Those of you who’ve worked with me for a while know I moonlight as a quant. Though, I wouldn’t be running this newsletter if any of my models worked.

Regardless, it has made me, shall we say, “opinionated” about things like how to invest. In looking at my savings for retirement, I decided to refresh my understanding of various portfolios, like 60% stocks, 40% bonds, and all the weightings in between.

At first, I went about it with brute force. I wanted to generate all possible portfolios and then estimate how well they would have done regarding risk-adjusted returns over the last ten years. Then, I’d pick the best one to implement in my savings.

This ended up taking too long. Each portfolio took around 200 ms to estimate, around 5 per second. Meanwhile, each additional asset you added meant you had to estimate 10x more portfolios. Even at 5 seconds, tens of thousands of portfolios would take a long time. This slows cycle time regarding what asset to try and add next.

Enter Optimization

This problem is called “portfolio optimization.” It involves finding the best portfolio given some historical returns. It finally dawned on me that optimization techniques might be helpful!

Various mathematical techniques try to maximize or minimize a function's output. That was precisely what I was doing here. I had a function that calculated weights like 10%, 20%, etc., and spat out some risk-adjusted return.

I spun up these functions and shrank 8-hour run times into 60-second run times, with results that were competitive with my old methods. Fantastic!

There are various optimization approaches, but I want to focus on Bayesian optimization.

I’ll most likely butcher this, but this form of optimization treats each of your inputs like the results from a poll. Oh, we got 48% of the vote, ±3%. That last bit is your error bars.

It uses these results to guess the next best set of weights to try. Let’s try it with a simplified example of only stocks and bonds.

Our initial guess says we should try 60% stocks ±5% and 40% bonds ±5%. The Bayes optimizer “samples” that distribution, picking ten or so random portfolios that all fall within those error bars.

It then runs our simulation and gets risk-adjusted returns for each of them. It then updates (using something called the Bayes rule) its prior estimates and comes up with new ones. Based on the latest samples, it is found that the best portfolio is 64% stocks ±4% and 36% bonds ±4%. And so the cycle continues.

This way, it makes “smart guesses” based on what it knows to decide what to try next.

What does this have to do with Strategy?

If you’ve been a beta reader for my book or talked to me in the last year, you may have heard me talk about a “business model” approach. I don’t mean this abstractly, but instead, like an Excel spreadsheet that boils down your EBITDA to lead generation and conversion rates from sales and sprint velocity from engineering.

Each variable is multiplied or added together to reach EBITDA (or some other profit metric) eventually. It is the one spreadsheet to rule them all.

In Bayes optimization, the algorithm generates a simplified model of your problem—we plug in some numbers with a random distribution and get some value out. It then learns more about this simplified model from experiments.

Likewise, in business strategy, we use the model I just described—the master model of your business. Each number, from conversion rates to sprint velocity, is an estimate. Maybe they’re based on measurements or industry research, but you plug them all in.

Then, you do what we call sensitivity analysis. You wiggle your estimates and see what drives EBITDA up the most. Would we make a difference if we pushed sprint velocity up? Or is it our conversion rate that’s holding us back?

By building a model with initial estimates and then wiggling those estimates, you get a guess of where you should focus your subsequent strategic efforts. Let’s say conversions are what’s holding EBITDA back the most.

Then, you brainstorm tactics that might improve conversions, try them out for a quarter or two, and check back. What did you learn? Perhaps conversions improved, and so did EBITDA. Perhaps conversions didn’t improve, and neither did EBITDA. Or, perhaps conversions improved, but EBITDA did not.

Either way, you have new information to update and tighten up your estimates about your model and a new round of wiggling to see how to improve things even more.

Active Learning

In both Bayesian optimization and Business Strategy, this process is called “active learning.” You want to learn as much about the space as possible. Bayes does a good job of balancing “explore” versus “exploit.” Bayes will deliberately sample parameters far away from your best guesses to see what’s there. It just samples them less.

Likewise, you want to be sure you are sampling things far from your business model. You may be an expert in email campaigns and have never touched TikTok. Most of your budget should go to email campaigns, but you should put some into TikTok to explore it. Firms in their life cycle need to spend more money on exploration, while more mid-life cycle firms or features should focus more on the exploit side.

How can you put active learning into practice in your business strategy? Email me with your ideas.