risk and reward

Risk Aversion vs. Ambiguity Aversion and 401(k) Plans

risk and reward

In a news briefing regarding Saddam Hussein’s weapons of mass destruction before the invasion of Iraq, former Defense Secretary Donald Rumsfeld famously stated:

“Reports that say there’s—that something hasn’t happened are always interesting to me, because as we know, there are known knowns; there are things that we know that we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns, the ones we don’t know we don’t know.”

Although he received much derision at the time such as the Plain English Campaign bestowing its Foot in Mouth Award upon him, Mr. Rumsfeld actually delivered a profound explanation of different types of uncertainty. Canadian columnist Mark Steyn called it “in fact a brilliant distillation of quite a complex matter.”

At Index Fund Advisors, we refer to the quantifiable part of uncertainty (or the known unknown) as risk. From an estimated measure of risk such as standard deviation, we have a reasonably good idea of the range of possible outcomes and their respective probabilities. For example, if we say that the U.S. stock market has an expected return of 10% with a standard deviation of 20%, then we are 68% certain that the return for the next year will be between -10% and 30%, and we are 95% certain that the return will fall between -30% and 50%, assuming a normal distribution of annual returns.

The non-quantifiable component of uncertainty (or the unknown unknown) may be considered to be ambiguity. Nassim Nicholas Taleb coined the term “black swan” to describe highly improbable (or commonly believed to have been highly improbable until they happen) events that have a large societal impact. As we like to point out, a black swan does not necessarily equate to an adverse event. For example, ten years ago with all the talk about peak oil, nobody predicted that the US would become the world’s largest producer of oil and natural gas, yet here we are as of 2013 well on our way to energy independence, according to the Energy Information Administration. Perhaps that should be categorized as a “green swan” event?

One of the basic assumptions of standard finance theory is that humans are rational utility-maximizers with decreasing marginal utility of wealth which is just a fancy way of saying that we are risk-averse. Ignoring how people behave in Vegas (which we agree should stay in Vegas) or their proclivity to engage in activities such as base-jumping off a 2,700 foot building, we can expect that most people, when given the choice between receiving $100 with certainty or flipping a coin to possibly win $200 will choose the former. The additional amount above the $200 that needs to be offered to get someone to switch from the certain $100 to the coin flip indicates their degree of risk aversion. For example, somebody who will only switch if the prize exceeds $300 is substantially more risk averse than the person who would switch for $220. The primary take-away from risk aversion is that it does not make sense to take a monetary risk where the odds are not in your favor, unless you are receiving compensation in a different way such as entertainment.

All the risks that we at IFA advise our clients to take are risks that carry an additional expected return. For example, we advise our clients to hold portfolios that are designed to capture the risk premiums that are associated with exposure to small cap and value stocks. One risk that does not carry an additional expected return is concentration risk (owning only a few stocks), and another risk that carries a negative expected return is manager selection risk. Wise investors avoid both of these risks.

As a counterpart to risk aversion, ambiguity aversion refers to our preference for risks with known probabilities over risks with unknown or vague probabilities. It was formalized by Daniel Ellsberg in 1961 when he noted the preferences of subjects to take a gamble where probabilities were easily quantified over a similar gamble where the probabilities are unknown. For example, imagine two urns filled with red and black balls. The first urn contains exactly 50 red and 50 black, while the second urn contains an unknown number of each one. If you are offered $100 for drawing a red ball, you will most likely choose the first urn where you know you have a 50% chance of success. In other words, better the devil you know than the devil you don’t know.

One practitioner who has done a great deal of work on ambiguity aversion is Professor Craig R. Fox of UCLA. Collaborating with Amos Tversky (one of the founding fathers of behavioral economics) in 19951 he formulated the more general Comparative Ignorance Hypothesis which states that people prefer to act in situations where they feel relatively knowledgeable or competent. For example, when subjects were given a choice between receiving $50 for certain or receiving $150 for correctly predicting whether a certain stock would go up or down the next day (which reasonable people would agree the odds are at least as good as flipping a coin, albeit no better). When the control group was given the straight choice, 68% of the subjects chose to gamble on their prediction.  Interestingly, when the experimental group was given the choice but was also told that the same choice would be given to a group of economics graduate students and stock analysts, only 41% elected to play. In the context of “expert opinion”, the subjects in the experimental group somehow felt that they had much less of a chance of being right in their prediction, so they became abnormally risk averse and chose the sure thing.

In a later paper2 where Fox collaborated with Martin Weber, they tested how people’s choices are influenced in the context of intimidating information. Specifically, when asked to estimate whether the prior year’s inflation rate in Holland was greater or less than 3.0% with the same $150 payoff for being correct and the same $50 sure thing alternative, 56% of the participants chose to play the game. However, when asked to read a paragraph containing technical yet useful information such as the current unemployment rate and money market interest rate, only 36% chose to play. Again, there was no rational reason for them to suddenly become abnormally risk averse, but whoever said that humans are completely rational creatures, other than economists? Rather than trying to eliminate our irrational tendencies (which is probably impossible), a better course of action would be to develop an awareness and understanding of them for the purpose of limiting the potential harm they may inflict.

An understanding of ambiguity aversion and comparative ignorance has a real world application in the design and execution of voluntary defined contribution retirement plans such as 401(k)s. For many participants, the investment choices are shrouded in ambiguity, especially when they have mysterious-sounding names like Davis New York Venture Fund, so the participants gravitate towards choices that they think they understand such as their own company’s stock or U.S.-only mutual funds. The former is definitely sub-optimal because plan participants already have a huge exposure to the fortunes of their own company, and the latter foregoes the opportunity to obtain a higher expected return for the same amount of risk via international diversification. Furthermore, they may shrug their shoulders and simply go into all the choices in equal amounts (naïve diversification), or even worse, they may choose to avoid risk altogether by putting all their savings into a stable value or money market fund, making it a virtual certainty that they will not have enough saved at retirement. While well-meaning, plan administrators may think that these behaviors can be mitigated by including articles on topics such as asset allocation with the participant enrollment materials, they may end up making a bad situation even worse. A better alternative is to structure the choices so that it is very clear which ones are reasonable for a worker of a given age or risk capacity. Furthermore, rather than tasking plan participants with building a portfolio (which they are probably not qualified to do), participants should be given the option of choosing a risk-appropriate globally diversified portfolio. Regarding explanations of the funds’ or portfolios’ objectives, simplicity is always preferable to complexity.

To summarize, at IFA we often say that investors are paid for bearing risk and should not expect to be rewarded for anything else. While investments by their very nature will always be a mixture of quantifiable risk and unquantifiable ambiguity, both of these have an upside as well as a downside. If you would like to learn more about IFA’s approach to 401(k) plans and how it minimizes ambiguity from the perspective of plan participants, please visit ifa401k.com.


1Fox, Craig R., and Amos Tversky, “Ambiguity Aversion and Comparative Ignorance,” Quarterly Journal of Economics, Vol.  110, No. 3. (August 1995), pp. 585-603.

2Fox, Craig R., and Martin Weber, “Ambiguity Aversion, Comparative Ignorance, and Decision Context” Organizational Behavior and Human Decision Processes, Vol. 88, No. 1. (May 2002), pp. 476-498.