When you start to look at warrants in depth, you will find numerous references to several letters of the Greek alphabet. Delta, gamma, rho, theta, and vega are all used to denote certain key parameters which can be used in warrant pricing and valuation. They are all sensitivity coefficients which allow investors to measure how the value of a warrant will be affected by a change in another variable.
They have particular application when using hedging strategies. You can find much more detailed scrutiny of the Greeks, as they are known, in numerous works on futures and options, including works by the expert John Hull, but for now here is a brief explanation.
Delta
The delta is probably the most important to tackle and to understand. It is the change expected in a covered warrant price for a given change in the underlying instrument. This is an estimate of the true gearing or leverage which will actually occur. For call warrants with a cover ratio of one the delta will always fall between 0 and 1.
At 0, no movement is expected in the warrants. At 1 the warrant can be expected to move penny-for-penny with the underlying asset. Typically the delta will be around 0.50 for a call warrant which is ‘at the money’. The delta will move towards 0 as a warrant moves out-of-the-money, or towards 1 as the warrant moves in-the-money.
Most of the time investors will be aiming for medium-delta warrants. The received wisdom is that the comfort zone is in the range between 0.4 and 0.6.
Gamma
One problem with watching the delta is that it is constantly changing with the price of the underlying asset. The degree of change in the delta is measured by the gamma, which has an obvious application in dynamic models which attempt to simulate what will happen to a warrant price for different changes in the underlying asset.
The gamma will tend to be greatest when warrants are at-the-money, and it will tend to be much higher for a shorter-dated warrant than for a long-dated one.
The fact that the gamma is at its peak when the warrant is ‘at-the-money’ indicates that a good strategy can be to buy warrants which are slightly out-of-the-money. If they are successful and move in-the-money, the so-called ‘gamma acceleration’ effect kicks in to help the value of the warrants, because the delta can rise markedly in these circumstances.
Rho
The level of interest rates is unlikely to feature heavily in warrant decision-making, except perhaps in relation to the impact on the underlying asset, but for what it is worth, rho measures the sensitivity of warrant prices to changes in interest rates.
Warrants are not generally highly sensitive to changes in interest rates. Rho is largely of interest to financial modellers working on statistical forecasts, and is often included for completeness rather than utility.
Theta
Theta measures the rate of decay in the value of the premium, or time value, and is usually expressed simply in terms of pence lost per day or week.
A warrant losing 0.05p of time value per day will have a daily theta of 0.05. As with the other variables, the theta is not constant and will change according to the parity ratio and of course the time remaining.
The theta will tend to be higher for short-dated warrants.
Vega
The final Greek is vega, which measures the sensitivity of a warrant price to changes in volatility.
Vega is at its highest when a warrant is at-the-money, and tends to be higher for longer-dated warrants.
Using the Greeks
Issuers recognise both the need for investors to forecast what might happen to a warrant price for a given change in the underlying, and the difficulty of doing so. In response they frequently publish pricing matrices which indicate what the warrant price may be for a range of underlying prices. This information is very helpful when posing ‘what if?’ questions and in determining more generally whether a warrant is likely to meet your needs.
Final word
You should resist the temptation to be swept away by the attraction of all those decimal places. Because the Greeks are constantly fluid, using them for valuation purposes can be like catching an eel in a fast-flowing river. In spite of their apparent precision they are best used for guidance and to understand risk. Typically they are used to illustrate potential profits; they are perhaps even more powerful when used to show the extent of losses when things go wrong.
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