Rethinking the Risk-Free Rate, Exploding a Fundamental Assumption

After the Great Recession (2008 to the present), it is in vogue to criticize the risk-free rate of return as a spurious concept. This is not surprising given the twin sovereign debt crises of the European Union and the United States; both countries’ debt instruments previously served as proxies for the risk-free rate of return.

Lost in the current discussion, and perhaps from the concept's very intellectual beginnings, is an examination of first principles. Put differently, what exactly does risk-free mean? Is this measure philosophically sound and reflective of reality? Here is a rethinking of the risk-free rate that should help to frame discussions about rewards versus risks.

First principle: Actions are always risky.

Why are actions always risky? Because the future is always unknowable. While it is appropriate to assign probabilities to uncertain outcomes, probability is in an asymptotic relationship to 100% certainty. Probabilities will never be 100%. One cannot even state with 100% certainty that there will always be change as, in the future, that may be the final change.

Until an event has occurred the success of a probabilistic prediction cannot be measured. Due to the unknowable nature of the future, all actions always contain a component of risk. Confidence can only be stated in calculus-like terms: for example, “the probability of x occurring approaches 100%.”

Lying at the heart of this discussion is an implication: we live in a universe of action. When in history has there been a time when there was no action? Never.

Rewinding effects back from their causes and all the way back through history leads to whatever came before the Big Bang. At this moment, if it can even be called a moment, there was no action and therefore no risk.

Everything that we know subsequent to the Big Bang has involved unfolding action and, hence, risk. Risk is therefore inescapable as action is inescapable. As an investor, even doing nothing is a risk that we call an opportunity cost.

Furthermore, any theory, no matter the discipline, and even including finance, must be in accord with the laws of nature. It does not make sense to talk of a risk-free rate of return and simultaneously associate that with an action — namely, investing.

Second principle: Investing is always risky.

Investing is always risky, because investing is an act in which outcomes can only be stated at probabilities of less than 100%.

Third principle: Expected return is the inducement for taking on risk.

What would induce an investor to surrender his/her low-risk liquid position? Higher expected return in an asset in which that return is high enough to induce the investor to surrender his/her liquidity.

Fourth principle: The risk-free rate of return is always zero and is in accord with a state of zero action.

Inherent in the concept of a risk-free rate of return and in the context of a reward-versus-risk framework is a glaring paradox: Rewards compensate risks, so how can there be a reward for no risk, or no action as is implied by the term “risk-free rate of return”? Put another way, since return is the price paid to induce risk taking, why pay a return for zero risk? Therefore the risk-free rate of return does exist, and it is always zero.

What we are left with then are several conclusions about the risk-free rate of return:

• The very name “risk-free rate of return” as traditionally used is oxymoronic and logically inconsistent with the reward-versus-risk theory it was designed to support.
• That the very concept of a risk-free rate of return as described in the past is out of accord with how the universe has actualized.
• To be in accord with reality, the concept of the risk-free rate of return needs modification.

All of this said, the idea that expected rates of return contain a bedrock component, a starting point if you will, is a good concept. It is a practical concept and provides a natural basis for philosophical discussion about reward versus risk.

For example, the bedrock rate of return implies a continuum on which investments may be placed in order of the magnitude of their reward-versus-risk tradeoff. This is intelligent. However, the bedrock component of expected rates of return should never have been named the “risk-free rate of return” as all investments entail risk. This also implies that all investments have expected rates of return greater than zero. Unfortunately, the nomenclature confusion of the risk-free rate of return has led to confused and oxymoronic investor expectations of certain return in exchange for zero risk.

A proposal: Renaming the concept of the “risk-free rate of return” to the:

Lowest-available-risk expected rate of return

This suggestion has several merits:

• Its meaning, unlike its predecessor, is clear from its name, and it avoids the distorted thinking associated with the risk-free rate of return.
• Its meaning is in accord with nature, in which actions inexorably lead to risks. That is, the lowest-available-risk expected rate of return is nonzero.
• It recognizes that the bedrock expected rate of return is not absolute, but instead is relative to all other expected rates of return. Hence, the use of the word "lowest."
• It recognizes that the bedrock expected rate of return changes over time, relative to the conditions of the moment. Hence, the use of the word "available."

In conclusion, there is no such thing as a risk-free rate of return, just as there is no such thing as our world without action. Yet, the concept of a bedrock expected rate of return is a good one in need of a better description that is more reflective of reality.

The opinions expressed in this piece are those of Jason A. Voss, CFA alone.

Super nova photo from Shutterstock.