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Hedge Fund Monthly

 Hendrik Klein, Director Da Vinci Invest Ltd July 2006

As part of alternative investment ideas, volatility trading strategies could be filed under the existing category of “volatility arbitrage” and “relative value arbitrage”.

Options are often viewed as complex financial instruments on the capital markets, so the opportunities of volatility as a source of investment returns are often overlooked. Implemented by an experienced derivatives trader, volatility-orientated trading strategies often have a stabilising effect on an investor’s portfolio because of their correlation to classic long-only bond investments, for example, bonds, shares and property. They reduce the risk and often act as an insurance against external shocks.

What is volatility? Why is it so important for options trading?

Theoretical foundations laid by the German mathematician, Gauss, as “Gausschen normal distribution” works on the principle that coincidental values fluctuate around a middle value in the shape of a bell curve (log normal distribution). The economists, Markowitz, Black & Scholes and Sharpe expanded on this in their formulae of portfolio theory and option price calculation.

The middle value = expected value = strike, ie using Black & Scholes formula, one can calculate the probability of a particular option making money. This makes it possible to compare all options, irrespective of their base price, term and market direction.

Fluctuating around the middle value is portrayed as a standard deviation/variance and, calculated on a yearly basis, is described as volatility. The definitions of volatility refer to the time of the calculation and the dates which serve as a basis. The “historical” volatility is the historic, annual variance of profit/prices. The “implicit” volatility is produced from the current paid market prices. On the basis of these two volatilities, the options trader estimates the “expected” volatility and if he is correct, the “expected” volatility matches the “future” volatility. The estimate of future volatility is probably simpler than predicting share rates for many options traders. Arbitrage profits could, for example, be achieved if one were to sell a 5000 DAX call option with high volatility in December 2005 and buy a 5000 Put Dax Option with low volatility in December 2005. The market risk is then balanced out by the DAX future. This arbitrage relationship is also known as call/put parity. The well-developed derivatives share markets no longer allow such “free lunches”, but there are still many opportunities for experienced options traders.

The options theory assumes constant volatilities for different options. Expensive analysis software systems allow different base prices and terms to be displayed graphically. In this way, the volatility surface in reality resembles a rough ocean with continuous waves and changing wind directions and strengths. As an experienced sailor/options trader, one can ride the waves and use the right wind breeze to make progress in one’s portfolio and trade gains without risking a lot. The different volatility structure on the basic price level is also known as skew/smile. On a term level the term is defined as the volatility curve cross-section. In order to profit from different wind strengths and directions, there are a wide variety of options combinations, eg straddles, strangles, vertical spreads, calendar spreads and many more. The constantly changing market risk is balanced out by the basic values which make up delta hedging. The delta displays how strongly an option or an option portfolio has been influenced in its option price by the market direction.

Skew/Smile

Skew/Smile shows a cross-section of the volatility surface and calculates the implicit volatility independently of different basic prices at a given term. For most share and index options the following is true: the lower the basic price, the higher the implicit volatility, as extraordinarily strong negative price crashes occur more often in practice than is accepted in theoretical models, for example, on 11 September 2001 or the 1987 October crash. This is why options buyers pay higher risk premiums for put options (and/or sellers demand higher premiums), which are expressed in the form of higher implicit volatilities (the same is also true because of call/put parity for calls, which make money). Investment funds hold shares which are secured by buying from the puts and simultaneously selling covered calls. Additional premium income can thereby be cashed and can still have a negative effect in the case of extremely quickly rising markets due to missed price profits. In practice, it is well known that quick price movements tend to go down. Upwards movements tend to take place in an ordered and slow fashion.

The steep gradient of a Skew can be the result of two important factors: the risk attitude of the market participant as well as supply and demand according to hedging elements. The factors are constantly changing so that options with the same basic price but different terms can display completely different implicit volatilities and the skew curve can have a flatter or steeper distribution. Furthermore, the skew for interest and currency options is very different to that of share options.

Term

With term, the graphic step through the volatility surface for the implicit volatility of options for different terms at the same basic price is displayed. It takes into account the different volatility sensitivity of individual expiry months and certain peculiarities, such as, several bank holidays, where there is no trading.

The graphic display of skew and term requires high-performance software and reliable data. Volatility strategies are the preserve of the professional options trader with a large portfolio. Private investors should profit from this via investment vehicles, eg funds, certificates etc.

Two types of strategies

Basically, one can differentiate between volatility spreads and gamma trading strategies. A possibility for a volatility spread would be, for example, to sell short-term options (front month) with a high implicit volatility and at the same time, to buy the delta-neutral number of one-year options with a low implicit volatility. This can be displayed via short and long straddles or also by simple call-call or put-put combinations in the same basic value with the same basic price. In this way, a virtually market-neutral position is reached which can then be balanced out in futures by delta hedging. A trading profit would arise if the premium of the short-running options declined more quickly and strongly than adjusted by the trading result from future hedging in the one-year options.

In contrast to the relative volatility spread strategy, in gamma trading strategy, one is predominantly betting that the implicit volatility of an option does not agree with the expected volatility as seen from an absolute point of view. In other words – one bets on the absolute change of volatility. If one uses the long gamma trading strategy, the aim is a particularly large profit if unexpected external shocks occur, eg political elections, terrorist attacks and environmental catastrophes. With the short gamma trading strategy, on the other hand, one is betting on quieter waves, or better still, no waves at all. In the case of the both volatility strategies, market direction only plays a subordinate role, or in some cases, no role.

Concluding view

Volatility strategies can make an interesting addition to an investor’s portfolio because of their slight correlation to share profits. Every investor should have market-neutral alternative investments as a back up.