Posts filed under “Mathematics”

Possible versus Probable

Its Friday, and has become my wont, this is the day of the week I like to kick back, wax philosophical about various thoughts kicking about me noggin.

One of the things that I have been noticing of late is the way so many people seem to confuse facts with forecasts. Twitter is rife with this issue, as 140 characters plus a dearth of actual thinking turns out to be a bad combination.

Where I see this more than anywhere else in the investing world is the significant confusion between Possibility and Probability.

Stated differently, more than a few investors are lumping all of the non-zero probabilities together as one similar trade. They are not, for reasons I shall soon make clear, the same thing. This has been true with many people, from Pension fund managers down to mom & pop investors.

Let’s define the terms Possible and Probable so that we all begin with the same basic understanding of these words. Something that is Possible may — or may not — come to be. There is no statistical insight provided, it is merely an outcome that may or may not come to pass. It is possible that you could get hit by lightning, or win the lottery, or marry a supermodel. When we describe something as possible, we mean there is a non-zero likelihood of that outcome — it could happen; we just don’t know if it will or will not, but it might.

What seems to confuse investors about possible is the statistical likelihood of occurrence. Can a company on the verge of bankruptcy go on to become the biggest company in the world? It is possible — and Apple (AAPL) did just that over the course of a 15 year from 1998-2012. But think about all of the many tens of thousands of companies that have been on the verge of going belly up. Is it possible that they could do the same? Well, the answer is Yes, it is theoretically possible — but not very probable. And indeed, experience teaches us that most insolvent and near insolvent firms actually do go bankrupt eventually.

Probability is a the term for the branch of statistics dealing with chance and outcome.

Possibility is binary — can this happen or not?

Probable is more nuanced mathematics — there is a n% chance of a given outcome, where n = a number between 0-100.

Anything that is Probable must by definition be Possible; However, not everything that is Possible is going to be Probable.

And therein lay the rub.

Lately, I have seen this error come up in two areas — long term Pension Funds, and Venture Capital. The most common mistake is to conflate the two — mistake what is possible for something that is probable.

With Pension Funds, we have an issue of national import in that many of these defined benefit plans are significantly underfunded. To catch up, some of these have been directed to add more Hedge Fund exposure. There is an accounting reason — but not a good investing reason — for this based on idea of expected returns. While the tiny minority of funds that create Alpha means that there exists a theoretical possibility for Hedgies to help pension funds make up their shortfalls, the high fees and under-performance makes it rather improbable that this will occur. This is to say nothing of the long odds that Pension funds will pick the next Ray Dalio or Jim Simons.

Hence, the possibility of better performance perversely leads to the probability of worse performance.

In Venture Investing, the dream of 100X returns is the tantalizing possibility that keeps investors coming back to the VCs — despite the very long odds that your fund will find the next Instagram. The poor track record of the past decade, the limited ability to select VCs that will outperform, means that the dream is a possibility, but the odds are improbable.

Whenever asked about Angel or Venture investing, I say the same thing: Assume it goes to zero. That is the highest probability, most likely outcome. Invest no more money than what you are comfortable lighting up in flames (i.e., going to nothing).

Who should focus on the Possible? Writers, dreamers, artists, futurists, designers, technologists, entrepreneurs — the people who imagine the future. Nothing I wrote here should discourage any of these sorts of folks from pushing for the possible, (however improbable). It is how nearly all of human progress has been made, pursuing the improbable.

For investors, however, you are best served by sticking with the Probable. Understanding the difference will save you a lot of capital over the long run.

Category: Hedge Funds, Investing, Mathematics, Philosophy, Venture Capital

Most Human Males Never Retired (they just died)

Click to enlarge Source: The Motley Fool   “The entire concept of retirement is unique to the late-20th century. Before World War II, most Americans worked until they died.”   The quote above is from Morgan Housel. He has become the most consistently interesting writer on Motley Fool (a site I never really grokked). I was reminded…Read More

Category: 401(k), Employment, Investing, Mathematics

How You Are Unlikely to Die

Awesome graphic via The Economist: click for giant graphi

Category: Digital Media, Mathematics, Weekend

10 Thursday PM Reads

My afternoon train reading: • Your Brain in Love (Scientific American) • Big Wall Street Buyouts Might Be a Bullish Sign (The Slant) • Less-Trusting Millennial Investors Pose Challenge to Advisors (Advisor One) • The Biggest Financial Asset in Your Portfolio Is You (NYT) • Why Inflation Doves Are Really Hawks (Employment, Interest, and Money)…Read More

Category: Markets, Mathematics

Top 110%

Source: Dilbert

Category: Humor, Mathematics

Self-Description, Black & White Edition


Category: Humor, Mathematics

QOTD: On Bias, Correlation and Objectivity

I love the way this unfolds: Someone did a study — I have no idea if its serious or not –  that suggested eating more chocolate improves a nation’s chances of producing Nobel Prize winners. One of the Nobel prize winners responded with the appropriate amount of snark: “Eric Cornell, who won the Nobel Prize…Read More

Category: Humor, Mathematics, Psychology, UnScience

Mandelbrot: Fractals, Chaos and Other Mathematical Visions

Source: Scientific American

Category: Mathematics, Science, Video

Defining Risk Versus Uncertainty

Longtime readers will recall that I find the Uncertainty meme to be mostly silly (see this and this). The foolishness continues to come up amongst allegedly serious people. I find many of these folks (mostly) devoid of original thought, choosing instead to repeat things pundits of questionable insight have previously said (PoQI™ is a registered trademark…Read More

Category: Mathematics, Philosophy, Really, really bad calls

The Dangers of Non-Modeled Narrative Story Tellers

  “He can take a model and turn it into a narrative”   Right after the election, Felix wrote a post “When quants tell stories.” Clever as it was, I had issues with the underlying premise – namely, that the value of Nate Silver’s modeling lay more in the narrative tale as told by Silver…Read More

Category: Investing, Mathematics, Philosophy, Politics, Quantitative, Really, really bad calls