The Probability Distribution of the Future

The best colloquial definition of risk may be the following:

“Risk means more things can happen than will happen.”

We found it through the inimitable Howard Marks, but it's a quote from Elroy Dimson of the London Business School. Doesn't that capture it pretty well?

Another way to state it is: If there were only one thing that could happen, how much risk would there be, except in an extremely banal sense? You'd know the exact probability distribution of the future. If I told you there was a 100% probability that you'd get hit by a car today if you walked down the street, you simply wouldn't do it. You wouldn't call walking down the street a “risky gamble” right? There's no gamble at all.

But the truth is that in practical reality, there aren't many 100% situations to bank on. Way more things can happen than will happen. That introduces great uncertainty into the future, no matter what type of future you're looking at: An investment, your career, your relationships, anything.

How do we deal with this in a pragmatic way? The investor Howard Marks starts it this way:

Key point number one in this memo is that the future should be viewed not as a fixed outcome that’s destined to happen and capable of being predicted, but as a range of possibilities and, hopefully on the basis of insight into their respective likelihoods, as a probability distribution.

This is the most sensible way to think about the future: A probability distribution where more things can happen than will happen. Knowing that we live in a world of great non-linearity and with the potential for unknowable and barely understandable Black Swan events, we should never become too confident that we know what's in store, but we can also appreciate that some things are a lot more likely than others. Learning to adjust probabilities on the fly as we get new information is called Bayesian updating.


Although the future is certainly a probability distribution, Marks makes another excellent point in the wonderful memo above: In reality, only one thing will happen. So you must make the decision: Are you comfortable if that one thing happens, whatever it might be? Even if it only has a 1% probability of occurring? Echoing the first lesson of biology, Warren Buffett stated that “In order to win, you must first survive.” You have to live long enough to play out your hand.

Which leads to an important second point: Uncertainty about the future does not necessarily equate with risk, because risk has another component: Consequences. The world is a place where “bad outcomes” are only “bad” if you know their (rough) magnitude. So in order to think about the future and about risk, we must learn to quantify.

It's like the old saying (usually before something terrible happens): What's the worst that could happen? Let's say you propose to undertake a six month project that will cost your company $10 million, and you know there's a reasonable probability that it won't work. Is that risky?

It depends on the consequences of losing $10 million, and the probability of that outcome. It's that simple! (Simple, of course, does not mean easy.) A company with $10 billion in the bank might consider that a very low-risk bet even if it only had a 10% chance of succeeding.

In contrast, a company with only $10 million in the bank might consider it a high-risk bet even if it only had a 10% of failing. Maybe five $2 million projects with uncorrelated outcomes would make more sense to the latter company.

In the real world, risk = probability of failure x consequences. That concept, however, can be looked at through many lenses. Risk of what? Losing money? Losing my job? Losing face? Those things need to be thought through. When we observe others being “too risk averse,” we might want to think about which risks they're truly avoiding. Sometimes risk is not only financial. 


Let's cover one more under-appreciated but seemingly obvious aspect of risk, also pointed out by Marks: Knowing the outcome does not teach you about the risk of the decision.

This is an incredibly important concept:

If you make an investment in 2012, you’ll know in 2014 whether you lost money (and how much), but you won’t know whether it was a risky investment – that is, what the probability of loss was at the time you made it.

To continue the analogy, it may rain tomorrow, or it may not, but nothing that happens tomorrow will tell you what the probability of rain was as of today. And the risk of rain is a very good analogue (although I’m sure not perfect) for the risk of loss.

How many times do we see this simple dictum violated? Knowing that something worked out, we argue that it wasn't that risky after all. But what if, in reality, we were simply fortunate? This is the Fooled by Randomness effect.

The way to think about it is the following: The worst thing that can happen to a young gambler is that he wins the first time he goes to the casinoHe might convince himself he can beat the system.

The truth is that most times we don't know the probability distribution at all. Because the world is not a predictable casino game — an error Nassim Taleb calls the Ludic Fallacy — the best we can do is guess.

With intelligent estimations, we can work to get the rough order of magnitude right, understand the consequences if we're wrong, and always be sure to never fool ourselves after the fact.

If you're into this stuff, check out Howard Marks' memos to his clients, or check out his excellent book, The Most Important Thing. Nate Silver also has an interesting similar idea about the difference between risk and uncertainty. And lastly, another guy that understands risk pretty well is Jason Zweig, who we've interviewed on our podcast before.


If you liked this article you'll love:

Nassim Taleb on the Notion of Alternative Histories — “The quality of a decision cannot be solely judged based on its outcome.”

The Four Types of Relationships — As Seneca said, “Time discovers truth.”