Practical analysis for investment professionals
20 March 2012

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.

About the Author(s)
Jason Voss, CFA

Jason Voss, CFA, tirelessly focuses on improving the ability of investors to better serve end clients. He is the author of the Foreword Reviews Business Book of the Year Finalist, The Intuitive Investor and the CEO of Active Investment Management (AIM) Consulting. Previously, he was a portfolio manager at Davis Selected Advisers, L.P., where he co-managed the Davis Appreciation and Income Fund to noteworthy returns. Voss holds a BA in economics and an MBA in finance and accounting from the University of Colorado.

Ethics Statement

My statement of ethics is very simple, really: I treat others as I would like to be treated. In my opinion, all systems of ethics distill to this simple statement. If you believe I have deviated from this standard, I would love to hear from you: jason@jasonapollovoss.com

33 thoughts on “Rethinking the Risk-Free Rate, Exploding a Fundamental Assumption”

  1. Husni Jaza says:

    Hi Jason,

    Good article !!

    1. Hello Husni Jaza!

      Thanks very much for your comment and I am happy that you enjoyed the piece.

      With smiles!

      Jason

  2. kenani says:

    Very good article!

    1. Hello Kenani!

      Thanks very much for your feedback. I hope that things are going well in Kenya! You might want to look at our pretty wide coverage of investment in Africa as covered on The Enterprising Investor blog: http://blogs.cfainstitute.org/investor/ My colleagues and I are trying hard to present the investment story on the continent of Africa well. I am certain that we would all like to hear your first hand experience of the investing climate there.

      With smiles!

      Jason

  3. Ed Oliveira says:

    Good article Jason. I like the idea of renaming and rethinking of the risk free rate. Their is no real risk free rate and names/concepts like ‘the bedrock rate’, or ‘lowest-available-risk expected return’ seem more appropriate.

    1. Hi Ed,

      Thanks very much for the feedback and I am so pleased that you liked the piece.

      With smiles!

      Jason

  4. Mike says:

    “At this moment, if it can even be called a moment, there was no action and therefore no risk.”

    There certainly was risk, because there was the potential for action, even though no action existed.

    Risk is about what might happen in the future. If there is a possible future, then there is risk.

    Just sayin!

    1. Hi Mike,

      I completely understand your point and thanks for making it as I hope it will add to further discussion and refinement. Your comment also focuses on the very point I was hoping to communicate: there is no such thing as “risk free” and so that imagination, thoughts, words and actions are all in alignment, or undistorted, requires a change in nomenclature.

      I will add in the spirit of just sayin’…

      Only by looking backward toward the moment before the Big Bang can we say that there was a potential for action. Because we take the unfoldment since that moment as self-evident we ‘know’ there was potential. But can we say that there was even time, or even moments, or even potentials pre-Big Bang? Was there even a consciousness that was aware of these things? Hard to say. This is, of course, the great unanswerable question: How do we have something from nothing? In the end, it seems we find ourselves in supposition/faith as any opinion about this is as good as anyone elses opinion.

      With smiles!

      Jason

      1. Hi Jason,

        I Believe Lawrence Kraus has an answtor to your question: “How do we have something from nothing?” – at least as far as the universe is concerned:

        http://www.amazon.com/Universe-Nothing-There-Something-Rather/dp/1451624468/ref=la_B000AP7AZS_1_1?s=books&ie=UTF8&qid=1381338424&sr=1-1

        http://www.youtube.com/watch?v=EjaGktVQdNg

        About the article, what would your suggestion be for the Lowest-available-risk expected rate of return? A cases by cases analysis? Use some benchmark? Which one?

        1. Hello LAP,

          Thanks for the link to the La. Kraus book, I will certainly take a look at it.

          As for what I recommend, I wrote a follow up post which answered this very question. Here is the link for that piece: http://blogs.cfainstitute.org/investor/2012/10/04/rethinking-the-risk-free-rate-offering-alternatives/

          With smiles!

          Jason

  5. Ash Amin says:

    Hi Jason,

    I enjoyed reading your mini article and think that you are spot on. The notion of “risk-free rate” was flawed from the beginning.

    Fundamentally, any investment involves taking on risk with the expectation of return. The higher the risk, the higher the expected of return and vice versa. And so, a risk-free (i.e. zero risk) rate of return has to be zero which is exactly what you have pointed out. Furthermore, the ongoing EU credit crisis and the downgrading of U.S. has revealed that previous assumptions regarding the risk-free rate needs to be revised.

    Your alternative name for the risk-free rate of return is more accurate and descriptive, only problem is that its quite a mouthful, but I’m sure you can come up with a shorter version. Good luck!!!

    Ash

    1. Hi Ash,

      I am flattered by your comments. Thank you! Also, thanks for explaining why you liked the piece.

