options policework

A moontower user sent this [paraphrased] message in our Discord the morning of Jan 9th:

NLR [VanEck Uranium and Nuclear ETF] had a price shock on Jan 2 and has been ‘fast grinding up’ since then. Did I “lose” here because RV climbed up faster than RV and my losses are ‘gamma’ driven?

Now the most important part — what can I learn / what should I do as part of my process?

We are going to do the post-mortem in steps. The first task is to take inventory of the scene. Basic policework. “What happened?”

Once that’s established, we can at least start to disentangle bad luck from decision quality and finally wrap up with risk management/hedging/whether we should close the position or not.

Arriving at the scene of the crime

What do we know? Our friend sold a small amount of 1-month NLR at-the-money straddles in December. To be discreet, I’m going to guess the date to be December 15th and the strike to be the 126 line and IV was ~41%

Below is a simple time series of:

constant maturity 30d IV LAGGED vs 30d realized vol

By lagging IV, we align it with the 30-day realized vol that was experienced in the subsequent month. We can see that the RV (faint green line) our friend experienced far exceeded the IV (dark blue line) of the straddle they sold.

A chart like that is a handy compression, but since it is:

1. using constant maturity vols (ie interpolated) and
2. floating (the IV is taken from the .50 delta call each day)

…the chart is not high-resolution to discuss p/l, but can only gesture roughly to its direction. It’s a blurry picture of a license plate as the driver speeds away.

We will get down to the contract level, but first, we want to develop a sense of proportion about notable move sizes.

Realized vol

✅Jan 2nd was the steepest one-day move: 7.1% or about 112% vol annualized. Nearly 3 standard devs.

✅ Over 8 days, there was a 13% cumulative rally, or 73% annualized vol.

The calculation: 13% *sqrt(251/8) = 73% annualized vol move

Any funny business under the hood?

• NLR’s largest component, CCJ, is ~9% of the basket. It rallied a bit over 7% as well which is frankly underperforming the basket since CCJ is a higher vol than the ETF.
• Its second largest component is DNN ~6% but lots of names in the basket are close to that size. DNN was up 14%…but its normally twice the vol of the ETF already.

In z-score space, the ETF and its 2 largest holdings all moved about the same amount.

All these clowns are riding in the same car. Its a 1-corr move, in a beginning-of-the-year inflow to this sector.

💡For those of you who trade around rebalancing and calendar anomalies, perhaps this is a thread to pull on?

Drilling down to the option contract level

The NLR option volume in the month preceding Jan 9th was not notable. There was a spike in puts traded on Jan 5th, but this was already after the largest single-day move happened

The largest component, CCJ, did not have any noteworthy volume in the prior month either.

What stands out in NLR is how small the open interest is in general. This is not a liquid option name.

Price and P/L

From December 15th to Jan 9th, the Jan 126 straddle expanded from $12.75 —> $15.50 as the stock went to $140. No surprise, the call went to >.90 delta.

So the short straddle position lost $2.75, assuming you did not hedge any of the delta on the way up.

If you’re intent is to trade vol, allowing the delta to ride like that is introducing a lot of noise into your trade expression that was supposed to be about vol.

What if you sold the straddle and hedged the negative gamma daily by bringing your deltas back to neutral? In other words, buying shares after they rallied and selling them as they fell in opposition to the changing straddle delta.

Our service includes an attribution visualizer which allows you to decompose your daily and cumulative p/l due to realized and implied vol changes as the option and stock price move around. It is from the perspective of an option buyer. In this case, we are selling, so just flip the signs. We also need to double the numbers since we are assuming a straddle hedged daily, not a single call or put as the tool assumes.

The total ACTUAL delta-hedged p/l as of January 8, the day before the friend messaged the group, would have been -$.51 per contract or -$1.02 for the straddle. The loss would have been less than letting the straddle ride, since the stock trended up and each rebalance would have forced the hedger to buy on the way up.

If the stock chopped around at 70 vol but still landed on the strike, hedging would have locked in a bunch of negative gamma scalps while the straddle decayed.

Hedging makes your p/l reflect the vol that was realized but whether this is good or bad for you, ex-post, depends on whether the stock chopped or trended.

Ex-ante, you want your hedging to be aligned with the reason for your trade, which in this case is presumably the expectation that IV would have a risk premium above realized, since the trade was selling 1-month atm straddles.

A note on attribution

The chart doesn’t track the sum of unexplained p/l although it is displayed in the summary (not shown). The “unexplained p/l” is the balancer which makes the theoretical attribution tie out with the actual p/l. It is a catch-all for the higher-order greeks, mostly vanna and volga, which reflect the fact that your gamma and vega, respectively, are not constant during a single day’s move.

The bulk of the p/l on that big day is due to realized. It’s fair to say from the summary that realized p/l explains most of the result. This is what we’d expect from an option with only a few weeks until expiry.

No smoking gun

Given the lack of notable action in the option volume in either NLR or its components, the uniform behavior of the moves in the complex, a boring IV chart to close out 2025, and the fact that the move happened on the first business day of the year, that this result was a bunch of methodical but unanticipated sector flow. Approximately 2.8 sigma move in one day, or about 1/200 probability, a bad beat with roughly the same probability of being dealt pocket aces (1/221 because 4/52 * 3/51).

[Stock moves are fat-tailed, so the probability is actually larger than 2.8 sigma would predict, but the fact pattern here still suggests a bad beat. The IV wasn’t suspiciously high in December, there wasn’t any telegraphing flow].

