# Applying Analysis to Calls—the "Greeks"

Keep the major market theories in mind when you analyze stocks, and remember that exceptionally rich option premium is not a dependable standard for stock selection. Moderate volatility in a stock's price levels may work as a positive sign for options trading, as it demonstrates investor interest. A stock that has little or no volatility is, indeed, not a hot stock and such conditions will invariably be accompanied by very low volume, a consistently low P/E ratio and, of course, lower option premium levels.

With the distinctions in mind between different causes and patterns of volatility, the selection of stock may be based on a comparative study of the past 12 months. First, ensure that the stocks you are considering as prospects for purchase contain approximately the same causes for their volatility. Then apply volatility as a test for identifying relative degrees of safety.

A series of calculations are used by options analysts to study risk and volatility in options. These are collectively referred to as the

*Greeks*because they are named after letters in the Greek alphabet. These calculations are for the most part useful for comparative purposes in options analysis. It is good to know

*what*they reveal, but the calculations themselves are beyond the interests of most traders. However, if you subscribe to a service that compares options for you, then it makes perfect sense to know what the Greeks reveal.

Fundamental and technical tests are complemented with the use of another feature in a stock's price used to define volatilityâthat is the stock's

*beta*. This is a test of relative volatility, in other words, the degree to which a stock tends to move with an entire market or index of stocks. A beta of 1 tells you that a particular stock tends to rise or fall in the same degree as the market as a whole. A beta of 0 implies that price changes of the stock tend to act independently when compared to price changes in the broader market; and a beta of 2 indicates that a stock's price tends to overreact to market trends, often by moving to a greater degree than the market as a whole.

Because time value tends to be higher than average for high-beta stocks, premium value, like the stock's market value, is less predictable. From the call writer's point of view, exceptionally high time value that declines rapidly is a clear advantage, but it would be shortsighted to trade only in such stocks, especially if you also want stability in your stock portfolio.

Another interesting indicator that is helpful in selecting options is called the

*delta*. When the price of the underlying stock and the premium value of the option change exactly the same number of points, the delta is 1.00. As delta increases or decreases for an option, you are able to judge the responsiveness (volatility) of the option to the stock. This takes into consideration the distance between current market value of the stock and striking price of the call; fluctuations of time value; and changes in delta as expiration approaches. The delta provides you with the means to compare interaction between stock and option pricing for a particular stock.

The calculation of delta (the delta ratio) is a study of the relationship between the stock's price movement and value of the option. When this relationship does not move as you would expect, it indicates a change in market perception of value, probably resulting from adjustments in proximity between market price and striking price. This change is worth tracking through the delta, since it presents occasional opportunities to profit from unexpected price adjustments. The delta ratio is also called

*hedge ratio*.

Delta measures aberrations in time value. If all delta levels were the same, then overall option price movement would be formulated strictly on time and stock price changes. Because this is not the case, we also need to use some means for comparative option volatility, apart from the volatility of the underlying stock. The inclination of a typical option is to behave predictably, tending to approach a delta of 1.00 as it goes in the money and as expiration approaches. So for every point of price movement in the underlying stock, you would expect a change in option premium very close to one point when in the money. Time value tends to not be a factor when options are deep in the money. Time value is more likely to change predictably based on time until expiration. For options further away from expiration, notably those close to the striking price, delta is going to be a more important feature. In fact, the comparison of delta between options that are otherwise the same in other attributes will indicate the option-specific risks and volatility not visible in a pure study of the stock itself. Time value can and does change for longer-term options close to the money. The delta can work as a useful device for studying such options. The relative volatility of the option is the key to identifying opportunities.

Accompanying these indicators of relative volatility, you may also follow

*open interest*. This is the number of open option contracts on a particular underlying stock. For example, one stock's current-month 40 calls had open interest last month of 22,000 contracts; today, only 500 contracts remain open. The number changes for several reasons. As the status of the call moves higher into the money, the number of open contracts tends to change as the result of closing sale transactions, rolling forward, or exercise. Sellers tend to buy out their positions as time value falls, and buyers tend to close out positions as intrinsic value rises. And as expiration approaches, fewer new contracts open. In addition to these factors, open interest changes when perceptions among buyers and sellers change for the stock. Unfortunately, the number of contracts does not tell you the reasons for the change, nor whether the change is being driven by buyers or by sellers.

## Applying the Delta

The delta of a call should be 1.00 whenever it is deep in the money. As a general rule, expect the call to parallel the price movement of the stock on a point-for-point basis, especially when closer to expiration. In some instances, a call's delta may change unexpectedly. For example, if an in-the-money call increases by 3 points but the stock's price rises by only 2 points (a delta of 1.50), the aberration represents an*increase*in time value, which rarely occurs. It may be a sign that the market perceives the option to be worth more than its previous price, relative to movement in the stock. This can be caused by any number of changes in market perception. The deeper out of the money, the lower the delta will be. Figure below summarizes movement in option premium relative to the underlying stock, with corresponding delta.

