On what basis?
Over the past few weeks we’ve built a system for understanding how we make decisions.
First, we needed to understand that people come to problems with different priors – good and bad.
Then, we needed to understand the importance of consulting the base rate.
Last week, we added a wrinkle:
The usefulness of the base rate depends a lot on whether it is group indexed or individually indexed.
Why spend so much time on probabilities?
Because we need to understand probabilities to estimate our level of risk.
After all, nearly every decision we make entails some form of risk…whether we know it or not.
This week, we introduce a big idea that will that I will reference many times throughout the rest of this series:
The difference between risk and uncertainty.
Risk is a situation where you have an idea of your potential costs and payoffs.
“Hmm. I’ve got a 50% chance of winning 100$, and it costs 60$ to play. Is this worth it?”
When you’re faced with risk, statistical analysis is your friend.
“Well, let’s see. 50% of 100$ is 50$, so that’s my average payoff. The cost is 60$, so I would average out at a 10$ loss. That’s not a good bet.”
Uncertainty is a situation where you don’t know the potential payoffs or costs.
“Hmmm. I’ve got some chance to win some money. I don’t know how much, or what my chances are. Is this worth it?”
Using statistical analysis in situations of uncertainty will almost always lead you astray. Instead, we need to turn to game theory (which we’ll discuss in a future email).
If I could leave you with a single takeaway, it would be this:
To act rationally, we need to understand whether we are experiencing risk or uncertainty.
This is much harder than it sounds.
To explain why, let’s borrow a bit from the world of investment…
And discuss derivatives.
A “derivative” is something that shares a relationship with something else you care about.
The thing you care about is called the “underlying.”
Sometimes it’s hard to affect the underlying. It can be easier to interact with the derivative instead.
I’ll pick an embarrassing personal issue as an example, because why not?
Let’s discuss body fat and attractiveness.
I was (and sometimes still am) insecure about how I look. I think this is a pretty common feeling. I didn’t think of myself as physically attractive, and I wanted to improve that.
My physical attractiveness is the underlying. The thing I cared about.
It’s hard to directly change your attractiveness. Your facial features, bone structure, facial symmetry, etc, are permanent, short of serious surgery.
So, instead of directly changing my attractiveness, I looked for a derivative, something that was easier to change.
The derivative I settled on was body fat percentage.
“The less body fat I have,” I reasoned, “the more attractive I will be. Body fat and and attractiveness are related, so by changing the former I can improve the latter.”
(Of course, this sounds well-reasoned in this description. I’m leaving out all the self-loathing, etc., but I can assure you it was there).
The relationship between the derivative and the underlying is the basis.
In my head, the basis here was simple: as body fat goes down, attractiveness goes up.When we express the basis in this way – as a formula that helps us to decide on a strategy – we are solving a problem via algorithm.
“If this, then that.”
Humans are hard-wired algorithmic problem solvers. Our super-power is the ability to notice the basis and use algorithms to predict the future.
We are pattern-seekers, always trying to understand what the basis is
(“I’ve noticed that the most attractive men have less body fat…”)
And once we think we know the basis, we tend to use it to try to predict the future…
(“If I lose body fat, I will become more attractive…”)
Or explain the present…
(“He is attractive because he haslittle body fat.”)
The amazing thing about this kind of judgement is that it’s often more accurate and useful than, for example, complex statistical regression or series analysis.
Simple rules of thumb have served us well for thousands of years.
But there is a danger hidden inside this way of thinking.
Let’s introduce one more concept:
Basis risk is the damage that could occur if the relationship between the underlying and derivative isn’t what you thought…
…Or doesn’t perform as you expected.
You believe that the more water you drink (the derivative)…
The better you will feel (the underlying).
Thus, the basis is:
Drink more water = feel better.
So you drink 3 gallons of water a day from your tap.
You didn’t realize that your tap water comes from a well located just off the grounds of a decommissioned nuclear power plant.
The water you’re drinking contains trace amounts of radiation that will, over time, cause you to grow 17 additional eyeballs.
In small amounts, the effect was unnoticeable…
At your current rate of 3 gallons a day the effect is…
(hold for applause)
Your problem was misunderstanding the basis.
Drink more water = feel better
Drink more water = feel worse.
The basis risk was severe health complications and an exorbitantly high optometrist bill.
We love to solve problems via algorithm, but if the relationship between derivative and underlying isn’t what we thought it was – or isn’t as tight as we thought it was…
It’s critical that we get the basis right. We must understand how changes to the derivative affect the underlying.
But this is much harder to do than it might seem.
For one, the world is complex.
Things that seem related often aren’t; things that ARE related don’t behave in the ways we expect.
Every part of the system affects every other part; the chain of causation can be difficult to pry apart.
But even when we DO work out the basis correctly, it can change over time.
Let’s return to my struggles with body image; specifically, the relationship between body fat and attractiveness.
Assume, for a moment, that you believe my presumptions to be true, and that less body fat really does make someone more attractive.
Will that basis always be true?
After all, we’re not discussing laws of nature here. We’re discussing people – messy, complicated, and ever-evolving.
We don’t need to resort to hypotheticals to imagine a world in which body fat was considered attractive…
We can find examples of idealized bodies with non-zero body fact percentages in the ancient world:
Even today, “curvy” bodies are attractive:
The basis between body fat and attractiveness is ambiguous, and has changed over time.
Whether it’s a “dad bod” on TV or a Roman statue, less body fat isn’t ALWAYS better for attractiveness.
If body-image-problems-Dan doesn’t update his algorithm…
He could end up dieting, stressing, struggling, even hurting my long-term health…
And actually decrease his overall attractiveness, the very thing he was trying to improve.
(Why am I speaking in the third-person now?)
This is the basis risk.
This is what happens when the relationship between derivative and underlying changes over time.
This is what happens when we drift from risk…
The algorithm stops working.
The formula says “X” when it should say “Y”…
And everyone suffers as a result.
All of us are INCREDIBLE at creating algorithms and TERRIBLE at updating them.
We tend to view updating algorithms as “changing our minds” or “being wrong…”
Rather than as acknowledging that the world is complex…
And that even if we were right yesterday, that doesn’t mean we’re right today.
The key to managing our basis risk is constantly monitoring how well the underlying and the derivative track with one another.
The moment these start to drift apart, we need to be able to admit that the correlation isn’t what we once thought it was….and to update our algorithms.
Maybe that way we can actually have our cake…
And eat it, too.0