An opportune time to remember one of the reasons gambling and poker experience is helpful…from why poker is used to train traders:

This is one of the great teachings of poker. Short-term results are noise. He explains that in Limit Hold’em, even a high edge hand has only .02 big bets worth of expectancy vs a standard deviation of 2.5 bets.

[Kris: In investing language, a .008 Sharpe for one trial. The SP500 has a daily expectancy of about 3 bps and 100 bps standard deviation for a daily Sharpe of .03. The poker hand has almost 4x the noise of the daily SP500 return.]

Since poker teaches that you will make the right decision and still lose money, it trains you to emotionally decouple decision quality from result quality.

This is a ceaselessly profound concept. Not because it’s so clever, but because of how it resists internalization. It’s easy to understand, it’s hard to apply the understanding to how we receive the world.

As police work goes, there will be no verdict or even charges brought as to whether the decision to sell the straddle was sound. We do get research inspiration. Is sector dispersion especially high on the first of the year? First of the month? Is there more volatility in general on those days? If so, is the median volatility higher or the mean (ie is it being driven by outlier-type moves)? We don’t know if selling the straddle was bad, but we do get new questions. This is what a career in trading looks like. If you don’t like this type of problem, then hooray, I’ve saved you a bunch of time compounded over your life. You’re welcome.

Regardless of the outcome, we still have this business of risk management.

Should our friend have hedged or closed the trade?

The following is true but unknowable in advance:

• If the stock is trending, you want to hedge aggressively. Buy delta as it rallies, sell it as it falls.
• If the stock is mean-reverting, you want to sit on your hands.

Your risk approach cannot depend on what you don’t know. And it must depend on what you consider tolerable.

The combination of these constraints will dictate how big your position can be. We’ll call this your limit. From there, you are simply monitoring how big your position is under various scenarios to that limit. If it is greater than the limit, you must reduce it.

I’ll give a simple example, but know this is a vast topic and a chief concern (and unsolved problem…there’s no single answer to this) of any risk-taking outfit.

Let’s say you are willing to tolerate 1% volatility in your total portfolio due to a particular trade on your average day. If you have a $1mm portfolio, that’s $10k. To a first approximation, that means keeping your swings due to delta below $10k. Call NLR a $140 stock with a 48% vol. For a typical day, that corresponds to 3% moves or $4.20.

$10k/4.2 is the daily swings associated with ~2,400 shares or 24 100 delta options. Or 48 50 delta options.

So what is NOT conservative about this risk-based sizing:

1. “Typical day” is being proxied by 1 standard dev (ie the 3% daily vol). If moves are normally distributed, that means about 1/3 will be greater than that or more than a week out of every month will be composed of bigger moves. And that’s ignoring fat-tailedness
2. We aren’t accounting for adverse vol changes. If you are short options, trades are negatively skewed so we’ll want to be more conservative still.

What IS conservative about this risk-based sizing:

1. If you hedge your deltas even once a day, you will not have as much daily variance in your p/l due to delta, which is effectively what we’re describing above.

How does this shake out?

A good starting point!

In the case we’ve been following, if our friend used a rule like this, it woud have prescribed 48 50 delta options or 24 straddles.

The straddle went from $12.75 to $15.50 on a bad beat with no hedging.

The loss = 24 straddles * -$2.75 * 100 = -$6,600

If our friend hedged daily, mirroring the attribution visualizer recipe, the loss would have been:

The loss = 48 contracts * $-.51 * 100 = -$2,448

Notice the constraint:

This makes sure delta is positive for the sake of the calculation AND doesn’t allow you to oversize a position just because you chose a skinny option.

I came to this example from the perspective an option seller. If you are a buyer the most you can lose is your premium if you DON’T delta hedge. You can use your risk tolerance for losing money as your premium spend limit.

If you do delta hedge, you can lose many multiples of your premium. For example, if you buy an OTM put and the stock grinds down slowly to your strike, you will be buying shares all the way down. You will lose not only on your stock trades but also on the premium going to zero. T

I’m going to pause for a second to level with you because I do feel some almost paternal responsibility stemming from the privilege of many smart but also young readers who come to this letter to hear from me because of my gray hair and specifically because I won’t treat options like the next house-flipping get-rich trend.

This topic of risk is so vast that its discovery is an ongoing project throughout your career. You are shaping and being shaped by the rules you create and their feedback, so to think there’s an “answer” is to not appreciate how many facets there are to managing risk across a portfolio of non-linear instruments.

To recap…this was a “3 standard deviation” move and the loss was comfortably below our tolerance. You can season to taste, but this is overall a conservative approach that you can experiment with. This is a point-to-point p/l, so the rule is providing some flex for tough marks along the path. Like I said, a starting point.

🔗If interested, my treatise on hedging If You Make Money Every Day, You’re Not Maximizing

What the risk management decision is NOT about

I’m saying this because the fact that you already have a trade on is not a reason to keep it on. If you don’t want to put the trade on fresh, you should get out. There’s an opportunity cost to your capital.

If a trade you have on is not bad but just fair, then the decision comes down to whether the variance is acceptable. If there are costs to getting out of a coin flip that you can sweat the risk on, then it’s ok to save the transaction costs. You can refine that a bit to “is the coin flip’s expectancy the same as my cost of capital” yadda yadda, but you get the gist. There’s a cost to reducing variance (ie hedging or closing) and it’s perfectly fine tto avoid it if the risk is tolerable. There are a lot of risks in life you don’t bother hedging.

Finally, rules aside, if you are regularly running risk that makes you lose sleep, impairs your judgement, or threatens to blow you up even 1% of the time, the size is wrong. 1 in a 100 is inevitable if you plan on doing this for awhile.