## The indicators

**How do various Indicators affect the price of a warrant?**

Indicators are important, especially given the fast pace of warrant trading. You not only have to know what they are, you also have to be able to interpret them.

Static indicators facilitate a qualitative price assessment of similar warrants at a given point in time. These indicators should only be used to compare warrants with similar features.

One of the most important indicators when valuing warrants is the premium over intrinsic value. The major advantage of this indicator is that it is easily calculated, thus providing a quick overview of which warrants are worth investing in. When buying warrants, the aim is to invest a small amount and then make a proportionally larger gain from any movements in the price of the underlying. The premium over intrinsic value shows (in the case of calls) how much more it would cost to acquire the underlying by exercising the warrant rather than buying it directly.

We know, however, that a warrant is more valuable the longer its time to maturity, and an indicator, which fails to take this time aspect into account, is flawed. A more sensible way of comparing warrants is therefore to calculate the premium over intrinsic value per time unit, usually per year of time to maturity.

But even this annual premium over intrinsic value is limited in its usefulness as it is not seen in relation to the warrant. It is obvious, for example, that a premium of TRY 0.25 has to be treated completely differently depending on whether the warrant costs TRY 0.5 , TRY 1.0 or TRY 10.0 . The best way to compare warrants using this indicator is therefore to calculate the percentage premium. This premium shows how much more (in percentage terms) it would cost to acquire the underlying by exercising the warrant rather than buying it directly, thereby serving as a useful criterion for comparing warrants

Based on the same examples used above used to explain the “moneyness” of warrants, see below a table showing the percentage premium over intrinsic value:

Premium over intrinsic value is calculated as follows (see the glossary for more detailed explanation):

Call warrant: warrant price + strike price – underlying price

Put warrant: warrant price - strike price + underlying price

Premium over intrinsic value for call warrants represent how much more it would cost to acquire the underlying by exercising the warrant rather than buying it directly. Premium over intrinsic value for put warrants represent how much more it would cost to sell short the underlying by exercising the warrant rather than shorting the underlying directly.

Stating that a warrant is cheaper the lower the premium is too simplistic. A comparison of warrants is only worthwhile if they have similar maturities and intrinsic values. Generally speaking, warrants with a high intrinsic value have low premiums and warrants with a low or no intrinsic value will have higher premiums. A comparison based on the percentage premium however serves two main functions. First, it provides investors with a quick and clear overview of which warrants are attractive. Secondly, when investors have decided on a particular underlying, it enables them to compare the premiums of warrants with similar maturities and strike prices and then opt for the least expensive.

**Leverage**

Arguably the most widely known warrants indicator is leverage, which shows the extent to which a warrant moves in line with its underlying. Current or simple leverage can be calculated by dividing the price of the underlying by the price of the warrant. If the exercise ratio is not 1, this is also priced into the warrants.

Simple leverage is based on the assumption that price movements in both the underlying and the warrant will be equivalent. This assumption, however, does not generally hold true.

Let us take the example of a warrant granting the right to buy a share that is trading at TRY15. The strike price is say TRY20, and the warrant is set to expire in two months. The warrant costs TRY1, producing a simple leverage ratio of 15: 1 = 15. According to this ratio, a 10 percent rise in the price of the share to TRY16.5 would lead to a 150 percent rise in the price of the warrant to TRY 2.5 . In practice, however, this would never happen as the share price would still be a long way off the strike price of TRY 20. If the share fails to move “into the money” within the two months to expiry (.i.e. rises above TRY 20), the warrant will expire worthless. This ratio is therefore only ever applicable to warrants with a high intrinsic value but not at all for those without this value. This is exactly why elasticity – also referred to as the omega – is more commonly used (see below).

Another key indicator is the break-even point, which shows the price level of the underlying at which the owner of the warrant will make a profit. Taking the example of a warrant costing TRY 1, a strike price of TRY 20 and an exercise ratio of 1:1, the share price would have to exceed TRY 21 in order for the investor to make a profit.

Alongside static indicators, dynamic indicators also provide key information on warrants.

Dynamic indicators reflect changes in the price of an option relative to changes in the price, maturity or volatility of the underlying. As opposed to their static counterparts, they allow investors to make a forecast of the future price movements of warrants from a specific point in time and are generally determined using option valuation models. They are only valid for a short period of time and must be recalculated every time any key influential factor changes.

