rises during choppy trading when share prices are swinging rather than moving in one clear trend. And also when prices are trending down. This is true of individual shares as well as of entire markets and it appears prima facie to be true for India.

Daily volatility is conveniently expressed in terms of the high-low range of an index (such as the Nifty) as a percentage of its daily close or (High-Low)/Close *100. This may be less correct than dispersion measured from the average of all daily quotes but it can be done more easily on publicly available data.

Since January 2002, the daily average of this crude measure of volatility is 1.88 per cent. The median is 1.58 per cent . So, half the sessions have seen volatility less than 1.58 per ent. From January 2002 to April 2007, the Nifty rose 253 per cent "� a CAGR of 27 per cent.

Take the 2002-2007 average as our benchmark. Compare 2004-2007.

In calendar 2004, the market gained 8.79 per cent from January to December. The average daily volatility that year was 2.14 per cent. Thus, above-normal volatility was associated to below normal gains. In 2005, the volatility was 34.11 per cent while the market gained 1.67 per cent. That means above-normal gains were associated to below-normal volatility.

In 2006, the daily volatility was 2.14 per cent while the market gained 39.86 per cent "� this time, above-normal gains was associated to above-average volatility.

There were two large selloffs. In May 2004, the central government changed and, between May-September 2004, the Nifty suffered a peak-trough loss of 29 per cent. The volatility spiked to 5.23 per cent. The other selloff in May 2006 saw the Nifty lose 31 per cent; as volatility rose to 4.44 per cent. If we omit that period, the Nifty's 2006 volatility was 1.80 "� below normal.

Since January 1, 2007, the Nifty is down 6.84 per cent. Daily volatility has averaged 2.17 per cent. We can split 2007 into two phases. From January to early February, the Nifty gained 4.49 per cent while volatility was 1.46 per cent (below normal). Since February, the market has dipped 8 per cent and volatility has been 2.70 per cent.

There is an apparent relationship of higher daily volatility with periods of decline. To prove such a relationship would require statistical rigour well outside the scope of this column. Nevertheless it is significant enough to trigger thoughts for a trader.

How do you exploit or hedge volatility, with or without clear price direction? If daily volatility is inversely linked to prices, can we create trading tools that exploit this? The best instruments are highly-leveraged derivatives.

The traders' model would have to be finetuned. You could compare something like a 10-day moving average of volatility as a trigger to trade the volatility. Your "sell" signal would be a session that displayed excessive volatility versus 10-DMA and "buy" vice-versa.

Your trading perspective would depend on date till settlement. You would consider the frequency distribution of higher volatility sessions. Work out how often a session of say, volatility of 2.25 would trigger a downtrend, etc.

If you got an effective model, there's money to be made. A less complicated and safer method may translate high volatility and lower prices into reasonable profits by exploiting the fact that high volatility also translates into differences between spot and futures prices.

During up trends, futures positions tend to run at premiums to spot whereas during down trends, futures run at discounts to spot. It's possible to arbitrage a cash-and-carry position when the future is at a premium by simply buying cash and selling the future. By reversing close to settlement when prices align, you lock in the profit. If you find such positions close to settlement, a 1 per cent gain can annualise into substantial returns.

A reverse cash and carry occurs when futures are at a discount to spot. Then, the stock must be sold and the futures bought in the initial trade.

This involves stock-lending, with additional charges and regulatory hassles. However, Sebi has finally agreed to resurrect a stock-lending mechanism and allow institutional participation.

Exploiting cash-futures arbitrage isn't really on the cards for retail players because it requires massive volumes. But it is possible to buy arbitrage funds. These relatively new instruments have given returns marginally better than debt funds. The enabling of stock-lending and the promise of high volatility for the near future may boost returns considerably in 2007-08.