[caption id="attachment_12521" align="aligncenter" width="400"] Changes in an option's delta.[/caption]

Time value is reasonably predictable in the pattern of change, given looming expiration. It does not move in a

*completely*predictable manner, since perceptions about the option are changing constantly.

#### Example

**A Delta Increase:**You bought 100 shares of stock at $48 per share. During yesterday's market, the stock rose from $51 to $53, based largely on rumors of higher quarterly profits than predicted by analysts. The 60 call rose from 4 to 8, an increase of 4 points (and a delta of 2.00).

The same strategy can be applied when you already have an open covered call position and you are thinking of closing it. For example, your call is in the money and the stock falls 2 points. At the same time, option premium falls by 3 points, for a delta of 1.50. This could be a temporary distortion, so profits can be taken immediately on the theory that the overreaction will be corrected within a short time.

## The Rest of the Greeks

Beta and delta are the most popularly used and cited of the Greeks; but there are more levels of analysis as well. Another is*gamma*, which is a test of how rapidly delta moves upward or downward in relation to the price of the underlying stock.

The gamma changes as the stock's price moves away from the option's strike price. For example, when an option moves from out of the money and goes in the money, the delta tends to increase. How quickly that occurs is where gamma comes into play. You may also consider gamma a method for measuring extrinsic value. In other words, gamma will be at its greatest level when the stock's market value is at or near the option's striking price. When options are deep in the money or deep out of the money, gamma will be close to zero.

For example, if a stock is at $39, a call with a striking price of 50 may have a delta of 0.50 and a gamma of 0.05. When the stock moves up to $40 per share, the delta is going to grow by the same degree as the gamma (0.50 plus 0.05, or 0.55). Because delta can only by 1.00 at the most, this trend is limited and most meaningful when market value of the stock is very close to the option's striking price, which is always the most interesting price relationship where options are involved. Gamma is always expressed as a positive number, whether related to a call or a put; it is only a measurement of delta's trend. The delta will change to the degree of the gamma. In the example of a gamma of 0.05, if the stock moves one point, delta will change by 0.05, or 5 percent of the stock change; so if the stock moved up two points, delta would increase by 0.10 (5 percent of two points), from 0.50 to 0.60. Delta moves by the percentage of the gamma.

You can use delta and gamma in combination to test the relationship between a stock and its options, and to select one company over another because of levels in these price-responsive trends. You will also observe that as expiration nears, the gamma for at-the-money options is going to increase rapidly. It is quite likely that gamma will grow at about trice the price movement of the stock, because the delta is responding to the combined forces of pending expiration and in-the-money or at-the-money price changes. In comparison, out-of-the-money options near expiration are going to have very low gamma trends; and as expiration is closer, the gamma trend confirms the ever-lower expectation that the option will move in the money.

Another interesting Greek is the

*tau*, which is also termed

*vega*by some analysts. This measures the relationship between an option's price and changes in the underlying stock's volatility. Whether applied to a call or a put, tau is always a positive number.

The less volatile a stock, the cheaper its options. So if and when volatility increases (especially if measured as an expansion of the stock's trading range), option values will rise as well. Defining "volatility" as the percentage of range off a stock's 52-week low, you can quantify vega in the same manner, on a percentage basis. This becomes very interesting because it assigns a percentage value to an option's premium; and it also places a numerical value on a stock's market risk. This is useful for comparisons between stocks and their options.

On average, stocks are expected to show around 15 percent volatility. For example, if a stock has traded between $20 and $23 per share, the three-point spread represents 15 percent volatility (3 Ã· 20 = 15 percent); as a stock's value changes, vega tracks that change.

Another Greek,

*theta*, reveals the strength or weakness of time value (exclusive of extrinsic value), also known as

*sensitivity*of the price in relation to the time remaining until expiration. Many options traders consider theta the most important of the Greeks because time sensitivity defines value, notably near expiration.

Theta is valuable as a comparative study between two or more options (and their underlying stocks). Based on a stock's specific volatility, time decay may be quite rapid or fairly slow; and identifying the degree of theta characteristic of a particular stock is a valuable analytical exercise.

The Greek

*rho*is also a sensitivity measurement, but is far less directly involved in valuation than most other Greeks. Rho compares pricing of options to trends in interest rates, based on the theory that the higher market interest rates trend, the higher call pricing. This Greek is less useful than most others, however, because it is not easy to translate long-term trends such as interest rates, into action steps for fast-moving markets such as options. The general observation of rho is an oddity: As interest rates rise, call prices will follow, but put prices will tend to fall. In this regard, rho becomes an expression of market sentiments based on interest rates, with the results seen in option prices.

The Greeks are collectively an interesting series of observations concerning option trends and tendencies. All options traders are aware of changes in valuation based on the proximity issues: between striking price of options and market value of the underlying stock, and between today and expiration. The Greeks are useful for tracking the changes in all three forms of value (intrinsic, extrinsic, and time) but are also best used to make comparisons in option valuation between two different companies. Time, volatility, and chance all play roles in valuation; the Greeks are useful in observing how prices and values react to ever-changing market conditions.

By Michael C. Thomsett