A quantitative theory of financial wellness
Most people assume that their financial wellness exists in a linear relationship with their financial situation. For every change in their financial situation their financial wellness will respond by a similar amount.
This linear function can be illustrated in graph form as follows:
The absolute values can be considered arbitrary for our purposes, what’s important is the relationship between the two.
The x-axis represents the change in a person’s financial situation. Assume that positive numbers indicate an increase — perhaps a new job with a higher salary or some kind of windfall — and negative numbers indicate a decrease — perhaps a job loss or unexpected bill.
The y-axis represents their overall financial wellness score. I’ve written more about what this represents here, but in essence it measures a person’s ability to set and achieve their financial goals, weather an adverse financial shock, manage their day-to-day finances without feeling stressed and have the financial freedom to make the choices that allow them to enjoy their life.
This linear relationship can be represented in its classical mathematical form as:
y = mx + b
Wherein:
- m is the slope of the line
- b is the y-intercept of the line
- x is the change in a consumer’s financial situation
- y is the consumer’s financial wellness score
This formula enables us to extrapolate this assumption and start to test whether this linearity is born out in reality.
In our graph above we set the slope (m) at 50%, so any change in our financial situation by 1 unit should see a corresponding change in our financial wellness score of 0.50. That makes sense, right? An extra $500 in our pay packet would help us improve our ability to tick most of the boxes in financial wellness.
But let’s extrapolate this further. Assume it’s a change of 10 units in our financial situation. This linear relationship tells us that we should see a corresponding change in our financial wellness score of 5. In other words, a tenfold increase in our financial situation results in a similar tenfold increase in our financial wellness.
That doesn’t stack up 🤔
Why? Because we know from a number of studies that the effect of an increase in a person’s financial situation on their wellness attenuates as it increases. Yes, a person with a financial situation a factor greater than another person’s is likely to have a higher sense of well being (primarily because they can exert more control over their life) but it doesn’t mean their financial wellness will be the same factor greater as well.
Similarly, a person whose income fell by 20% would suffer a much more precipitous fall in their financial wellness than this linear relationship would suggest.
A quantitative model of financial wellness
So, we’ve proved the received wisdom wrong. What’s a more accurate model of this relationship?
Drawing on the academic literature and our own proprietary research we think it looks a lot more more like this:
What our model suggests is that rather than the relationship between our financial situation and financial wellness being linear it is in fact concave. The further we move away from our current financial situation the further our financial wellness deviates from this linear trajectory that we assumed it follows.
Data points and factoids that were incompatible with the previous linear model now show near perfect compatibility with our new model. We have a model that actually fits reality.
Having established a more accurate model of this relationship we can now start to think about the wider implications of this.
I’ll write more about this in the future, but for this specific post I want to focus one area that had a profound impact on me: The emergence of a second order derivative in the relationship.
In mathematics the second order derivative is the measurement of the rate of change of the change itself.
If you’ve ever caught anything that was flying through the air your brain has subconsciously calculated the second derivative of the flight of the object well enough that you can stick your hands out at a point where the object will be a split second later.
In our graph this second order derivative governs the increasingly precipitous drop in financial wellness as our financial situation changes to the negative and the increasing attenuation of it as it changes to the positive.
What the emergence of this second order derivative means is that most people’s relationship between their financial situation and financial wellness is effectively a short volatility trade.
“Wait, whaaaat??”
Let me explain.
On a daily basis we make many decisions which involve an implicit bet against change. For instance, when we sign a new lease or commit to a relationship with a partner we’re making an implicit bet that the situation in the future will be roughly the same as it is right now (or, hopefully, slightly better). Volatility is a more complex expression of change. When volatility remains subdued those bets settle and we’re none the wiser. However when volatility spikes those bets can suddenly be brought into sharp focus.
An example: In March 2020 many of us were leasing tiny apartments in the center of a large metropolis because we used the city as our living space. But then a global pandemic arrived and quarantine suddenly brought our new situation into sharp focus.
In our financial lives however the situation is even more acute. So many of the decisions we have to make involve us selling volatility to get access to what we want.
For instance, when we take out a mortgage or other form of consumer credit we’re betting against the risk our financial situation changes for the negative — what is in effect the left tail of the volatility distribution. Equally when we do things like avoid tackling our underlying money beliefs because it’s just too painful we’re effectively betting against the risk that our financial situation changes for the positive — the right tail of the distribution.
By allowing us to visualize this implicit short vol position we suddenly have a quantitative model for why so few people actually attain financial wellness irrespective of their financial situation:
Long convexity
With this quantitative model in hand we can now build on its framework to try and work out how to fix this. Let’s start with what an ideal state would look like in this model:
In this situation as a person’s financial situation changes negatively they’ve managed to cushion the impact on their financial wellness, and as it changes for the positive they’re able to truly maximize it.
In other words they’ve unwound their short position and gone long convexity allowing them to hedge the left tail risk whilst leveraging into the right tail.
How does this look in practice? Well, unwinding a short vol position effectively requires us to lessen the probability and impact of change from our current situation.
Again there’s already many tasks we do intuitively in our wider lives in an attempt to do this: Going to the gym, eating healthy, quitting smoking, not drinking too much alcohol etc. These are all designed to lessen the probability and impact of volatility in our lives.
The same is true with our financial situation and wellness relationship. There are regular tasks that we can perform to lessen the probability and impact of volatility.
However, what our model shows clearly is that simply hedging vol is not enough. To truly attain financial wellness we need to also build a position that gives us long exposure to convexity. This means thinking as much about the right tail as we do about the left:
This is one area where many traditional attempts to fix financial wellness go wrong. They focus exclusively on some very practical tasks that are primarily focused on the left side. We think that both sides require a similar level of focus if a person is to truly attain financial wellness.
The final insight I’d like to share is around how we’re thinking about the actual mechanics that a person uses to attain this ideal state.
The reason most people end up shorting volatility is because it’s easy. Selling volatility involves no upfront cost. In fact most people collect some form of “payment” from it — breaking the speed limit gets you places faster, smoking tobacco releases nicotine which calms us, going out partying every night means we avoid FOMO.
To “buy” ourselves into a long vol / convexity position we need to regularly perform tasks that involve an up-front cost — in time, money, mental energy (calories) — with no immediate payback. Going to the gym, saying no to that bar invite, quitting smoking — all require us to invest upfront for no immediate payback.
Today for the majority of people that up-front cost is too high. In our view the greatest opportunity exists in working out how to reduce or eliminate those upfront costs so that attaining and sustaining financial wellness is as indistinguishable as selling vol.
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With thanks to Greyson, Paul & Christopher 🙏
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