Kim can reduce her exposure to theta and vega by buying an OTM call. The trade-off here is that she also reduces her immediate delta exposure.Depending on how much Kim believes Disney will rally, this may or may not be a viable trade-off. Imagine that instead of buying one Disney March 35 call, Kim buys one Disney March 37.50 call, for 0.20.
There are a few observations to be made about this alternative position.First, the net premium,and therefore overall risk, is much lower, 0.20 instead of 1.10. From an expiration standpoint, the breakeven at expiration is $37.70 (the strike price plus the call premium).
Since Kim plans on exiting the position after about three weeks, the exact break-even point at the expiration of the contract is irrelevant. But the concept is the same: the stock needs to rise significantly. Exhibit 4.6 shows how Kim’s concerns translate into greeks.This table compares the ATM call with the OTM call. Kim can reduce her theta to half that of the ATM call position by purchasing an OTM.This is certainly a favorable difference.
Her vega is lower with the 37.50 call,too. This may or may not be a favorable difference. That depends on Kim’s opinion of IV.On the surface, the disparity in delta appears to be a highly unfavorable trade-off. The delta of the 37.50 call is less than one third of the delta of the 35 call, and the whole motive for entering into this trade is to trade direction!Although this strategy is very delta oriented, its core is more focused on gamma and theta.
The gamma of the 37.50 call is about 72 percent that of the 35 call. But the theta of the 37.50 call is about half that of the 35 call. Kim is improving her gamma/theta relationship by buying the OTM, but with the call being so far out-of-the-money and so inexpensive, the theta needs to be taken with a grain of salt. It is ultimately gamma that will make or break this delta play.The price of the option is 0.20—a rather low premium. In order for the call to gain in value, delta has to go to work with help from gamma. At this point, the delta is small, only 0.185.
If Kim’s forecast is correct and there is a big move upward, gamma will cause the delta to increase, and therefore also the premium to increase exponentially. The call’s sensitivity to gamma,however, is dynamic.Exhibit 4.7 shows how the gamma of the 37.50 call changes as the stock price moves over time. At any point in time, gamma is highest when the call is ATM. However, so is theta. Kim wants to reap as much benefit from gamma as possible while minimizing her exposure to theta.
Ideally, she wants Disney to rally through the strike price—through the high gamma and back to the low theta. After three weeks pass, with 23 days until expiration,if Disney is at $37 a share, the gamma almost doubles, to 0.237.
When the call is ATM, the delta increases at its fastest rate. As Disney rises above the strike, the gamma figures in the table begin to decline.Gamma helps as the stock price declines, too. Exhibit 4.8 shows the effect of time and gamma on the delta of the 37.50 call.
The effect of gamma is readily observable, as the delta at any point in time is always higher at higher stock prices and lower at lower stock prices.Kim benefits greatly when the delta grows from its initial level of 0.185 to above 0.50—above the point of being at-the-money. If the stock moves lower, gamma helps take away the pain of the price decline by decreasing the delta.
While delta, gamma, and theta occupy Kim’s thoughts, it is ultimately dollars and cents that matter. She needs to translate her study of the greeks into cold, hard cash. Exhibit 4.9 shows the theoretical values of the 37.50 call. The sooner the price rise occurs, the better. It means less time for theta to eat away profits. If Kim must hold the position for the entire three weeks, she needs a good pop in the stock to make it worth her while.
At a $37 share price, the call is worth about 0.50, assuming all other market influences remain constant. That’s about a 150 percent profit. At $38, Exhibit 4.9 reveals the call value to be 1.04. That’s a 420 percent profit.On one hand, it’s hard for a trader like Kim not to get excited about the prospect of making 420 percent on an 8 percent move in a stock. On the other hand, Kim has to put things in perspective.
When the position is established, the call has a 0.185 delta. By the trader’s definition of delta, that means the call is estimated to have about an 18.5 percent chance of expiring in-the-money. More than four out of five times, this position will be trading below the strike at expiration.Although Kim is not likely to hold the position until expiration, this observation tells her something: she’s starting in the hole. She is more likely to lose than to win. She needs to be compensated well for her risk on the winners to make up for the more prevalent losers.