The alpha model of Theseus

To be human is to constantly choose between old and new. Should you listen to your favorite playlist or try some new music? Keep your current phone or update to the latest model? It’s a tough call. On the one hand, individuals often exhibit conservativism and react too slowly to new information, a fact which plays an important role in some theories of behavioral finance. On the other, Warren Buffett has achieved great success using steadfast adherence to a few simple principles, and I doubt he listens to a lot of new music.

The choice gets more complex when it involves multiple parties. When you are buying a product, you expect today’s version to be the same as yesterday’s. Hence the consumer outrage surrounding the introduction of New Coke in 1985. I personally am outraged by every intrusive update, ham-handed redesign, and inane rebranding inflicted upon us by our Silicon Valley overlords.

But much as I would prefer to live in an unchanging world, that’s not the way it is. We live in a dynamic world that changes unpredictably over time. Decision theory teaches us that in such a world, the optimal response is to update our beliefs and our strategies as new information arrives.

And that brings me to the topic of systematic investment. Suppose you hire systematic equity manager XYZ based on their track record from 2005 to 2025. But then you discover that the researchers at XYZ are constantly revising their alpha model, so that the 2025 model has only 95% overlap with the 2024 model and only 36% overlap with the 2005 model.

How should you react to these facts? Are these changes like New Coke, unwelcome and intrusive? Do the continuous updates invalidate XYZ’s whole track record? Warren Buffett doesn’t change his strategy over time; why should XYZ? Is XYZ admitting that their 2005 model was actually terrible?

I think that’s the wrong reaction. First, let’s talk about the track record. Yes, it’s true that the actual performance of XYZ over the past twenty years represents model vintages that are no longer used, and thus the historical track record does not reflect today’s model. But let’s be frank, XYZ’s realized track record (a) is heavily influenced by random events, (b) has limited predictive power for future performance and (c) is only part of a larger mosaic of relevant information about XYZ. You shouldn’t be selecting XYZ based solely on their realized track record, any more than you should be selecting XYZ based solely on historical simulations using their 2025 model.

More broadly, when you invest in a systematic manager, you aren’t investing in a specific model, you’re investing in a specific team with a specific research process. That process includes methods for evaluating new signals, monitoring existing signals, and assessing market conditions. Going forward, the performance of XYZ will depend on the decisions made by the XYZ team using the XYZ process, and that’s what you buy when you invest with XYZ.

Science is the process of updating your worldview with new information. While it is an open question whether your alpha model should be extremely persistent or extremely adaptive, I can’t see a world in which the optimal response is to never update your alpha model at all.

The Honda Civic was first introduced in 1972. If you are looking to buy the best one, I’d recommend buying a 2025 Civic as opposed to a 1972 Civic. Every year, on average, the Civic gets better as Honda incorporates the latest technology. While it’s always possible that Honda will bungle the update (as many believe occurred with the 2012 Civic), there’s just no way that the optimal car design is unchanged since 1972. Let’s face it: compared to today’s cars, the cars of the 1970s were shoddy deathtraps.

The Ship of Theseus is a philosophical paradox about how to think about identity and permanence. If every year you replace some of a ship’s components, at what point does it become a new ship? Here’s Plutarch writing over two thousand years ago:

… they took away the old planks as they decayed, putting in new and strong timber in their places, insomuch that this ship became a standing example among the philosophers, for the logical question of things that grow; one side holding that the ship remained the same, and the other contending that it was not the same.

From a practical perspective, the paradox is irrelevant. Which would you prefer to climb aboard, a well-maintained ship with planks of “new and strong timber,” or a leaky ship with rotten old planks? I’d go for new and strong. There’s nothing wrong with the fact that the later vintages of the ship have minimal overlap with older vintages; constant updates are a feature, not a bug.

What’s the optimal rate of change? Is faster always better? No. There’s no reason to replace all the planks every year; that policy would incur high costs and no benefit. More generally, while there are rare instances in which 0% overlap is desirable between vintages (for example, if you are switching from a horse and buggy to a Honda Civic), in noisy information environments it’s typically optimal to slowly update your model as new evidence accumulates. Based on first principles, all we can say is that the optimal overlap between vintages is more than 0% and less than 100%.

There are many areas in life where unswerving loyalty and inflexible commitment are admirable, for example, when rooting for the Boston Red Sox. But my loyalty is to the Red Sox and not to a particular roster of players. While there will always be a place in my heart for the 1978 Red Sox, it’s just not practical to have zero turnover (roster turnover is typically around 25% per year).

With the Ship of Theseus, you need an inflexible commitment to a rigorous schedule of preventive maintenance. With quantitative equity strategies, you need unswerving loyalty to a rigorous research process.

Love the ship, not the planks. Love the research process, not the model vintage.