Every investment decision you make is a verdict on risk and uncertainty.

The credit crisis of 2008 made investment risk de rigueur. The proliferation of volatility controlled and lower-risk alternative strategies, coupled with the entrance of terms such as systemic risk, liquidity trap, and risk aversion into common parlance, has signaled a change in how investors think about risk.

When we speak of risk, we tend to mean downside risk. This is, of course, an incomplete picture. In simple terms, risk is the degree and magnitude to which an event differs from what you expect. Formalizing this as some sort of probability distribution—perhaps a bell-shaped curve—we can see that all investment decision-making originates with some inference about the magnitude and likelihood of some event or set of events.

The three histograms on the next page loosely illustrate this concept. In the first graph, we posit all possible events that could occur over a given time period, in this particular example the three-month return to global equities. In the second graph, we assign probabilities to each of these events. This is a fairly general exercise, but what distinguishes investment decision-making from many of its fellows is illustrated in the third chart. Here we apply a risk-aversion function to each event.

This function accounts for the level of risk aversion that someone investing in the market brings to the investment experience. Assuming a relatively high level of risk aversion (in this case a risk aversion coefficient of 8), the 1% chance of a 22.9% drop in the market now becomes a 1% chance of a 54% loss as experienced by the risk-averse investor. The expected utility of this scenario—found by summing the actuarial value of each utility adjusted return—falls from 4.02% to 0.16%. If the investor had almost no risk aversion, the expected utility would fall only to 3.6%. Investment risk is how you experience market fluctuations—it isn’t an objective state of affairs.

In other words, investment risk isn’t simply the variance of returns. It is the value each principal assigns to a given scenario. A risk-neutral investor, if such a beast exists, experiences the variance in his or her portfolio as the calculated standard deviation, or Value-at-Risk, of that portfolio. But the risk-averse investor experiences variance in a different manner. Investors are risk-averse; they apply more weight to bad events than to good ones. This is why when we talk about risk we usually focus on the downside. It’s more memorable.

**Risk vs. Uncertainty**

The term uncertainty is often used synonymously with risk. But for investors, it is important to define uncertainty as something else— the possibility of something utterly unprecedented happening. It is the possibility of an event occurring that falls outside the probability distribution.

This is more formally referred to as Knightian Uncertainty, after Frank Knight, the University of Chicago economist who introduced the concept in his 1921 book Risk, Uncertainty and Profit. Knight was trying to explain how profits were possible given perfect competition. If everyone observes the same probability distribution and is motivated to maximize profits, the traditional model says profits should be driven to zero.

In Knight’s view, the only thing that could allow for profits and perfect markets was the occurrence of an event entirely outside the probability distribution—an event without precedent that could not be quantified or imagined by anyone.