Revisiting the Covered Call Experiment

Yes, you in the front? What is your question?

Source: Sketchplanations. Clearly a close cousin of the bullet hole patterns in the returning airplane analysis. Note: let’s avoid this in our trading. Also, this is not really related to this post. It is just so good I wanted to share. h/t here.

I’m quite appreciative that I got a few questions from the prior post on the covered call experiment done by Kris & Mark. You can see their video here and last week’s post is here.

The question revolved around the idea that I floated regarding option premiums as representing the expected pnl of replicating the option. I wrote:

Personally, I was a bit surprised by the results and I’d like to pursue it further. One of the ways that I think about options is buying future liquidity now. Options pricing is based on an estimate of replication. Replication is buying and selling the underlying to end at an expected value of the option price. So it seems to be that if I sell a covered call that I’m selling that replication. Since I, as an individual, don’t have great trading rates or an amazingly efficient dynamic hedging strategy, selling that to a sophisticated options market maker ought to be accretive. Yet this research suggests otherwise.

Losthighway reframed this paragraph in what I think is a really easy to digest way:

Let me just check I was understanding your point. I was thinking that you were giving something like the following argument

(a) (arbitrage constraints tell us that) we can think of selling a covered call as selling the replication of the underlying

(b) normally if X can make more money M than Y from the use of R then it can make sense for Y to sell R to X for some sum less than M. For example if I am really bad at collecting overdue sums owed to me but you are good at collecting ones owed to you it can make sense for me to sell my outstanding overdue receivables to you at a discount. That helps us both, and is accretive to what I would have brought in if I hadn’t sold.

(c) market makers can make more money than I can via being able to buy and sell the underlying so as to replicate the option

Therefore

(d) Unless trading costs are too high to make it worthwhile, we should expect that there is a price between the value of the option to me and the value to the market makers such that if I sell it to them we can both do better than if there was no sale. Efficient market forces should lead us to expect that that kind of price should be offered.

So far so good for theory, but we don’t observe that. Question is, why?”

I can think of a few reasons why that may not be. First, it may be that TSLA is a very high volatility stock. The high volatility means that there is not much information content in the price and path of the price. Therefore, the study is too small to have great confidence in it.

Second, the price path of TSLA might be autocorrelated, i.e., it behaves (or behaved) with momentum. Recall that at the very core of option pricing is the assumption that each day’s move is an independent event. This may not be true for TSLA or for all of time series of TSLA’s trading. It may not be true for smaller capitalization stocks. Or it may not be true for high volatility stocks as the high volatility forces stops/deleveraging trades in both directions¹.

Third, maybe it is a bit subtler that all of the above and it is the downside risk that hurts the situation far more than I realized. That is, if TSLA drops significantly, the capital base is eroded and then a far lower call strike is sold thereby locking in a loss.

Fourth, given the volatility of TSLA, it is entirely possible that there were opportunities to buy back the options at nearly zero and the trading system did not do that. Consider TSLA at $400 and selling a 30-day $450 call for $11 (60 vol). TSLA drops to 350 with 10 days left. The now 10d $450 call is worth $0.08. Perhaps if there were a strategy to buy back sold options at 0.25 or less that would have a major impact. This may seem to be optimizing, but IMO the point of selling an option is to receive the premium. If the premium is essentially zero, then the trade goal is achieved even though the trade is still on. Since the sold call is now approximately zero (no matter what the implied volatility), it has become “return-free risk” (h/t Jim Grant’s phrase).

I’m going to throw out #1. Of course, we will always benefit from more data. Partly I want to expunge it simply because it is a fact of life. We need to acknowledge the reality of data paucity without giving up entirely.

As to the rest, it seems far more likely than not that it is some combination (I don’t mean to keep out anything that I’ve omitted, just making the note that it has to be more likely to include multiple factors than just one).

Some experiments that we can run to begin to figure this out:

1. Run the experiment and see what happens if we buy rather than sell the 25d calls

2. Go through each trade, measure what the option pricing model tells us is the probability of expiring above (this is not delta but N(d2)). They are typically close, but deviate as volatility goes higher. Compare that probability to the observed events.

3. Measure the 3rd (skew) and 4th (kurtosis) measures for TSLA to determine how non-normal they are.

Let’s throw that on the to-do list :)

Warren follows up to Losthighway’s comment and asks:

Could this work the other way, in the sense that market makers are good at both replicating the long and the short options? If that is the case why would it be accretive to only sell them the option?

To which my answer is that 1) good question! and 2) this is all true except that the trade is not symmetric. Consider the two cases. Case 1: I sell the option to the mm and i do ... nothing but i do get to collect the best estimate for what I can earn trading that options. Money in my pocket. Case 2: I buy the option and now it is incumbent on me to earn back the premium that I paid up front. Buying the option requires action.

For those that are familiar with swaps, this is akin to a swap between fixed and floating. Floating here would be the pnl that one can generate trading the underlying. Fixed here would be the option price.

1. For example, TSLA is $400. Speaking tongue-in-cheek and hypothetical, the random (independent) move has TSLA rally to $433. However, that then causes a short to cover their position (whether due to the risk group or the trader’s stop-loss). Collectively, those stops send TSLA further to $441. This then brings in momentum traders looking to keep things going. Yes, I’m making up a narrative so take it stylistically.