VIEWS: 18 PAGES: 47 POSTED ON: 10/25/2009
THE GREEKS “DELTA (D), GAMMA (G), THETA(T), VEGA(V), RHO(R) “It all sounds Greek to me” • Delta is usually related to options in terms of referring to the rate at which an option contract will move in tandem with the underlying security. • Delta was originally thought of as the hedge factor in determining how many options were needed to act exactly like the underlying investment. • One of the biggest frustrations for an option trader is having an option that is in the money move maybe 1/2 to 3/4 for every point that the underlying security moves. This is a major frustration for traders, but most of this frustration is due to a lack of understanding of how Delta works and influences their option contracts. Every option has a Delta value. They range from 0 to 100 in value. The put options have a value from 0 to –100 in value. • Example, if a option has a DELTA of 50, this means that for every 1 point move in the underlying security, the option contract would move 50%, or in this case of an option priced at $1.00, a 1/2 of a point. • Usually options that are near the money have Delta close to 50. In addition, as these options go deeper into the money the Deltas on those options tend to be closer to 70 or 80. The deeper in the money, the higher the Delta of the option. • DELTA • Example: KLK is trading at 47 and the KLK July 45 call is priced @ $4.50 with a Delta of 70. • Simply translated: for every one point move in KLK the July 45 call (with a Delta of 70) will move .70 or 70%. • So if KLK went from 47 to 49, then the July 45 call, which was trading at 4.50, will have gone up to 5.90 (a 1.40 move, which is 70% of 2 or $1.40) • Add that 1.40 to the 4.50 and the option is trading at 5.90. • Let's take a look at a couple of situations so you can see if you have it down. • Please take note that this figure is strictly for illustration purposes so that one can see how generally Delta prices are figured. • This is just a simple table to look over to get a visual of how Delta is figured and let you look at various examples FIGURE 14-1: Look below to see how much the option will move based on the following underlying Deltas. • Delta is just one of the calculations that help one understand why an option will move in the way it does. However, Delta alone is not the only factor that determines option movement. Delta is just the most common due to the fact that large traders use it to hedge their positions at all times. Understanding why your options move as they do is an important part of the overall understanding of option pricing system. We will look at another important Greek term called Gamma next. • The Gamma of an option tells you how much the Delta of an option changes as the underlying stock or index changes. When we examined Delta, we learned that every option has a Delta, but we need to expand on that knowledge to include the fact that : • the value of that Delta changes as the stock value changes. As the stock goes up or down in value, the Delta also changes. Scenarios • Example: A call option, which is near the money and has a Delta of 50, would see an increase or decrease in that Delta as the price of the stock rises or falls • (e.g. If the hypothetical stock RRR was at 200 and went up 20 points and it RRR 200 call increased 10 points, the Delta, which was at 50 may change and go up to a Delta of 60. The higher the stock goes, the greater the Delta becomes of that option as it moves deeper into the money). • • Gamma tells you the rate at which the option will increase or decrease as the stock moves up or down. • (i.e., If the RRR 200 call, had a Gamma of 3 • this would mean that the Delta would increase 3% for every point rise in the stock.) • With the stock trading at 200, Let's look at the example below. • Delta Gamma • RRR Jan 220 Call @ 4 50 4 • (The above option has a Delta of 50 • The above option has a Gamma of 4.) • This would mean that if the stock goes to 205 • the option that was at 4 would go to 6 (because of the Delta being 50, then the Gamma of 4) would increase the Delta to 52 because (4% increase of 50 is 2, 50+2 = 52 Delta). STOCK GOES TO 210: • If the stock goes up another 5 points to 210, the option would go up to 9 1/8, and the Delta of 52 would now go up to 54 because of the Gamma of See the Table Below • RRR 200 205 210 • • • • • RRR JAN 220 Call Delta >>>>>>>>>> Gamma >>>>>>>>> 4 50 4 6 52 4 9 1/8 54 4 Note: This is a hypothetical example of how Delta relates to the Gamma function. In the real world the Gamma would also change in relationship to the stock. • Puts and calls have Gamma values, and understanding Gamma will help you to determine how much the Delta of your option will change. By using Gamma, you know how much the Delta will change and Gamma will let you know how quickly you must adjust your positions. • Please keep in mind that this would require constant monitoring and a lot of time. • Unless you are a trader who wants to constantly monitor positions, this should just be a lesson for you to become familiar with how Gamma and Delta work together, and give you a better understanding of their innerworkings. • Option Hedgers are always adjusting positions attempting to keep these positions Delta NEUTRAL. • Now, let's recall our definition of Gamma, it defines the rate or the speed or how much an option will increase or decrease Delta points as the underlying stock moves. • The Delta on a call option increases with the increase of the stock, but as a stock decreases, so does its Delta. • • Gamma just tells you how fast the change is taking place (e.g. An option with a Gamma of 0.5 would tell us that for every point rise in the stock, we would have a 1/2 point rise in the Delta of the option being traded. If the Gamma were 2, the Delta would increase 2 points for every 1 point move in the stock.) See example below: The Real World GAMMA, DELTA……Houston …we have a problem! • Unfortunately, just as Delta is not constant, • Neither is Gamma. • Gamma changes in value, just like Delta. • The Gamma is highest when the option is at the money. • The further out of the money the option is, the greater decreases in the Gamma, meaning slower and smaller changes of the Delta. • Also, as it gets closer to expiration, Gamma will change. Impact of GAMMA and DELTA • Gamma is significant because it helps you manage and measure how much risk you are taking. • We learned that Delta was important because it taught us that options move