Path dependency and options
By buying options, we trade path dependency for time dependency.
Options are the most comprehensive tool for risk management. When applied wisely, they are the ultimate Alpha generator. Therefore, options hold a special place in my toolbox.
So, it's time for a write-up on options. Today, we go back to elementary school and recall the first of three variables describing the motion of a physical object: distance, velocity, and time. Price movements are also subject to description with these parameters, which are the essence of technical analysis and risk management.
In the first case, they are part of the Big Five in price – direction, magnitude, volatility, probability, and time. In the second, they describe options as a risk management tool. Today, I reflect on the first advantage of long call options—they do not need a stop loss.
All principles, formulas, and tables discussed below apply only to long positions in call options. They are invalid and even dangerous when applied to other option strategies.
The price reaches my take profit, and I am still losing
Financial markets are self-emerging complex systems—(almost) an infinite number of participants with different motivations and capabilities interact in myriad ways. Typical for any complex system is a lack of linearity and an abundance of paradoxes.
One paradox is that we can be directionally correct while remaining on the losing side. At first glance, the reason is apparent: inadequate timing and poor position management (entry point, stop loss, take profit).
Look at these three points—entry price, stop loss, and take profit—as physical objects on a map. They can be reached by taking different routes, and the outcome is a function of the path taken.
Every position we take on the markets has one purpose: to get to the point of “Take Profit.” However, this does not always happen because the price does not move in a straight line. The best scenario is that the price heads directly toward our destination, “Take Profit.” The second outcome is that the price hits our stop loss straightaway. The most annoying occurrence is when the price reaches “Stop Loss” first and then reverses back to go through “Take Profit.”
We have three scenarios. In the first one, the price hits a stop loss and continues down, i.e., we realize a loss. In the other two scenarios, the price reaches our take profit, but we score win only in one.
The scenarios show that the position outcome depends on the distance traveled. This is called path dependency, and it is typical for complex systems such as financial markets.
So, let’s go deeper into details. I present three scenarios for possible outcomes to get into the idea. I purchased ABC company shares with the following parameters:
Entry price $100/share
Stop loss $70/share
Take profit $190/share
Risk reward 1:3
The scenarios look like this:
· The price goes directly to stop loss - we lose $ 30;
· The price first reaches the stop loss, then turns up and hits the take profit level - we lose $30 again;
· The price goes directly to the take profit level - we win $ 90.
This simplified example shows that reaching a take profit can be done in two ways, yet the outcomes differ. In one case, we won $90; in the other, we lost $30.
How do options outperform the outright purchase of shares in this case?
For call options expiring at least 12 months from the day of purchase, even if the $100 price of the underlying asset becomes $1, we still have the optionality of winning eventually. In the worst case, we lose the option premium. If the share price crashes by 99% and never returns (at least until the option expires), we will only lose the premium.
The characteristics described make the options immune to path dependency. By buying a call option, we make a trade - we put a time limit (the expiration date) to protect ourselves against path dependency.
The ABC position played with call options would look like this:
Price of the underlying (ABC company share): $100/share
Option strike price: $190
Option expiry date: after 12 months
Option price: 10$
We enter in one tranche with $100 (buy ten option contracts)
Stop Loss: wait until the option expires, when its value will be zero.
Take Profit: when ABC shares reach the strike price of $190, the option price is $40. At that point, we earn $300 (10 options*$40 - 10 options*$10 = $300)
Risk reward 1:3
Let's look at a hypothetical path of ABC share price and how the option price changes:
· ABC price $100, option price becomes $10
· ABC price $90, option price becomes $8
· ABC price $80, option price becomes $4
· ABC price $60, option price becomes $0
· ABC price $50, option price becomes $0
· ABC price $40, option price becomes $0
· ABC price $10, option price becomes $0
· ABC price $3, option price becomes $0
· ABC price $60, option price becomes $3
· ABC price $90, option price becomes $4
· ABC price $190, option price becomes $30
Regardless of ABC's share price path, the option holder has two options (I exclude option exercise): either the share price has reached the strike price by the expiration date—a gain of $400, or the share price has not reached the strike price—a loss of $100. There is no scenario where the share price reaches our take profit (before the option expires), and we realize a loss.
To recap, equity position means the price may hit the stop loss and then return to the take profit—in this case, we lose. However, when we buy options on ABC stock, we profit because our stop loss is not defined by price levels but by option expiration.
Despite how steep the underlying price decline (from $100 to $1 in the ABC example) is, buying a call option limits our loss to the option premium. The underlying price affects the option price until the latter becomes zero. Once the option has lost value, its price cannot have a negative value, no matter how much its underlying falls. At the same time, the fact that it has no value does not mean the option has lost its validity. The option is valid until the expiry date. If the price of ABC recovers enough before the option expires, its value will rise.
As you can see, after the bottom of $3, the ABC price makes a turn and reaches $190, where the option costs three times more than we paid for it. On the way up, the option gradually recovers its value.
If we buy ABC stock directly, we are exposed to path dependency. Price fluctuations may take us out when the price knocks our stop loss and later arrives at the take profit. With options, however, we are immune to this situation because we do not have a stop loss based on ABC's price. As long as the option has not expired, we can still win.
Final Thoughts
Path dependency in stocks can be described with the following metaphor: we travel to San Francisco, as our starting point is New York. We are not constrained in time, yet we have enough fuel only to cover the distance from New York to San Francisco. If we deviate to Houston, we will consume more fuel and not have enough to get to San Francisco. Eventually, we will be stuck between Houston and San Francisco. It's like hitting a stop loss on a stock position, which means we are irreversibly out of the game. In this case, our trip is bounded only by fuel, not time.
Let's now look at how options work using the same metaphor. We have unlimited fuel but 72 hours to get to San Francisco. It doesn't matter if we divert to Houston or another city if we arrive in San Francisco within the 72-hour time frame. In this case, our journey is defined only by time but not by fuel.
In the above examples, the finite fuel is path dependency, and the 72-hour limit is the time remaining before the option expires. By buying call options, we trade path dependency for time (and volatility) dependency.
Today, I shared some thoughts on options. In the coming days, I will cover two other variables in the distance traveled formula: velocity and time.