One Stone After Another
Vol #182: June 6th, 2024
Stone walls are heavy.
I knew this before I started the project, but I didn’t feel it until a few thousand pounds later. And that’s just the river rock. There’s at least six hundred pounds of mortar in the wall too.
When the material was delivered, there was nothing but boundless optimism. This new feature was going to add character, all the more so because it was done by hand - my hand.
Beyond a few small test cases to get the feel of “butter”, I had never done any masonry work before. Getting the mix right seemed important. When the mortar is too wet, it slides away and won’t stick. Too dry and it becomes brittle before fully curing. But the goldilocks proportions yield a spreadable frosting that binds, bolsters, and cements the stones into their ideal vernacular.
No matter how well researched and YouTubed they are, the novice is easy to spot because they are focused on controlling the wrong variables. Stone walls or software, there will always be corner cases. Measure twice because you can only cut once, but don’t worry about the precision of something three fasteners down the road. Reality gets in the way.
Each sixty pound bag of mortar was easier to mix than the last. No more bits flinging from an ill-conceived drill attachment, or lumps dropping in my Jordans from two summers ago. Working in the hot sun I even developed a system for gradually watering the mix that was going dry faster than I could piece the stones together.
But the glue that holds it all together isn’t the most important part. Settlers have been dry fitting stone walls for millennia after all. Like a game of tetris, what proves the most challenging is the linear nature of stone wall construction. The second row is built on top of the first, and the cap is only as good as its foundation.
Unlike bricks, river rock comes in many shapes and sizes. There are one inch skipping stones, and there are oblong chunks nearly a foot wide. Which piece fits in next is an optimization problem with a very short iteration cycle. Mortar smooths over a lot of our estimation errors.
With a pile of rocks four feet high and eight feet wide, there seems to be infinite choice. Somewhere in that pile sits the perfect rock to slot under a precariously balanced face stone. But I ain’t got time to find it. The scope is further narrowed because only two wheel barrows worth have been carted over to the work site.
There’s an initial filter of what gets brought over, but the clock is ticking and it’s time to make do with what you have. Just like a set of quotes that need to get out the door for an update, we have a form of the bin packing problem here. How can I get the biggest and best fitting rocks into that wall, without waiting to pick through the whole bunch?
Whether you’re trading or investing, opportunities come at you in sequence. On any given market morning, there’s a menu of prices to choose from, but endless offerings do not make for a strategy.
Before you dig into that rock pile looking for the perfect piece, know it doesn’t exist. That doesn’t negate the tremendous benefits of a well constructed wall or portfolio, but it helps frame how to think about your search.
At the risk of overengineering, we can consider the lessons of the secretary problem to better inform our masonry strategy. In this hiring scenario we have a fixed number of candidates and have to make a decision about who to hire after each subsequent interview.
The optimal policy here is to interview a small pool to get a texture of the distribution, and then once you find a candidate better than the best in that sample, hire them. The math says this will find you the best candidate overall roughly 37% of the time - not bad.
The reality of most hiring processes allows for batches of candidates to be reviewed - as with the bins full of stones for my wall. This will only improve your chances of finding the best fit. But ultimately a decision has to be made, and sacrificing production for precision is myopic. On a summer day, the definition of best tends towards the median.
We only have the choices presented to us at the time we’re free to roll a trade, get paid a bonus, or need money for a downpayment. Even if you knew how to time the market (you don’t), life comes at you on a totally different vector.
Deciding to be 50% allocated to equities is the easy part. Even wrapping your head around the range of outcomes and tradeoffs from a covered call can be tackled in an afternoon. But there’s no simple answer to the question of whether to trade the $47.50 or $50 strike. That’s as much feel as anything, and you only have the setups available when it's your time to roll.
Strike Pickins
This problem further extends to the execution of a strategy over time. Developers reflexively turn to backtesting because it’s very difficult to conceptualize the chains of potential events. You can place the obviously bigger stones in a rough fit together, but how their shapes will combine with the next available dimensions is a rotation too many.
Embarking on an investment strategy requires defining some parameters. Maybe it’s just “sell some calls when they look fat.” That’s not particularly objective, but something like “sell the thirty delta calls in Apple” is a testable strategy. Looking at TheTape, there’s a chart of how much that typically pays. We can also see where the closest strike listing is trading right now.
As for how that’s going to work out in the future, that’s just a series of rocks coming down the pike. Events shift pricing and randomness has its way. Whether pricing or implementation related, each time looks a little bit different.
Part of what’s difficult about sticking to a strategy is this sequential dynamic. We only have math to combat the ever nagging question of “did something change?” Does this random variable confirm or deny my thesis, and what should I do now?
Decision points are when we pull up the menu of options, and decide whether to make a trade. You can’t send an order for the 1.3% premium the backtest last month promised. Butter is sliding off your trowel, and grass clippings are blowing in the mix.
The past haunts you quickly when you’re placing orders. Buyers or sellers remorse is inevitable in the short term. Stonework only gives you a brief window before leaving your pour selections set for good. But a few blocks down the line, and a few months later for your portfolio, you start to have something that looks pretty good.
As life and markets allot opportunities one by one, we have no choice but to start making some decisions. It certainly won’t look like how you planned. But it’s useful to prepare for this, because the only solution is to keep putting down one stone after another.
Process. You jump in the river, or you jump out. But while you are in, you have to swim.