at varying amounts in relationship to the stock • and you might also need several options to get the same result as the move of the underlying stock. • If we know Delta , we can determine how many options we need to equal the move of the underlying stock. Importance of GAMMA and DELTA • Gamma becomes important because Delta is always changing and as it changes we learned that one may need to readjust one's positions. • Knowing Gamma helps to determine how quickly the Delta is going to change and put you in a position where you might need to make adjustments. Traders use of Gamma • Active traders use positions with relatively low Gammas to reduce their risk. • The reason is because they want their Deltas to change less, so they don't have to re-adjust their positions as much. • Large Gamma positions are usually considered riskier, because you could be caught long or short much quicker than you would like to. • JUST A NOTE IN CLOSING on DELTA and GAMMA • Gammas like Deltas have a negative or positive designation. GAMMA Positions • Long Positions = Positive Gammas • Short Positions = Negative Gammas • Previously, we made references to how time affects an option as it gets closer to its expiration date. We discussed that the value of that option will decrease in price because of the reduction in the time left until that option expires. We also learned that every option has time value calculated in its premium, all out-of-the-money options are made up entirely of time value. • • • THETA • Theta is basically defined as the rate at which an option losses its value as the option gets closer to expiration. • Theta, when calculated, is usually done by a figure quoted in a certain number of points per day that the option premium will decay. The unique thing that is inherent in Theta is that the loss of value of the option premium because of time decay is based on the assumption that there is no change in the market price of the option or the conditions in which the option is being traded. • THETA • In other words, if you could isolate time value and measure strictly an individual variable • and assumed the price of the option did not move, that would be a true measure of how Theta functions. • The reason all those other factors are not considered is because they would influence the price of the options and affect Theta THETA • Example: volatility all of a sudden picks up in a stock, or there are earnings rumors, buy-out rumors, or various national economic news). • All of these factors would affect Theta, and that is why Theta, when analyzed, has to be looked at as if these other market factors were not in the equation. • Theta works both ways in relationship to a buyer or a seller. If you are a buyer of an option, you want the option with a low Theta, which has a very small erosion of premium as time goes by. THETA • If you are a buyer of an option, you want the option with a low Theta, which has a very small erosion of premium as time goes by. • On the other hand, if you are a seller of an option, you want a rapid erosion of the premium, giving the buyer less time to make a profit. THETA • Theta is often most important in examining spreads. • As you decide which spread to put on you could examine Theta and make a determination whether the time value within the spread is going to work for you or against you. By using Theta you can help better determine spreads that give you the best time value disposition and • • which spreads would be better for you ultimately when it comes down to making an educated decision as to which spread scenario might be best, when you have several choices to choose from. • This could be important, especially if you are a buyer or when examining the long side of your spread, whether bullish or bearish. VEGA • Vega has had various names associated with it over time, • such as Kappa or Omega. • We will refer to it has Vega. • Vega, in brief definition, is a value given in points that measures change in volatility. It measures a change in theoretical value for each 1-point variation in volatility. VEGA • VEGA tells you how much an option will increase based on an increase in the volatility of option and the underlying stock issue. • When you recall any number of your own personal option trades, as the volatility increased in you option, so did the premium and as volatility decreased or slowed down, the premium of the option decreased. • The main use of Vega is to help and determine how much risk you have from volatility increases and decreases. VEGA • Remember, you may have only several days to go on an option with little or no volatility, then all of a sudden: • some market event, like a "surprise" earning report, would could affect the volatility either positively or negatively and exaggerate the price of the option, even though there may be only a few days left before its expiration. • The net effect: • The option being grossly overpriced due to volatility from investor interest in that option. RHO • RHO • • is how an option reacts to changes in interest rates. This Greek has a minor effect on pricing, but does have an effect on premium, even if negligible. The Rho effect is similar to rises in interest rates. • As interest rates go up, the option premium must increase to keep the options in competition with other investment vehicles. The premiums that the seller receives need to be higher to compete with the other alternatives that an investor has in the investment market place to choose from. • Although Rho is part of the Greek family, its importance is minimal at best. The Real World • The Greeks are used by many traders to determine the various factors that I related to in the above text. • On the next slide you will find an example of the Greeks we discussed and how they look to traders and followers of their use. “IT ALL SOUNDS GREEK TO ME” All the GREEKS GREEKS – “The Bottom Line” • As a trader, you can see there are many, many trading tools that are available to attempt to give traders any type of edge in their attempt to maximize their trading profits. • The use of Greeks are just one of the many tools available to traders to help achieve that goal. However, always remember, even the best financial tools are not going to substitute for excellent judgment, good risk/reward analysis and a sound investment philosophy. • As a trader, always try and expand your horizons by examining new tools and philosophies that could potentially serve to increase your bottom line