      Regarding a less mouthful taxing term, what about relying on an acronym, LARERR?

      Smiles,

      Jason

  6. Jeffrey P Davis says:

    Your article is a useful deconstruction of a term that is the cornerstone of our business. Unfortunately, even “lowest-available-expected rate of return” is stilll as mythical as a unicorn. “Mike’s” comment addressed the time issue pretty well. To go deeper into the rabbit hole, though, isn’t it really the “lowest-available expected rate of return that I can find at this particular moment and is really my own opinion”? On a practical note, if T-bills cease being the consensus risk free rate, then a new label should be very much on the agenda for the academics out there….

    David Hume and Immanuel Kant would have a field day on this. Fun stuff. Thanks.

    1. Hi Jeffrey,

      I think your comment has provided useful clarification on exactly why I chose the verbiage I did with “lowest-available risk expected rate of return.” In an initial draft of this piece I had written the even bigger mouthful: “lowest available expected risk expected rate of return.” It seemed a bit unwieldy but was meant to convey exactly what you point out. Investor expectations of risk and return are the essential thing to log. This, of course, suggests that there is not a purely objective way of logging risk and return a priori. Only in looking backward is there an opportunity at pure objectivity.

      I think you are right that Hume would be all hot and humid about the discussion and Kant would say I can’t believe it!

      With smiles!

      Jason

  7. Paris says:

    Jason,

    I disagree with your characterization of the risk free rate. In essence, the only thing genuinely missing from the original RFR name is the underlying extension of “risk free rate for a given currency”. Frankly if the short-term Bill/Bond of the appropriate time metric were to go into default, then the currency that you are trading in also does not have the same given value that you are trading in. If a T-bill/bond goes into default, then the dollar also follows a devaluation which would make it move in tandem with these rates… as such relative to the dollar, the rates would be the same given the dollar and are thus ‘risk free’.

    Considering every investment calculation has an underlying assumption of currency, then the rate corresponding is ‘risk free’ relative to that currency.

    1. Hello Paris,

      Thank you for your comment and I am glad that my piece was thought provoking even if we disagree.

      With smiles!

      Jason

  8. Nandita says:

    Hi Jason,

    I appreciate your article. I wish to read more on this. Request you to share any recent research you may have come across on this issue.

    1. Hello Nandita,

      I am so glad that you appreciate the article!

      There is no research on this topic to my knowledge. Also, because it is a matter of personal philosophy about accurate nomenclature I am not sure that anything could be ‘researched’ properly. I can say that in my discussions with people subsequent to the publishing of this piece that about 2/3rds of folks have supported my view, with about 1/6 disagreeing and 1/6 not understanding the point I was making.

      Keep those comments coming – thanks for your interest!

      Jason

  9. Hello Jason,

    Interesting article. I agree with your statement that there`s no such thing as “risk free”. However, one of your statements is completely off base in my opinion.

    “Therefore the risk-free rate of return does exist, and it is always zero.”
    *I assume you mean to say “doesn’t exist”.

    Default Risk premium is already a separate component of interest rates. The fact that the consumption of the capital has been deferred is what drives the risk free rate. The opportunity cost of your capital is the risk free rate.

    In summary, risk free rate is not 0 because it ties down your capital.

    1. Hi Vitaly,

      Thank you for your comments, assumption, and for sharing your point of view.

      I meant it when I said, “Therefore the risk-free rate of return does exist, and it is always zero.” I did not mean to say “doesn’t” per your assumption.

      We will have to agree to disagree. Here’s why:

      1) If return is the reward for risk – an intelligent framework – then how can there be a notion of a “risk-free rate of return?” Or a return for no risk? The name “risk-free rate of return” violates the principle it names. That is somewhat like “the deathless execution method.” Also, the risk-free rate cannot be negative because then it offers a return to those who might short a financial asset that serves as a proxy.

      2) My post above is decoupling the philosophy of “risk-free rate of return” from any specific instrument. By replying as you did with “default risk premium” you are pre-supposing that the only way to philosophically understand the “risk-free rate of return” is via an interest rate framework.

      3) You reiterate that “the consumption of the capital has been deferred [and that] is what drives the risk free rate.” This is oxymoronic; see #1 above.

      With smiles,

      Jason

  10. Nimita says:

    Nice and thought provoking article Jason !

    1. Hello Nimita,

      Thank you for your feedback and I am pleased that you found it thought provoking…yea!

      With smiles,

      Jason

  11. Sudhir Mankodi says:

    Hi Jason, no environment is risk free and certainly stakes in investment related decisions are very high. In Bhagwad Geeta (the teachings of Lord Krishna to Arjuna on various matters agitating Arjuna’s mind) Krishna says that an individual should be prepared for consequences of one’s own action! At the time of making investment decision, the perceived risk may not be high. However, with the passage of time, the “assumed” circumstances change and what was perceived to be an excellent risk becomes a bad risk and difficult for recovery of even principal amount! The doer has to be prepared to face the consequences of his/her decision. Your suggestion of renaming the concept looks prima facie more rational but is nothing short of “self deception” as the risk remains where it was! I found the article quite interesting.

