• Noel Smith & Leo Capalleja

The Hidden Risk in Holding to Expiration

In the context of options strategies, while it is true that by covering early we reduce potential profit, we can dramatically increase our chances of long-term survival.


Often investors base their decisions on summary statistics such as expected return and standard deviation of returns. They assume that these statistics can provide a complete picture of risk/return and often fail to consider the effects of tail risk. These oversights can lead to dramatic draw-downs which can be extremely difficult to recover from. One real-world example of this is holding options too close to expiration.


Orange or Blue?


Consider the following scenario: An investor is given the choice to allocate capital to one of two strategies, named Orange and Blue. Both are options strategies with the main difference being that in Orange, options are held to expiration while in Blue, options are covered early.


Return distributions of two strategies that have the same mean and standard deviation but have different medians and tail risks.
Return distributions for Orange and Blue strategies. The strategies have the same mean and standard deviation but have different medians and tail risks.

Both strategies have the same expected daily return and the same standard deviation. However, Orange has a higher median return (nearly 10 times that of Blue) and a lower probability of loss on any given day (37% versus Blue’s 49%). An investor, armed with only this information, might reasonably choose to allocate to Orange.


Suppose the investor were then provided with a detailed daily payoff distribution of the strategies as seen above. We can see that Orange indeed has a higher median return but at the cost of significantly higher tail risk. Should this new information influence the investor’s decision?


Running Simulations


To investigate this further, we simulate Orange and Blue one thousand times each for a time frame of 20 years. For such a time frame, it is important to consider the influence of human psyche and fear on investment allocation. Therefore, we make the simple assumption that investors will not realistically tolerate draw-downs of more than 50% as these are extremely difficult to recover from.


With these simulation results, below, we can see the glaring weakness of Orange – it is almost 5 times more likely to experience a devastating 50% draw-down than Blue. While calculated risks are a cornerstone of savvy investing, “betting the farm” for a few extra points should never be considered a worthy trade-off. Worse yet is to unknowingly enter this scenario.


Simulation results for two strategies with the same mean and standard deviation but different return distribution shapes.
Simulation results for Orange and Blue strategies. The shaded areas represent 1,000 iteration paths over 20 years. Iterations that experience a draw-down of greater than 50% are knocked out.

Conclusion


In the context of options strategies, while it is true that by covering early we reduce potential profit, we can dramatically increase our chances of long-term survival. As a short options position starts to decay at a non-linear rate, it is overall less risky to cover or roll the position. In practice, this usually starts to occur about 2 or 3 weeks prior to expiration. The added theta profit as expiration approaches can lure yield-seeking investors to hold positions for too long, allowing gamma exposure to explode. At this point, the position greatly increases in risk as any short-term shocks will force out-sized delta-hedging activity.

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