**Delta**

A key indicator is the delta, which belongs to the family of modern valuation indicators otherwise known as the “Greeks” because they are named after letters of the Greek alphabet. In modern warrant pricing theory, this indicator represents the sensitivity of the price of a warrant to the price movements of the underlying. The delta of a warrant is calculated using warrant valuation models derived from financial theory. The delta of a call warrant lies between 0 and 1, and for a put warrant between –1 and 0. A delta of 0.70 means that, at an exercise ratio of 1:10, a TRY 1 rise/fall in the price of the underlying would lead to a TRY 0.07 rise/fall in the price of the warrant (0.70 x 1 x (1/10)). It can also be used as a rough guide as to whether or not the warrant will have intrinsic value upon maturity, meaning that it will not expire worthless. The probability that the above warrant will not expire worthless therefore stands at 70 percent. In mathematical terms, the delta is the first derivative of the warrant price with respect to the price of the underlying.

**Gamma**

Another key indicator is the gamma, which defines the sensitivity of the delta to changes in the price of the underlying. The higher the gamma, the greater the change of the delta to such price movements. A gamma of 0.02 means that if the price of the underlying rises or falls by 1 , the delta will change by 0.02 units. Warrants trading at the money have the highest gammas. Furthermore, the gamma is higher the shorter the time to maturity of the warrant.

Mathematically speaking, the gamma is the first derivative of the delta with respect to the price of the underlying and therefore the second derivative of the price trend of the warrant in relation to the price movements of the underlying.

**Vega **

The vega shows the influence that fluctuations in the volatility of the underlying have on the price of the warrant. You will remember that volatility is the range of fluctuations in the price of the underlying within a given period of time. Together with the price of the underlying, the vega is the most important factor that can influence the value of a warrant. This indicator measures the degree to which the price of the warrant moves when the implied volatility rises or falls by one percent. A vega of 0.25 means that if the volatility of the underlying changes by one percent, the value of the warrant will rise or fall by 0.25, adjusted for the exercise ratio. As is the case with the gamma, warrants trading at the money have the highest vega. In contrast to the gamma, however, the vega is higher the longer the time to maturity of the warrant.

From a mathematical perspective, the vega is the first derivative of the warrant price with respect to volatility.

**Theta**

We have already mentioned that the price of an warrant is comprised of its intrinsic and its time value, and that the closer the expiry date, the faster the time value erodes. The theta measures the loss of time value per unit of time, e.g. per day or week, assuming that the price of the underlying, along with all other parameters, remain the same until expiry. This indicator is usually shown as a percentage. A weekly theta of 1.5 percent means that, providing the underlying price remains unchanged, i.e. the intrinsic value remains constant; the warrant will lose 1.5 percent of its value every week. The theta is very much dependent on whether the warrant is in the money, at the money or out of the money. A warrant with a high intrinsic value will have the lowest theta. At-the-money warrants will experience the fastest loss of time value as they move towards their expiry date. Generally speaking, the time value of a warrant will erode the most during the three months before maturity.

Investors must be constantly aware of this loss of value, which is solely attributable to the decreasing time to maturity. The closer a warrant gets to its expiry date, the greater the price movement required in order to offset the ever growing loss of value and ultimately to generate a profit.

In mathematical terms, the theta is the derivative of the warrant price with respect to time.

**Rho**

The rho is the indicator used to measure the influence of interest rate changes on the value of warrants. The forward, rather than the spot price is used when pricing warrants. The forward price is comprised of the spot price plus a factor known as the cost of carry. This factor can be defined as the total costs of financing the underlying until the agreed expiry date of the warrant. These costs are affected mainly by the interest rate level and the expected dividend payments. A rho of 0.50 means that the warrant price – adjusted for the exercise ratio – will change by 0.50 if the market interest rate that is relevant to the term of the warrant rises or falls by one percentage point. As extreme short-term interest rate fluctuations are very rare, however, the rho can often be disregarded for most other warrants.

In mathematical terms, the rho is the derivative of the warrant price with respect to the interest rate.

**Omega **

Elasticity, which shows the percentage change in the price of the warrant relative to the percentage change in the price of the underlying, is known as omega. It is obtained by multiplying the delta by the leverage ratio. While the omega serves as a useful indicator, the fact that the delta changes with time means that it can only provide investors with a snapshot view.