Delta is without any doubt the Greek that is most widely used. There is nothing unusual in that, since the delta value tells how sensitive the option is for price movements in the underlying stock – the foundation of the option’s value. An option’s delta simply tells how much the option’s value changes if the stock price goes up 1 unit. For call options, delta is always a figure between 0 and 1. A call option with a delta value of 0.6 thereby rises with 0.60 units if the stock goes up 1 unit.
For put options the opposite applies: they have always a value between 0 and -1. The minus sign is explained by the fact that put options always lose value when the value of underlying rises. Thereby it is quite easy to imagine that an option with a delta value of exactly 0 is not very interesting for an investor. It will not be affected at all when the stock price moves. On the other, pricing fluctuations happen a lot with options that have a delta of 1 (-1). They will rise or decline just as much as the underlying stock.
This gives us a first tool to analyze the portfolio. A delta value of 0 quite simply represents an obvious minus option with little time to maturity – or in other words, something very unlikely needs to happen for a call option that is traded far below the strike price when there is one day left to maturity should reach a profitable level. A delta of one is on the other hand associated with obvious plus options, which real values are high at the same time as the sensitivity for the underlying stock is high.
Pari options normally have delta values around 0.5, which means that they will be 0.50 units more expensive when the stock rise 1 unit. A useful interpretation is that delta is equal to the probability that the option is ‘in the money’ on the expiry day. Pari options have, in other words, a chance of precisely 50 percent to expire positive. It is simple and concrete. Despite this, the thought of spending time with Greeks in the portfolio can still feel uncomfortable.
A common hedging strategy with focus on delta is to try to make the portfolio protected from movements in the underlying stock. It is called creating a delta neutral position and is achieved when the delta of the entire portfolio amounts to zero.
Consider an example where you have 100 shares with a price of 14 each. Then you have a portfolio with a delta value of exactly 100, since a stock in itself has a delta of 1. From here, one of the simplest ways to become independent of the stock price, to achieve short term delta neutrality, is to buy put options. Let us say that that you can buy a put option with a strike price of 16 and a delta of -0.5. Then you have to buy two contracts, corresponding to 200 shares, for the whole portfolio to have a delta of 0 (200 x -0.5 = -100). Instead of buying put options you can, with the same mathematics, write call options.
It seems straight forward enough – but option theory would not have been option theory if there was not a drawback. The problem with a strategy that only focuses on delta is that delta in inherently a variable. Delta is affected, among other things, by the level of the stock price, which is the actual reason why a plus option can have a delta of 1 and a minus option a delta of 0. The more a stock price goes up (down), the more ‘in the money’ a call option (put option) will be and the higher the call option’s delta will be. The other way around for a minus option also applies: the more the stock price decline (rise), the lower the call option’s (put option’s) delta will be. This implies that a delta neutral position actually just is protected against a small movement in the underlying stock. To focus on delta neutrality implies a constant need for adjustments in the portfolio as its delta changes. These adjustments also have to be more extensive as time passes, since delta tends to be more sensitive as they close on expiry.
Furthermore, as if the stock price and the remaining time to maturity were not enough, delta is also affected by the stock’s volatility. If the volatility in a stock rises, delta tends to move towards 0.5, since the uncertainty of whether the option will be at plus on the expiry day then increases. Regardless of how useful delta is in indicating the sensitivity of the option’s value, it can never be completely perfect. Luckily there are other Greeks available to complete delta when delta is not sufficient.