    1. Hi Sudhir,

      Thank you for your comments and also for the tie in to Bhagwad Geeta. The concept of zero was originally a metaphysical concept and meant a time before there was the 1, or the creation. So our views are completely in alignment. In the follow up piece to this one I said that the lowest-available-risk expected rate of return must be non-zero as there is a universe of action. So no delusions here, only accord with the principles I outlined.

      With smiles,

      Jason

      1. Sudhir Mankodi says:

        Liked your response

  12. Adrian Borg says:

    Hi Jason,

    This is a brilliant article on a topic that is considered fundumental in finance. Hopefully this will lead to further analysis of the term ‘risk-free’ to the ultimate realisation that in reality no action comes without a certain degree of risk (as you rightly pointed out). Well said!

    Please keep us posted with more articles like this.

    1. Hi Adrian,

      Such high praise! Thank you for sharing your thoughts. You might really like the follow up post to this piece where I discuss possible proxies for the “lowest-available-risk expected rate of return”: http://blogs.cfainstitute.org/investor/2012/10/04/rethinking-the-risk-free-rate-offering-alternatives/

      Also, I tend to be a bit more philosophical in my blog posts so you might also like:

      Capitalism: It’s as Much About Cooperation as Competition http://blogs.cfainstitute.org/investor/2012/07/16/capitalism-it-is-as-much-about-cooperation-as-competition/

      With smiles!

      Jason

  13. Osama says:

    Dear Mr. Jason

    I believe your thoughts goes very well with the Idea of Islamic Finance as the risk free is prohibited instead offers the idea of sharing both of risks and returns (Musharaka) , but someone could say that risk free rate is only a compensation for the inflation rate, don’t you think?

    again thanks for sharing your thoughts

    regards,,,

    Osama Hussein

    1. Hello Osama,

      Thank you for taking the time to share your thoughts!

      Your thought about comparing the risk-free rate to compensating for inflation is an interesting one. You could extend the argument out even further. That is, theoreticlaly the true risk-free rate could be the one that exactly compensates you for your risks. However, the risk-free rate is used prospectively by investment professionals, not retroactively. So this would require you have accounted for every possibility, not just probability. I think this is an impossible task.

      On the other side, is my theory that all actions entail preferences, and consequently they also entail risk. Thus, the only way to avoid risk is to have no preferences, or to engage in no actions – an impossibility. In this theoretical direction risk is equal to zero, and is always equal to zero. Zero return for zero risk. If you believe in a returns compensating for risks, which I believe is intelligent, then the zero point must have zero return and zero risk.

      Yours, in service,

      Jason

  14. Jeff Caira says:

    Hi Jason

    I like your theory on the risk free rate (perhaps because I agree that a true theoretical risk free rate should be zero.) When I was in graduate school many years ago it was said to be 3%, and that always struck me as very arbitrary. The way I think about it now is that for short-term periods for US government securities, our proxy for risk free, it should approach zero, but, for the reasons you mention, should not be zero. For longer-term periods it should include inflation expectations so that the “real”, rather than “nominal”, risk free rate remains zero.

    The risk free, or lowest possible risk investment rate, is also usually compared to available alternative investments, and by holding the asset one incurs opportunity cost. However, a risk free investment also solves practical problems that aren’t addressed in theoretical discussions. Suppose I have a suitcase with $1 million dollars in it. There is risk of me holding that suitcase beyond what I could earn by making an investment. My house could burn, I could be robbed, I could lose the suitcase at the train station. Not so with a risk free investment, so perhaps there is an argument for a negative return on a risk free rate since it not only compensates for the risk of action, but also for the risk of inaction.

    Thanks again for your interesting article.

    Jeff Caira

    1. Hello Jeff,

      Yea, I am so pleased that you found the article interesting. I fully understand your point about the possibility of the “risk-free” rate of return being negative. However, because securities can be shorted, the only rate that is truly neutral to both parties is theoretically, zero percent. Of course, the counter argument is that markets determine the clearing price between buyers and sellers. When I wrote this piece almost four years ago I could not imagine a world in which there would be price takers below zero percent interest! Egads! I think this is an example of people’s minds taking them into a place divorced from the actual meaning of number and numbers. Philosophically, zero percent literally corresponds to nothingness, or no actions undertaken. But arbitrage thinking allows rates lower than zero percent. Very strange times. In any case, even if zero percent as philosophy does not survive practical reality, the concept of taking the lowest-available rate does survive intact : )

      Thanks for taking the time to share your views!

      Jason

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