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What You Can Invest In

Covered Warrants

• Introduction
• Delta
• Gearing
• Effective gearing or leverage
• Gamma
• Theta
• Vega
• Rho

Introduction

As previously discussed, the price of the warrant results from the interaction of six parameters: the exercise price, the price of the underlying security, the maturity, the dividend yield, interest rates and implied volatility. These quantifiable factors are the input variables used in theoretical pricing models such as Black & Scholes. As there are many forces affecting the warrant's value, prices can change in ways which may surprise even the most experienced trader. It is therefore necessary to understand how changing market conditions are likely to affect a warrant's theoretical value.

Fortunately, along with the theoretical value, pricing models also generate sensitivity coefficients which enable investors to assess not only the direction of the resulting change but also its relative magnitude. It is important to bear in mind that several parameters can be changing at the same time. As a result, these coefficients give data which suppose that all other parameters remain constant. These coefficients have been assigned Greek letters: delta, gamma, theta, vega and rho.

Delta

The delta gives a theoretical answer to the question "How much will the warrant price move for a one point move in the underlying security?" Under some conditions, when a call warrant is very deeply in-the-money, its value changes at a rate almost identical to that of the underlying security. If the underlying security moves up or down one point, the value of the call warrant will change by an almost equal amount. Under other conditions, when the call is far out-of-the-money, its value may change only slightly, even with a large change in the price of the underlying security.

In theory, the warrant should never gain or lose value in sterling terms more quickly than the underlying security. The delta of a call warrant always has an upper bound of one. A warrant with a delta of one will move up or down one full point for each full point move up or down in the price of the underlying security. In other words, it is moving at 100% of the rate of the underlying security.

A call warrant should not move in the opposite direction to that of the underlying security as a result of the delta. A call warrant with a delta of nearly zero should move negligibly, even if the underlying security makes a relatively large move. Warrants that are at-the-money have a delta of approximately 0.50.

Note: the delta can be written as 1.00 (decimal format) or 100% (percent format).

For put warrants, the delta is negative: a rise in the underlying security will bring about a drop in the price of a put warrant.

Gearing

The gearing of a warrant (or parcel of warrants) is a measure of the number of underlying securities to which exposure is gained by purchasing one warrant (or parcel of warrants). It is calculated as follows:

Effective gearing or leverage

The price variation for a warrant will generally be higher (in percentage terms) than that observed for the underlying security. A warrant's effective gearing (sometimes called elasticity) is the relative percent change in a warrant's value for a given percent change in the price of the underlying security.

A warrant's effective gearing is not constant and is highest for warrants which are out-of-the-money and/or close to expiry. Expressed mathematically:

Gamma

The gamma is the rate at which a warrant's delta changes as the price of the underlying security changes. The gamma is usually expressed in deltas gained (or lost) per one point change in the underlying security, with the delta increasing (or decreasing) by the amount of the gamma when the underlying security rises (or falls) by one point. The gamma is highest when the warrant is at-the-money.

Theta

All warrants - both calls and puts - lose value with the passage of time. The theta, or time decay factor, is the rate at which a warrant loses value as time passes and is usually expressed as a proportion of the warrant's premium lost per day. For example, a warrant priced at 15.25p with a theta of 0.05 will lose 0.05 of a penny in value for each day that passes, when all other pricing parameters remain unchanged. If the warrant is worth 15.25p today, then it will theoretically be worth 15.20p tomorrow then 15.15p the day after ...

However, this factor is not constant: the closer to expiry, the higher the theta, as shown in the graph below. In addition, this factor depends on the relationship between the underlying security price and the exercise price: the theta is generally higher for at-the-money warrants than for the out-of-the-money and in-the-money warrants.

Vega

The vega indicates the sensitivity of the warrant's price to fluctuations in the implied volatility level for the underlying security. All warrants should gain value with rising volatility, therefore the vega for both calls and puts is positive. A warrant with a price of 10p and a vega of 0.2 will increase in value (with all other parameters remaining constant) by 1p given a 5 point increase in implied volatility (ie 5 x 0.2).

Note:

(i) An at-the-money warrant usually has a greater vega than either an in-the money or an out-of-the-money warrant, assuming all warrants have the same amount of time to expiry. This means that an at-the-money warrant should be more sensitive to a change in volatility.

(ii) The vega of all warrants declines as expiry approaches. Therefore a long-term warrant should be more sensitive to a change in implied volatility than a short-term warrant with otherwise identical characteristics. Indeed, time and volatility are closely connected. More time to expiry means more time for volatility to take effect, while less time to expiry may mean that any change in implied volatility will have only a minor effect on the warrant's value. Moreover, changes in the time remaining to expiry and changes in implied volatility often have similar effects on a warrant's value.

Rho

The rho indicates the sensitivity of the warrant's price to short-term variations in interest rates.

Note: It is important to remember that all the pricing parameters discussed in the previous chapter are constantly changing and that the value of a warrant will change just as fast and sometimes in surprising ways. The sensitivity coefficients discussed in this chapter are tools that help investors to estimate the impact that market fluctuations will have on the value of their warrant investment and, as a result, to understand the level of risk involved.

Example
Let's assume that Rio Tinto drops 5% in one day from 1050p to 997.5p. At the same time, implied volatility rises four points to 39%. What impact will these changes have on the price of an SG Rio Tinto call warrant?

As indicated by the delta, the move in the underlying would bring about a drop of 33p in the warrant's price (52.5 x 0.63). However, the four point rise in volatility will bring the theoretical price up by 7.72p, thereby mitigating the drop in the warrant price.

Note: Volatility can work either in favour of or against the investor depending on circumstances. As a general rule, a sudden dip in an underlying index or share will bring about a consequential rise in volatility. Conversely, rising markets tend to bring lower levels of volatility. It can therefore be dangerous to purchase a call warrant on an underlying that has just suffered a severe drop. This is particularly the case where subsequent movement consists of a gradual rise as the profit realised by the upside movement of the share can be largely neutralised by a fall in volatility.