We have all heard the term “the Greeks” as it applies to stock options. Most of us know that these factors somehow explain how certain parameters can impact the value of an option premium. To avoid facing some members of the BCI community claiming that “this is all Greek to me”, this article will serve as a review of this subject.
There are several factors that allow us to estimate the risks associated with our option positions. Together, they fall under the heading of the “Greeks” because most of them are named after Greek letters.
The Major Greeks:
Delta: Price sensitivity. The most commonly used Greek measures how much the theoretical value of an option will change if the underlying value of the stock moves up or down $1. The delta of a call can range from 0.00 to 1.00. The closer an option’s delta is to 1.00, the more the price of the option responds to a similar degree as the underlying stock, when the stock price moves. For example, if company BCI is trading at $38/share and the $40 call is selling for $2, with a delta of .50, the following would be true if all other factors remain constant:
- If BCI increases to $39/ share, the $40 call would increase in value to $2.50
- If BCI decreases in value to $37/share, the $40 call would decrease in value to $1.50
- In other words, for every change of $1 in share price the option value changes by one half that amount.
Gamma: Second order price sensitivity. The rate of change for delta with respect to the price of the underlying security, you can call it “the delta of the delta.” It is an estimate of how much the delta of an option changes when the price of the stock moves $1. When an option is deep in-the-money or deep out-of-the-money (several strikes above or below the market value of the stock), the gamma is small. When the option is near the money, the gamma is the largest. Gamma is used when trying to gauge the price of an option relative to the amount it is in or out of the money.
Theta: Educated covered call writers know that it is critical to sell our options early in the 1-month cycle. I always try to sell my options in the first week of a 4-week expiration cycle and no later than the beginning of the second week of a 5-week cycle. The reason has to do with the time value of the option premium and the erosion of its value over time. This is known as theta and it is one of the option Greeks. As Blue Collar Investors, we are selling time or Theta.
Theta is an estimate of how much the theoretical value of an option declines when there is a passage of one day while there is no change in the stock value or volatility. Theta is expressed as a negative number since the passage of time will decrease time value. If the time value of an option premium falls by $0.05 each day, its theta is said to be (-) 0.05. You will remember the equation for the value of an option:
Option Premium = Intrinsic Value + Time Value (extrinsic value)
Since intrinsic value only changes with the movement of the stock price, theta plays no role in this aspect of the option premium. However, it does have a major impact with time value and covered call writers should be aware of this relationship.
Theta’s role in reducing option value:
As an option approaches expiration Friday, theta has a greater impact on the option value. Let’s look at a 1-month graph of a hypothetical option value (figure below):
- Chart of theta
Theta- 1-month Chart
Notice how the decline in time value starts off gradual (red), accelerates (blue), and then “falls off a cliff” (green).
Theta and strike prices:
Since at-the-money (A-T-M) strikes have the greatest time value (ROO), they have the most to lose over time. Therefore, theta is greatest for A-T-M strikes and lower as options go deeper I-T-M or O-T-M.
Theta and volatility:
As volatility increases, theta increases and vice-versa. Higher volatility means greater time value so each day’s decay will be greater if there is no movement.
Theta and days to expiration Friday:
Theta increases as there are fewer days to expiration Friday.
Theta and covered call writing:
It is important to understand the general concept that theta plays a major role in devaluing option premiums especially for our 1-month contracts. This favors our strategy in three ways:
1- Allows us to capture a generous option premium shortly before its dramatic time value decline.
2- Allows us to close our positions profitably during the week of expiration Friday (if we chose to do so) as the cost to buy-to-close has dramatically declined, especially if the stock price has not changed.
3- Allows us to execute a mid-contract exit strategy at a reduced price.
Understanding theta also drives us to selling our options at the ideal time, not too early and not too late.
It is not necessary to analyze the specific theta of our sold options however, understanding the principles of theta and the impact it has on our option values will make us better investors.
Vega (the only “Greek” not represented by a real Greek letter): Volatility sensitivity. It is the amount that the price of an option changes compared to a 1% change in volatility. Higher volatility means higher option prices. This is because the greater volatility brings with it larger price swings and more likelihood of an option to make money. Vega is highest for A-T-M calls and lower as options delve deeper I-T-M and O-T-M. Vega also falls as the option gets closer to expiration.
Rho: Not considered a major Greek, measures the change in the option price due to a change in interest rates. As interest rates increase so does the option value as owning the underlying security will result in opportunity lost when interest rates go up. Buying a call option rather than the stock will allow the option buyer to use the “saved” cash to take advantage of these higher interest rates.
The bottom line is that it’s not essential to memorize the definitions of the Greeks (unless you’re going to appear on Jeopardy). It is helpful, however, to understand the concepts of how price, time and volatility play into the value of our option premiums and what that says about the nature of the underlying equities.
As we enter another earnings season, this week’s economic mixed reports leaned to the negative:
- The US economy added 80,000 jobs in June lower than the 90,000 anticipated leaving the unemployment rate unchanged
- The average workweek and average hourly and weekly earnings did increase slightly
- The ISM manufacturing index for June dropped to 49.7, lower than the 52.6 expected. This was the first time since July, 2009 that contraction in manufacturing was seen
- The service sector expanded for the 30th straight month in June but fell to 52.1 lower than the 53 expected. This was the 3rd decline in 4 months
- Construction spending rose 0.9% in June, more than expected (0.2%). Construction spending is up 7% from a year ago
- Factory orders increased by 0.7% in May, better than the anticipated (-) 0.2%
- Factory shipments rose by 0.5% in May, the 5th rise in 6 months
For the week, the S&P 500 declined by 0.5%, for a year-to-date return of 8.9%, including dividends.
A 6-month view of the S&P 500 using 50-d and 200-d simple moving averages (SMAs) show that the benchmark is currently trading above both moving averages with the most recent price declines shown below on lighter volume due to the holiday week. Corporate earnings have been a positive for the stock market as we enter the next earnings season so this site will be incorporating a higher percentage of out-of-the-money strikes for new positions (still favoring in-the-money strikes however):