In every options position, even if it is the buying of a call or a complicated strategy which involves many legs, we can estimate its aggregate Greek letters by adding up the values of the different sensitivity factors of calls and puts (legs) which are included in the strategy. We refer to this sum as position Greeks. This is a simple way to estimate the aggregate potential risks and benefits of a strategy (i.e. in dollars), relatively to changes in the factors that affect options prices.
Suppose that we have implemented an options strategy which has an aggregate position Delta of +$50. This means that if the price of the underline security rises $1 our position will gain $50 but if it declines $1 our position will lose $50.
If the position Vega of our strategy is +$70 this means that if the implied volatility rises 1% our position will gain $70 but if it declines 1% our position will lose $70. But what would have happened if the position Vega was -$70? Then a 1% rise in implied volatility would have caused a loss of $70 and a 1% decline in implied volatility would have produced a gain of $70.
If the position Theta is -2$ this means that every day our position is losing $2 due to time decay and if it is +$2 it is gaining $2/day.
If the position Rho is +$1 this means that if interest rates rise 1% we will gain $1 and if position Gamma is $3 we will have a profit of $3 if the underline security rises by $1 (through the effect of Delta to the option premium).
Notice that the sign in front of the position Greek is telling us if the implemented strategy is positively or negatively related to a particular Greek letter. We have positive sign when a rise in the factor that the Greek letter refers to, produces profits in our position and negative sign when a rise in the factor that the Greek letter refers to, produces losses in our position.
Below is a table which shows the polarity of Greek letters relatively to simple positions in calls and puts. By combining the Greek polarities and values, of the individual calls and puts in a strategy (legs) we can estimate the position Greeks for this particular strategy.
Lets examine Vega in order to better understand the notion of polarity. When someone is long in a call or a put Vega is positive as shown in the above table, meaning that a 1% rise in implied volatility will cause profits in his/her position, whereas if someone is short in a call or put Vega is negative and a 1% rise in implied volatility will cause loss in the position. Relatively to Delta, when someone is long a call or short a put a $1 rise in the underline security will produce profits, whereas when someone is short in a call or long in a put a $1 rise in the price of the underline will produce losses.
The same rationale is applied not only to simple option positions but also in complex strategies. If we want to find the position Greeks of a strategy we have to add the position Greeks of its legs, by taking into consideration their polarity according to the above table.
We will now estimate the position Greeks for an options strategy which is called ”covered call” and includes the opening of a long stock position and the writing of an equal number of OTM calls. An outright stock position has no Greek letters except Delta which equals to $1/share. So, suppose that we have bought 1000 shares and we are also short in 10 calls (1 option= 100 shares). The options Delta is 0.70 and Vega is 0.05. The table below estimates the position Delta and Vega of the strategy.
The position Greeks are telling us that a $1 rise in the stock price will give us a profit of $300 (position Delta). On the other hand, a 1% rise in implied volatility will cause a loss of $50 to our strategy (position Vega). All the other position Greeks can be estimated in the same way.