Tag: Black Swan

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.”

Nassim Taleb: The Definition of a Black Swan

Black Swan

In The Black Swan: The Impact of the Highly Improbable, Nassim Taleb offers a definition of a black swan. Taleb writes:

an event with the following three attributes. First, it is an outlier, as it lies outside the realm of regular expectations, because nothing in the past can convincingly point to its possibility. Second, it carries an extreme impact…. Third, in spite of its outlier status, human nature makes us concoct explanations for its occurrence after the fact, making it explainable and predictable.

Black swans are the inevitable byproduct of complex adaptive systems. Think about the world as a collection of interactions between components that are generally predictable but not always.

Knowing the behaviours of the individual part can allow you to extrapolate the behaviour of the group most of the time. However it won't allow you to predict the behaviour of each interaction. Occasionally these interactions will produce something unexpected and result in non-linear and non-predictable behaviour.

One of the biggest mistakes that people make with black swans comes with a big impact. A lot of people think that when outcomes occur outside of their expectations that the result is a black swan. This reasoning causes the belief that the outcome could not have been foreseen, because they didn't foresee it. While this reasoning loop relaxes our brain and allows us to avoid feedback, it also ensures that we are not learning how the world really works. We become close minded.

Just because something is outside of our expectations does not make it a black swan.

Still Curious? Pair with Taleb's definition of Antifragile.

Seth Klarman: The Forgotten Lessons of 2008

Seth Klarman: The Forgotten Lessons of 2008

In this excerpt from his annual letter, investing great Seth Klarman describes 20 lessons from the financial crisis which, he says, “were either never learned or else were immediately forgotten by most market participants.”

* * *

The Forgotten Lessons of 2008

One might have expected that the near-death experience of most investors in 2008 would generate valuable lessons for the future. We all know about the “depression mentality” of our parents and grandparents who lived through the Great Depression. Memories of tough times colored their behavior for more than a generation, leading to limited risk taking and a sustainable base for healthy growth. Yet one year after the 2008 collapse, investors have returned to shockingly speculative behavior. One state investment board recently adopted a plan to leverage its portfolio – specifically its government and high-grade bond holdings – in an amount that could grow to 20% of its assets over the next three years. No one who was paying attention in 2008 would possibly think this is a good idea.

Below, we highlight the lessons that we believe could and should have been learned from the turmoil of 2008. Some of them are unique to the 2008 melt- down; others, which could have been drawn from general market observation over the past several decades, were certainly reinforced last year. Shockingly, virtually all of these lessons were either never learned or else were immediately forgotten by most market participants.

