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Covered Warrants I

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22. Advanced analysis II (volatility)

Volatility is a term bandied about in the press to signify big market movements, but in the covered warrants market it has a much more precise usage which makes it of far more than descriptive importance. Two forms of volatility – historical and implied – are calculated, and widely used for valuation purposes.

More volatility in an asset means more opportunity for the price to move the right way and to achieve value for overlying warrants.

For covered warrant investors, volatility is good, a quality to be embraced, so there is no need to frown next time an earnest news reporter comments on highly volatile market conditions.

Historical volatility

Historical volatility measures the standard deviation of past movements in the underlying asset price. Volatility is a key input for ‘fair value’ analysis and for a number of other equations, so it is a useful figure to have to hand.

Most of the formulae are really seeking an estimate of future volatility, but in practice the extreme difficulty of forecasting such a thing means that historical volatility is used as a proxy.

For some guidance it is worth noting some of the current figures for major market indices and currencies, after a fairly tempestuous period. Figures for three-month and twelve-month historical volatilities at the end of July 2002, were as follows:

Index	3-month Volatility	12-month Volatility
DAX	44.27%	30.66%
Dow Jones	29.31%	22.08%
Nasdaq	48.51%	42.45%
S&P 500	30.26%	23.37%
Nikkei	29.30%	26.84%
EUR/USD	10.38%	8.83%
EUR/JPY	8.04%	9.05%

There are a few interesting points to note from this table.

1. The three-month volatilities are substantially higher than the twelve-month volatility figures for all of the stockmarket indices, clearly marking out the recent period as a time of greater price movement. The longer-term context helps to make judgements about whether current volatility figures are representative and likely to continue. Care must be taken when extrapolating from historical volatility figures.
2. It is notable that the Nasdaq market is much more volatile than the blue-chip and broader US indices.
3. The volatility figures for currencies are much lower, which should caution against making assumptions about certain volatility levels being cheap. Building experience of volatility levels is a good idea to understand what is expensive, what is cheap, and to place these important figures into their proper context.

Implied volatility

Implied volatility is widely used as an indicator of value. The idea is quite simple. In the Black-Scholes equations, historical volatility was one of the five inputs used to determine a fair value price. That fair value price can then be compared with the actual market price to form a judgement on whether the market valuation is high or low. This is useful, but labour-intensive.

There is a simpler way, which is by using implied volatility. Instead of attempting to derive a fair value from the standard set of inputs, the current warrant price is substituted into the formula and the volatility omitted. It is then possible to work backwards through the equation to calculate a figure for volatility implied by the current market price.

The higher the market price of the warrant, the higher the implied volatility of the asset. Effectively the implied volatility is the expected future volatility of the asset over the remaining life of the warrant.

Comparing implied and historic volatilities

The time-saving when comparing a range of different warrants on one underlying asset is that the implied volatility calculated for each warrant can then be compared with one known variable – the historic volatility. Other things being equal, the lowest implied volatility would belong to the cheapest warrant, and more generally:

If implied volatility > historical volatility, warrant is expensive
If implied volatility < historical volatility, warrant is cheap

Volatility is not so important for warrants which are either well in-the-money or well out-of-the-money. Near-certainty of exercise or non-exercise means that the volatility of the underlying is far, far less important than the asset’s absolute performance.

1. Introduction 2. What are covered warrants? 3. Comparison between corporate warrants and covered warrants 4. Advantages of warrants 5. Advantages of warrants – the magic of gearing 6. Disadvantages of warrants 7. Advantages & disadvantages - a summary 8. International warrants markets 9. UK warrant market 10. Types of covered warrant I (warrant terms) 11. Types of covered warrant II (underlying assets) 12. Types of covered warrant III (exotics) 13. Information on warrant terms 14. Warrant trading 15. Warrant pricing 16. Basic analysis I (underlying asset) 17. Basic analysis II (prices and terms) 18. Basic analysis III (gearing) 19. Basic analysis IV (intrinsic value) 20. Basic analysis V (premium) 21. Advanced analysis I (Black-Scholes Model) 22. Advanced analysis II (volatility) 23. Advanced analysis III (the greeks) 24. Risk 25. Trading strategies 26. Tax 27. Conclusion

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