To The Moon

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Welcome to Tiger Academy - 「Options Greeks Column」episode 3.

In our previous article, we mentioned that due to the presence of the gamma coefficient, at-the-money options make money the quickest. However, at the same time, as the expiration date approaches, at-the-money options also face the highest time decay risk.

So, how can one manage the risk of time decay, and is there a scenario where options with longer expiration dates have smaller time values?

Today, we will address these questions by exploring another Greek value of options - theta. First, let's understand what an option's theta value is.

1. what is the Theta of an option?

Theta represents the change in the option price due to the passage of time. In other words, it indicates how much the option price decreases with each passing day, assuming all other conditions remain constant. For example, if the theta value of a call or put option is -0.6, it means that the value of this option contract decreases by $0.6 every day, holding all other factors constant.

Why does the time value of options decrease every day? We discussed this in a previous article, "Day4.Why are options losing money when the stock price remains unchanged?" As a result, experienced options traders are familiar with the saying: Time is the friend of the seller and the enemy of the buyer!

Whether it's a call option or a put option, the theta value is always negative because time is constantly passing, and the expiration date is approaching. Therefore, under constant conditions, the time value is always diminishing. Furthermore, as the expiration date approaches, the time value erodes more rapidly.

In other words, the theta coefficient of an option increases as the expiration date approaches. This is why options near their expiration date carry more risk. Therefore, it's advisable to avoid holding options until expiration, especially those with expiration dates approaching.

For buyers, the suggestion is that to avoid the erosion of time value caused by holding options for an extended period, it's best to consider closing and selling the options well before the expiration date if the stock price moves in your favor and meets your profit expectations. There's no need to hold them until expiration and exercise them for profit.

In addition, when choosing the strike price, at-the-money (ATM) options have the highest time value (with no intrinsic value), and their theta coefficient is also the highest for the same expiration date. Time value erodes most rapidly for ATM options. Therefore, while earning accelerated gains through gamma, you are also exposed to theta risk. In situations of uncertain stock price expectations, it's advisable to avoid holding ATM and out-of-the-money (OTM) options. In contrast, in-the-money (ITM) options carry the lowest risk.

To summarize some key rules regarding theta:

1. Theta is always negative, while time value is always positive. Time value decreases as the expiration date approaches.

1. Longer expiration dates result in greater time value.

1. At-the-money (ATM) options have the highest time value.

1. Time value does not erode linearly; it accelerates as the expiration date approaches.

Of course, rules are meant to be broken, and the above points are based on general situations. In reality, there are instances that don't conform to these rules, which we refer to as Time Value Anomalies (TV anomaly).

For instance, while it's a general rule that time value is always positive, as we mentioned in a previous article, "DAY 9. Can options make money if the time value is negative?" It's possible for the time value to be negative for many deep-in-the-money options. Furthermore, under similar conditions, it's also possible for options with longer expiration dates to have smaller time values. Don't believe it? Let's continue reading.

2. Does a Longer Expiration Date Result in a Smaller Time Value?

Let's compare two put options with a strike price of $220 for Apple Inc., one expiring on October 20, 2023, and the other on September 20, 2024. The time value for the former is $0.56, while the time value for the latter is $0.01. The latter option has an expiration date that's nearly a year longer than the former, but its time value is significantly smaller. What's the issue here?

The reasons for this are twofold:

1. Market Expectations: Firstly, both of these put options have the same strike price, which means their intrinsic value must be the same. The reason the option expiring on September 20, 2024, has a lower time value is due to market expectations. Additionally, if we compare, this phenomenon primarily occurs in the range of strike prices at or above $220. For options with strike prices below $220, those with longer expiration dates still have larger time values. Why is this the case?

The reasons are quite simple， The market price of options, to some extent, reflects investors' expectations about the underlying stock. If it's widely believed that Apple's stock price won't exceed the $220 strike price in the near future (before October 20, 2023), then options with shorter expiration dates become more attractive because they are less likely to result in losses. On the other hand, if it's more probable that the stock price will rise above $220 by September 2024, investors are more cautious about the option expiring on that date, which results in a lower price and lower time value.

1. Liquidity: Options markets generally have lower liquidity compared to stock markets. When there's a significant difference between bid and ask prices, it can lead to substantial price fluctuations. If a new order is executed at a lower bid price, it can cause a substantial discount in the option price. Since an option's price is the sum of its intrinsic value and time value, this results in a significant discount in the time value. Additionally, longer-dated options, which tend to have less active trading, may experience larger discounts, leading to lower time values.

So, what's the significance of encountering such a time value inversion when investing in options?

3. Time Value Inversion: How to Approach It

In general, this situation is most likely to occur with deep in-the-money options. For buyers, since the passage of time poses a risk, it can be advantageous to purchase options with longer expiration dates but lower time values, assuming your trading strategy is long-term and you have a neutral stock price expectation. This is especially true for American-style options, where you can exercise them at any time before expiration, and, from an exercising standpoint, they behave similarly to shorter-dated options.

However, if you have specific expectations regarding the stock's future price at particular time points in your trading plan, you should still prioritize those time points.

For example, if Investor A expects Tesla's stock price to likely rise to above $200 in a week, it's still preferable to choose a call option expiring in a week rather than one expiring in a year.

One important point to note, in addition to the rules about time value mentioned earlier, is that while theta is always negative and time value continually decreases as the expiration date approaches, within the holding period, an option's time value can increase due to fluctuations in the stock price. This brings us to a Greek value we will learn about in the next lesson, which is Vega. If you're interested in this aspect, please stay tuned for our next article.

That concludes today's content. If you found this article helpful, please feel free to like and share it, and you may win some virtual coins!