- Logica

# Volatility Headwinds

Updated: Jul 4

*The following is an excerpt from Logica's April 2021 monthly letter. If you're a qualified investor interested in receiving the full version of our monthly communications, please subscribe.*

**"You know, I couldn’t do it [prepare the lecture]. I couldn’t reduce it to the freshman level. That means we really don’t understand it." **
**- Richard Feynman**

A question we often get asked is to explain (in plain English!) how unforgiving a volatility headwind can be. So, let’s jump into it and try to keep it simple. We’ll use the theory behind Black-Scholes options pricing model, but leave out the somewhat complicated mathematics, and if we’ve done a good job, the conclusions will hopefully be intuitive.

Scenario:

We hold an ATM straddle consisting of a $100 strike call and a $100 strike put on a stock that is trading at $100.

Volatility = 27.95%

Time to Expiration = 45 days

**According to the Black-Scholes option pricing model, our call and our put are worth $3.91 each.**

Now we do 2 things to simulate reality (approximating the volatility crush in March 2021):

Volatility drops from 27.95% to 19.40%. To isolate the variables, our thought experiment ensures that the underlying does not move, and that no time has passed.

**Each of our options are now worth $2.72**. We should notice something important: our at-the-money options have decayed in near exact proportion with volatility (vol from 27.95 to 19.40 is a 30% decrease, and our option prices going from $3.91 to $2.72 is also a 30% decrease).Additionally: no one escapes time. The passage of time must decay our options further. They’re not worth $2.72 anymore. Now that we’re at month end, with only 15 calendar days to expiration and not 45,

**each of our options are only worth $1.57.**

That’s the bad news. Here’s what these steps look like:

But here’s the good news: when volatility crushes like this, we can typically assume that the underlying asset rose in value. The question is how much does the underlying actually need to rise in order for us to break even on a naïve, ATM straddle? Well, if you don’t have quick access to a graph like we show above, here’s a back of the envelope intuition for environments like this where volatility crushes significantly and the underlying is rising: the value of our call option needs to double, because the value of our put option is going to be very close to $0**. **Said more simply: we need the underlying to rise approximately as much as the total cost of the straddle** (here, [$3.91*2], or $7.82).

**So our call option that we bought for $3.91 needs to reach nearly $8, **given that our put will lose a significant portion of its value when the trifecta of underlying appreciation, volatility crush and time decay occur. In our case, this means that we need the underlying to appreciate from $100 to nearly $108, i.e., a gain of just under 8% on the month.
As an aside: this is why a naïve straddle does well in months where the underlying experiences *significant* appreciation even alongside volatility crush: the put quickly loses a significant portion of its value after a few % increase in the underlying, and the call option position is allowed to accumulate delta over the course of the month. Of course, this means the straddle would be long delta at an increasing rate, and though it has an OTM put option on the books, should anything bad happen, it’s going to be a while before that defensive side kicks in (as anyone who has bought “lotto puts” as a hedge knows all too well).
Let’s consider that with more specifics: with one week to go in the month, let’s say the underlying had risen by 6%, well on its way to that 8% MTD gain needed on the call side: the naïve straddle would now hold an 80 delta call option and a -20 delta put option. This looks more like a typical “hedged long” position rather than anything remotely resembling a “neutral” profile that we started the month with, and its behavior over that final week will of course be commensurate with that imbalance – fantastic if the market keeps climbing, but dismal if it gives back, or anything worse. And here’s the real kicker, *the position would be down on the month at that point* in our example. Our thought experiment needed that additional upside move from +6% to +8% MTD just to break even! Should the underlying drop a couple percent, the likely rising volatility would be a boon, but the overly long/poor delta positioning would be overwhelming, resulting in a loss, and a month where the straddle would have *lost money* even though the underlying was +4%.
In summary, in an environment of declining volatility, there are no *great* solutions for long volatility strategies, as absent the significant risk of overly long delta exposure, the only posture is defensive. But there are ways to preserve as much capital as possible. As "boring" as capital preservation sounds, it greatly increases a portfolio's long term geometric return. Thus, during these times, one must essentially use their "alpha" to soak up as much of the headwind as possible. Then, recalibrate to take advantage of a more favorable environment.

It must also be noted, of course, that the difficulty in enduring State 2 above is the other side of the convex payoff that one experiences during times of crisis (when volatility spikes). This crisis return is * incredibly *valuable to a portfolio's long term geometric return, the details of which we'll elaborate on in a future communication.

***Remember noticing that our at-the-money options have decayed nearly exactly proportionally with volatility. When an option is not in-the-money, at a single point in time it is essentially “all volatility,” so when volatility crushes, the option’s worth deteriorates rapidly. The intuitive way to think about this is simply: because “volatility” is analogous to a “probability distribution,” when that distribution of likely events significantly narrows, the option is less and less likely to be worth anything ("in the money"). When volatility doesn’t crush, (assuming for sake of example: the underlying doesn’t move either), the option price deteriorates only due to time passing. *