Twenty Investment Lessons of 2008

  1. Things that have never happened before are bound to occur with some regularity. You must always be prepared for the unexpected, including sudden, sharp downward swings in markets and the economy. Whatever adverse scenario you can contemplate, reality can be far worse.
  2. When excesses such as lax lending standards become widespread and persist for some time, people are lulled into a false sense of security, creating an even more dangerous situation. In some cases, excesses migrate beyond regional or national borders, raising the ante for investors and governments. These excesses will eventually end, triggering a crisis at least in proportion to the degree of the excesses. Correlations between asset classes may be surprisingly high when leverage rapidly unwinds.
  3. Nowhere does it say that investors should strive to make every last dollar of potential profit; consideration of risk must never take a backseat to return. Conservative positioning entering a crisis is crucial: it enables one to maintain long-term oriented, clear thinking, and to focus on new opportunities while others are distracted or even forced to sell. Portfolio hedges must be in place before a crisis hits. One cannot reliably or affordably increase or replace hedges that are rolling off during a financial crisis.
  4. Risk is not inherent in an investment; it is always relative to the price paid. Uncertainty is not the same as risk. Indeed, when great uncertainty – such as in the fall of 2008 – drives securities prices to especially low levels, they often become less risky investments.
  5. Do not trust financial market risk models. Reality is always too complex to be accurately modeled. Attention to risk must be a 24/7/365 obsession, with people – not computers – assessing and reassessing the risk environment in real time. Despite the predilection of some analysts to model the financial markets using sophisticated mathematics, the markets are governed by behavioral science, not physical science.
  6. Do not accept principal risk while investing short-term cash: the greedy effort to earn a few extra basis points of yield inevitably leads to the incurrence of greater risk, which increases the likelihood of losses and severe illiquidity at precisely the moment when cash is needed to cover expenses, to meet commitments, or to make compelling long-term investments.
  7. The latest trade of a security creates a dangerous illusion that its market price approximates its true value. This mirage is especially dangerous during periods of market exuberance. The concept of “private market value” as an anchor to the proper valuation of a business can also be greatly skewed during ebullient times and should always be considered with a healthy degree of skepticism.
  8. A broad and flexible investment approach is essential during a crisis. Opportunities can be vast, ephemeral, and dispersed through various sectors and markets. Rigid silos can be an enormous disadvantage at such times.
  9. You must buy on the way down. There is far more volume on the way down than on the way back up, and far less competition among buyers. It is almost always better to be too early than too late, but you must be prepared for price markdowns on what you buy.
  10. Financial innovation can be highly dangerous, though almost no one will tell you this. New financial products are typically created for sunny days and are almost never stress-tested for stormy weather. Securitization is an area that almost perfectly fits this description; markets for securitized assets such as subprime mortgages completely collapsed in 2008 and have not fully recovered. Ironically, the government is eager to restore the securitization markets back to their pre-collapse stature.
  11. Ratings agencies are highly conflicted, unimaginative dupes. They are blissfully unaware of adverse selection and moral hazard. Investors should never trust them.
  12. Be sure that you are well compensated for illiquidity – especially illiquidity without control – because it can create particularly high opportunity costs.
  13. At equal returns, public investments are generally superior to private investments not only because they are more liquid but also because amidst distress, public markets are more likely than private ones to offer attractive opportunities to average down.
  14. Beware leverage in all its forms. Borrowers – individual, corporate, or government – should always match fund their liabilities against the duration of their assets. Borrowers must always remember that capital markets can be extremely fickle, and that it is never safe to assume a maturing loan can be rolled over. Even if you are unleveraged, the leverage employed by others can drive dramatic price and valuation swings; sudden unavailability of leverage in the economy may trigger an economic downturn.
  15. Many LBOs are man-made disasters. When the price paid is excessive, the equity portion of an LBO is really an out-of-the-money call option. Many fiduciaries placed large amounts of the capital under their stewardship into such options in 2006 and 2007.
  16. Financial stocks are particularly risky. Banking, in particular, is a highly lever- aged, extremely competitive, and challenging business. A major European bank recently announced the goal of achieving a 20% return on equity (ROE) within several years. Unfortunately, ROE is highly dependent on absolute yields, yield spreads, maintaining adequate loan loss reserves, and the amount of leverage used. What is the bank's management to do if it cannot readily get to 20%? Leverage up? Hold riskier assets? Ignore the risk of loss? In some ways, for a major financial institution even to have a ROE goal is to court disaster.
  17. Having clients with a long-term orientation is crucial. Nothing else is as important to the success of an investment firm.
  18. When a government official says a problem has been “contained,” pay no attention.
  19. The government – the ultimate short- term-oriented player – cannot with- stand much pain in the economy or the financial markets. Bailouts and rescues are likely to occur, though not with sufficient predictability for investors to comfortably take advantage. The government will take enormous risks in such interventions, especially if the expenses can be conveniently deferred to the future. Some of the price-tag is in the form of back- stops and guarantees, whose cost is almost impossible to determine.
  20. Almost no one will accept responsibility for his or her role in precipitating a crisis: not leveraged speculators, not willfully blind leaders of financial institutions, and certainly not regulators, government officials, ratings agencies or politicians.

Below, we itemize some of the quite different lessons investors seem to have learned as of late 2009 – false lessons, we believe. To not only learn but also effectively implement investment lessons requires a disciplined, often contrary, and long-term-oriented investment approach. It requires a resolute focus on risk aversion rather than maximizing immediate returns, as well as an understanding of history, a sense of financial market cycles, and, at times, extraordinary patience.

False Lessons

  1. There are no long-term lessons – ever.
  2. Bad things happen, but really bad things do not. Do buy the dips, especially the lowest quality securities when they come under pressure, because declines will quickly be reversed.
  3. There is no amount of bad news that the markets cannot see past.
  4. If you’ve just stared into the abyss, quickly forget it: the lessons of history can only hold you back.
  5. Excess capacity in people, machines, or property will be quickly absorbed.
  6. Markets need not be in sync with one another. Simultaneously, the bond market can be priced for sustained tough times, the equity market for a strong recovery, and gold for high inflation. Such an apparent disconnect is indefinitely sustainable.
  7. In a crisis, stocks of financial companies are great investments, because the tide is bound to turn. Massive losses on bad loans and soured investments are irrelevant to value; improving trends and future prospects are what matter, regardless of whether profits will have to be used to cover loan losses and equity shortfalls for years to come.
  8. The government can reasonably rely on debt ratings when it forms programs to lend money to buyers of otherwise unattractive debt instruments.
  9. The government can indefinitely control both short-term and long-term interest rates.
  10. The government can always rescue the markets or interfere with contract law whenever it deems convenient with little or no apparent cost. (Investors believe this now and, worse still, the government believes it as well. We are probably doomed to a lasting legacy of government tampering with financial markets and the economy, which is likely to create the mother of all moral hazards. The government is blissfully unaware of the wisdom of Friedrich Hayek: “The curious task of economics is to demonstrate to men how little they really know about what they imagine they can design.”)


Still curious? Check out Basically, It's Over: A Parable About How One Nation Came To Financial Ruin by Charlie Munger.