Traditional corporate equity warrants

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11. Analysis - gearing

We've seen already that gearing is the number one attraction of warrants. If a share price increases a little, an associated warrant can magnify this increase and rise greatly. Consequently, in a bull market, warrants will always be among the top risers on the stock exchange.

This section tries to analyse this feature of gearing. If a share price increases, say, 10%, how much will an associated warrant rise?

We'll start by taking a standard measure in finance called gearing, which mathematically can be defined as

gearing = value of exposure to asset / cost of exposure

This can best be illustrated by taking the example of a mortgage on a house. If a house costs £100,000, and a buyer borrows £90,000 and puts up £10,000 of his money, the gearing on this investment is said to be 10 times. This is because the buyer has a £100,000 exposure to the house market (the value of his house), and he bought this exposure with just £10,000 of his own money.

Simple definition of gearing

This definition of gearing can be extended to warrants. If a warrant is priced at 10p, and the underlying share is priced at 50p, the gearing is 5 times. The price of one warrant (10p) offers exposure to one share (of value 50p). So, our first definition of gearing is -

warrant gearing = share price / warrant price

Gearing decreases as the share price increases

Warrants tend to have the greatest gearing when they are at or out-of-the-money (when the share price is equal to the exercise price or below it). This is illustrated in the diagram on the right, case A. The warrant price in this situation tends to be small, and therefore the ratio of the share price to the warrant price high. As the share price increases, the warrant price must keep pace and increase as well (remember the exercise price is fixed). If it didn't, and the right column was less than the left column at any time, then it would be cheaper to buy shares via the warrants (by buying the warrants and exercising them), than by buying the shares in the share market. Thereby offering a riskless arbitrage. But as the share price and warrant price rise in tandem, the ratio between them falls. Technically, the intrinsic value converges towards the share price, and the gearing tends to 1. This explains why warrants deep in-the-money (share price high above the exercise prices) tend to be unattractive - because they have a very low gearing.

The effect of share price on gearing

In October 2001, the average gearing on warrants listed on the LSE was 3.0.

Using the gearing calculation in practice

We now know how to calculate the gearing on a warrant. Good. Can we do anything useful with the figure? Well, we can try to forecast the increase in a warrant price, for a given increase in the underlying share price. Taking the example of Gartmore European IT warrants (table below), on 23 May 2001, the gearing on the warrants was -

gearing = 366 / 145 = 2.52

The gearing of 2.52 implies the warrant price will increase 2.52 times greater than a given rise in the underlying share. For example, a share price rise of 10%, will see a rise of about 25% in the warrant price. To see if this works in practice, we'll look at the performance of shares and warrants over the period March - May 2001.

Over this period, the shares rose by 17.2%, while the warrants rose 42.4% - 2.46 times greater than the increase in the shares. This compares closely with the previously calculated gearing of 2.52. So, in this case, the calculated gearing on 23 May 2001, seems to have quite accurately forecast the relationship between movements in the share and warrant prices. That was easy.

But things are never quite that simple in the warrant market. The example above was somewhat rigged. If you are told that the exercise price on the Gartmore European IT warrant is 200p, you can calculate that on the 23 May 2001, the premium on the warrant was near zero. Warrants occasionally can be found trading at a zero premium but it is not common.

Let's take a more representative example: TR Property from Feb 2000 to Jan 2001. At the beginning of this period, the calculated gearing was 8.9. The performance of the shares and warrants is given in the table below.

Over the period, the shares rose 49.6%, while the warrants rose 195.6% - an increase 3.94 times greater than the shares. But the actual 'gearing' of 3.94, was nothing like the gearing of 8.9 calculated at the beginning of the period. What went wrong?

The exercise price on the TR property warrants is 47.5p. Knowing this we can calculate that the premium on the warrants at the beginning of the period was 29.0%. This is quite a different situation from the Gartmore Euro example, where the warrant premium was zero.

