Three definitions of risk (and why it matters)
What is risk, really? The answer might change how you approach your career and life.
I’ve spent years thinking about risk and risk-taking, and I’ve realized that it’s not so straightforward as we would like to think.
I can't do that. It's too risky.
I've had so many conversations with classmates at the GSB, most of them mainly focusing on potential startup ideas. With the unprecedented macroeconomic conditions, many people have fled to the safety of the known and the predictable. And the underlying logic behind all of these decisions has been based on "risk."
I used to be confused with the conclusions that people come to through their risk assessments, and it's because I realized that we had different conceptions of what "risk" is.
After thinking through this, I've categorized three different ideas of risk:
1) Risk as uncertainty
2) Risk as the probability of permanent loss
3) Risk is what is left over when you think you've thought of everything
Risk as volatility
Risk as uncertainty is the classical definition of risk. How much higher or lower will your investments be at the end of tomorrow? At the end of the month? What about at the end of the year?
The future is uncertain and filled with all sorts of different possibilities. When a future event has a more significant number of possibilities, it can be said to be "riskier" than if that same event had fewer outcomes.
Risk as uncertainty is often modeled as volatility. If you've ever talked about expected values, variance, or standard deviation, chances are that you were expressing risk as volatility.
It's a way to use math to quantify risk, ultimately giving us a more standardized way to think about uncertainty.
Risk as the probability of permanent loss
I spent many years believing risk to be akin to volatility. In my financial engineering and statistics classes, I was enraptured by the large set of incredible results that we could derive from modeling risk as volatility. Of course, much of this depended on assuming that risk was the same as volatility.
However, a few intelligent people shared some examples that shattered this illusion. Imagine that you had the opportunity to buy a stock, and I told you that you gain either $100 or $1,000,000. From a risk-as-volatility perspective, this is an incredibly risky bet — the standard deviation is over 700,000! However, everyone would agree that this situation has no risk since you are profiting either way.
To drive this point home further, imagine that instead of gaining either $100 or $1,000,000, you stood to lose either $100 or $1,000,000. The volatility (i.e., the standard deviation) is the same as in the previous example, where you were guaranteed to make money! So if you thought of risk purely as volatility, you would say that each of these situations is equally risky — which would be absurd.
This example is helpful because it points out an implicit assumption of risk. From a practical standpoint, when we say something is risky, we actually mean that there is a lot of downside volatility. We certainly like volatility on the upside, as in the first example of gaining either $100 or $1,000,000, but we want to avoid volatility on the downside. Risk is closer defined as downside volatility.
To be more precise, risk is the probability of permanent loss.1
Of course, such a definition of risk invites a bevy of questions. In your framing, what are you trying to optimize for? What does it mean to lose something permanently? How do you determine the probabilities?
This definition makes risk much more difficult to model mathematically but is much more useful and close to our natural conception of risk.2
I would rather have a risk metric that is approximately right than precisely wrong.
Risk as the residual unknown
I recently learned about another novel definition of risk, this time from Morgan Housel: Risk is what is left over when you think you've thought of everything.
Say you've spent many hours preparing for a presentation, and you've prepared for all sorts of contingencies. You're ready if you stand up in front of the audience and experience a bout of stage fright. If someone in the audience heckles you, you have prepared a series of retorts to destroy them.
But you probably haven't prepared for the possibility that everyone in the audience spontaneously combusts. Or if a herd of party hat-wearing T. Rex's charges through the auditorium doors as you deliver your first joke.3
By this definition, risk is fundamentally unknowable and unmanageable.
In the framework of knowledge, with options of being 1) a known known, 2) a known unknown, or 3) an unknown unknown, risk sits in the bucket of unknown unknowns.
No matter how much you prepare and how much you think, risk eludes you. When you have captured an uncertain "risk," it escapes your grasp.
Ultimately, this is more attractive as a theoretical concept than practical utility. Using this framing helps you to think more broadly and creatively about mitigating potential downsides, but it's ultimately more of a philosophical ideal.
Defining risk
So, if you decide to make future decisions where you're measuring risk, you must clarify how you think about risk management. What is risk to you?
Is it volatility?
Is it the probability of permanent loss?
Or is it fundamentally unknowable?
One thing is for certain: the most significant risk is not to define risk itself.
The nuance of "permanent" loss is essential here. Assume you are going to sell a stock in two days. If you knew the stock would go down by $10 on the first day and up by $30 on the final day, there isn't any risk. Even though there is a temporary loss on the first day, you will gain $30 on the last day, and therefore there is no permanent loss. As a result, there is no risk from this perspective. It's a nuanced adjustment to the definition, and I hope to cover this in more detail someday.
Of course, people still try to model risk from this probability of permanent loss framing using metrics like value at risk (VaR).
I told you that the T. Rex picture would be relevant somehow.