Graham Westmacott CFA

Portfolio Manager

Susan Daley CFA

Associate Portfolio Manager
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Risk, Uncertainty & Ignorance

Between the conception
And the creation
Between the emotion
And the response
Falls the Shadow
(The Hollow Men, T.S. Eliot)

I do not know when I am going to die. I do know my possible future states (alive, dead) but the timing of the transition from one to the other is not known. That is, the timing of my death is uncertain.

Note uncertainty is different from risk. In a fair coin toss there is a 50% risk of calling heads when the outcome is tails. In a coin toss, not only are the possible future states known (heads, tails) but also the probabilities of those states are known. There is risk but not uncertainty.

And then there is ignorance. We are ignorant when not only are the probabilities of events are unknown, but the possible future states are unknown. For example, we have been, and remain, substantially ignorant of the impact of the internet on human development.

Don Rumsfeld, former U.S. Secretary of Defense, famously summarized these distinctions:
“There are known knowns; there are things we know that we know. There are known unknowns;  that is to say, there are things that we now know we don’t know. But there are also unknown unknowns; there are things we do not know we don’t know”

What has this to do with investing? A reasonable summary of the goal of investing is to select assets that will fare well when future states of the world become known. To a first approximation we might argue that the past 80 years of capital markets likely encompass most of the states of economies (inflation, recession, deflation, asset bubbles, etc) that we are likely to see in the future. If so, the rational response is to say we are in a risky world and given the long experience, we can estimate how frequently different events occur and the impact of these events (returns distribution). However, over the past 3 years we have experienced events that surprised us – we had attached close to zero probability to a collapse in US house prices, and the consequences. If we only lived in a risky world (with no uncertainty or ignorance) investing would be relatively straightforward decision of finding the right combination of risk and return. In short: diversify, then buy and hold and wait for the expected outcome.

In reality there are two challenges with this approach. The first is that many investing opportunities involve uncertainty and ignorance. Should our investment approach change when we are faced with not only risk, but also uncertainty and ignorance? Whether it should or not, we have known from studies in the 1960s by Daniel Ellsberg, a Harvard psychologist, that normal human behaviour is biased against uncertainty. To understand his study, consider two urns. Urn A has 50 red balls and 50 black balls. Urn B also has black balls and red balls but you don’t know how many of each. You can reach inside the urns but you cannot see the contents. If you can win $100 by drawing a red ball, which urn do you choose? Most people choose Urn A. If the experiment is repeated with the only change that you win a $100 by drawing a black  ball then most people still choose Urn A. Logically, this is a paradox because, in the experiment, you would only choose Urn A if you believed that you had a better chance of drawing a red ball, implying that there are more blacks ball in Urn B. Our responses are dictated, not by logic but by an aversion to uncertainty.

To contemplate investing in a world of uncertainty, we adapt a framework suggested by Richard Zechauser (2006).

In the table above, we are using Easy and Hard relatively. Normal financial markets are in Box A. Absent insider information, we all have access to the same information about the state of companies and the economy.  Some individual investor’s suffer from overconfidence (or underestimate uncertainties) and forget that they are trading against Goldman Sachs and make selective bets that in aggregate do not pay off.  At PWL Capital we discourage this type of behaviour (see Winning the Loser’s Game by Charles Ellis). Box B is rare in liquid, transparent markets, but you could envisage private situations, perhaps around a local real estate deal, where you have knowledge that others would find hard to estimate.

Box C is more interesting. Our prime exhibit in Box C would be what are variously called structured notes or principal protected notes (PPNs). The banks love them because they neatly exploit the Ellsberg paradox discussed above. A typical PPN might invest in an equity index or basket of stocks. The investor will be guaranteed the return of their principal plus a portion of the growth of the underlying index at a specified future date (typically 5-7 years).  The investor is attracted both to the limited downside risk and the certainty of getting their money back at a specified future date. The banks have done their homework and have defrayed their risks in the market and through clever packaging passed on the costs – and a considerable profit - to the investors. A recent paper (Bernard, Boyle, & Gornall) suggests an average overpricing of 6.5% by issuers: the cost of uncertainty aversion.

What about Box D? The best known champion of Box D is Warren Buffett. An example of Buffett’s activity in this sector is his participation in the California earthquake and hurricane re-insurance market. No-one knows when the next Big One will hit California and a 100 PhD’s with vast computing power doesn’t change that uncertainty. In these circumstances many Wall Street investors leave the field. On some policies premiums equalled half the maximum potential payout. Buffett commented “We will do more than anyone else if the price is right…We are certainly willing to lose $6 billion on a single event. I hope we don’t." (http://seeking The lesson here is that, provided your pockets are deep enough to meet the potential loss, there is the potential to make significant gains, because many traditional players who would hope to have an informational advantage, find they cannot and walk away from the uncertainty.

Most investors bump up against uncertainty, not when considering earthquake reinsurance, but when considering something more familiar: retirement. One of the challenges of retirement planning is that it attempts to connect the aggregate risks of the market with the personal and idiosyncratic uncertainties of individuals. How can I be sure I don’t run out of money? The answer requires both making assumptions about future market behaviour and making an individual assessment about how long they are likely to live. Other uncertainties are the pink slip, a bad diagnosis, or a disappearing spouse that can drive a truck through the best-laid plans. The statistical approach is of no help: we do not die “on average”, we perish as individuals, and, more importantly, live as individuals. The average mortality of Canadians is much less interesting than our own mortality.

Your Money and Your Brain: How the New Science of Neuroeconomics Can Help Make You Rich, chapter 7, by Jason Zweig (new York:Simon & Schuster Inc., 2007)

The Known, the Unknown, and the Unknowable in Financial Risk Management: Measurement and Theory Advancing Practice, edited by Francis X. Diebold, Neil A. Doherty, and Richard Herring (Princeton, NJ: Princeton University Press, 2010)

Locally-Capped Investment Products and the Retail Investor, Carole Bernard(University of Waterloo), Phelim Boyle( Wilfrid Laurier University)  and William Gornall University of Waterloo, Working Paper, January 2010

By: Graham Westmacott | 0 comments