If the warrant had retained a premium of 29% over the period under review, the actual gearing would have been closer to the calculated gearing. But at the end of the period, we can calculate that the premium had in fact fallen to about zero - a collapse in the premium.

The reason for the difference then is that the premium on the warrant fell, causing the warrant to increase less than it might otherwise have done; and therefore the actual gearing was less than forecast by the calculated gearing.

Note: it is common for a warrant premium to decrease when the share price rises. This is because, as shown above, the gearing falls as the share rises, and therefore the warrant becomes less attractive. However, having fallen to zero, the premium cannot fall much below that.

When a warrant starts with a premium of zero, its future behaviour can be predicted fairly accurately in the case of the share rising. In most cases, the premium will remain around zero (it can not fall to a significant discount), and therefore the actual gearing will be close to the calculated gearing. But for all warrants when the premium is not zero, our first approximation for forecasting gearing does not work so well. We need to refine the model.

Implied gearing

It can be seen from the above that the key to forecasting actual gearing, is being able to predict the behaviour of the premium. Will it stay the same, increase or fall?

Unfortunately, there's no precise way to forecast the behaviour of warrant premiums. The best method is probably empirical observation - how has the premium reacted in similar circumstances before? For example, if in the past a warrant premium has fallen from 23% to 15%, when the underlying share has risen from 45p to 60p, there's a good chance that the premium will display similar behaviour if the share rises from 45p to 60p again. But this type of observation is not always possible.

Because premium forecasting is not an exact science, one way to approach this is by making an assumption on the behaviour of the premium. And a common assumption made is that if the share price doubles, the premium will fall to zero.

We can calculate (below) the effect of this assumption on the TR Property example above.

The adjusted gearing calculated with this assumption is sometimes called the implied gearing.

In this case, the implied gearing of 6.35, gives a somewhat better approximation to the actual gearing of 3.94, than the original simple calculated gearing of 8.93.

This formula for implied gearing can be expressed as -

implied gearing = ((2x - 1) / y) -1)

where,
x = parity ratio (share price / exercise price)
y = warrant ratio (warrant price / exercise price)

The above assumption for the implied gearing (that the premium will go to zero if the share price doubles), is quite conservative. In practice, warrants deep out-of-the-money, or with a long maturity, will likely retain some premium even if the share doubles. In which case, an alternative calculation for implied gearing assumes the premium falling to zero when the share price triples.

Further amendments to the gearing calculation are always possible, including the application of advanced options valuation techniques. However, the basic gearing calculation itself is sometimes sufficient, and the experienced investor can mentally adjust the gearing figure according to the prevailing parity ratio and premium.

Note on terminology

Gearing is a general financial term describing the exposure one investment gives to another. Implied gearing is a term more specific to the warrant market, describing a particular method for estimating the relative performance of the warrants to the shares. Leverage is the general American term for gearing. In the UK, the term leverage is sometimes also used specifically for implied gearing.

Summary

Gearing is one of the most important concepts in the warrant market. It relates the value of the warrants held to the value of the exposure given to the shares. The gearing calculation can be used to forecast the relative performance of the warrants against the shares. But this is not an exact science. The simple calculation of gearing can be found to be inaccurate in many cases; but the calculation can be improved with various assumptions made. However, the basic gearing calculation has the virtue of being simple (it can be calculated in one's head), and for many investors it is perfectly adequate for a first approximation.

1. Introduction 2. What is a warrant? 3. The warrant market 4. Advantages of warrants over shares - the magic of gearing 5. Further attractions of warrants 6. Disadvantages of warrants 7. Fundamentals - warrant terms 8. Fundamentals - intrinsic value and parity ratio 9. Basic analysis 10. Analysis - time value and premium 11. Analysis - gearing 12. Analysis - break-even and capital fulcrum point 13. Analysis -sample spreadsheets 14. Analysis - summary 15. Investing strategies 16. Dealing in warrants 17. Warrant exercise 18. Further topics 19. Further information 20. Conclusion

• Andrew McHattie on Covered Warrants