Practical analysis for investment professionals
04 October 2012

Rethinking the Risk-Free Rate: Offering Alternatives

Posted In: Economics, Philosophy

In an earlier post, “Rethinking the Risk-Free Rate, Exploding a Fundamental Assumption,” I criticized the concept of the “risk-free rate of return” as both illogical and not reflective of reality. Although I acknowledged the logic of having a bedrock rate of return that serves as a minimum acceptable rate of return, I proposed renaming it the “lowest-available-risk expected rate of return.”

In this follow-up post I’ll offer some alternative bedrock rates of return for consideration. My preferred, for reasons explained below, is multifactor productivity growth.

First, some context: As imagined, the “risk-free” rate of return is supposed to be the rate that investors may always count on earning no matter the current state of the world. Therefore, it is supposed to be the bedrock rate of return that is the foundation of all other rates. If you are an equity investor, you begin building your required rate of return on equity using the “risk-free” rate. Likewise, if you are a buyer of fine art you are also supposed to use the “risk-free” rate as your bedrock required rate.

At a minimum, all investors, regardless of asset class, want a portfolio to earn at least the rate of the bedrock rate of return.

This suggests something fundamentally important about any possible alternative candidate for the bedrock rate of return: It must be universal. In other words, a bedrock rate of return must cut across all possible investments such that investors in commodities, art, education, real estate, businesses, equities, bonds, options, or any other asset would all view the bedrock rate of return as their starting place for crafting a required rate of return. Since each of the preceding activities is an economic activity, a bedrock required rate of return should also reflect actual economic growth, defined as getting more from the same set of resources, or getting the same from a smaller set of resources.

With that in mind here are a few alternatives.

Alternative Risk-Free Rate 1: Average Real Gross Domestic Product Growth

Gross domestic product (GDP) growth reflects the growth of the entire economy, and consequently of all of its assets. Yet inflation erodes the value of any asset whose worth is denominated by currency. Modifying GDP for the deleterious effects of inflation to arrive at real domestic product is necessary and noncontroversial. Yet even real GDP growth has a philosophical problem that limits its use as an alternative risk-free rate. Growth in the population also causes growth in the economy. But, just because there are more mouths to feed does not necessarily mean that the individuals that make up an economy have found a way of getting more from the same set of resources, or the same from a smaller set of resources. Here economic actors are just using resources up, rather than finding ways of using them more efficiently. Thus, even real GDP needs to be adjusted for population growth.

Alternative Risk-Free Rate 2: Population-Adjusted Real Gross Domestic Product

Yet even a population-adjusted real gross domestic product is problematic as a risk-free rate of return alternative. Why? Because children and the elderly are not generally economic actors. Put another way, children and the elderly, in having money spent on them or in spending their savings, do add to gross domestic product — but they do not necessarily add to actual economic growth as I have defined it. Because the elderly are more likely to contribute to actual economic growth than are children (and for the sake of simplicity), I recommend simply backing the population growth of some years prior out of real GDP growth to remove the “more mouths to feed” problem.

So how far back in time must we go when examining population growth? Most would agree that children do not begin contributing to the economy until they are around 15 years old, and most are not truly self-sufficient until around 25 years old. On average, the population growth for the preceding 15 to 25 years in the United States is 1.6%.

I dealt with this very issue in my prior writing and concluded that, in the United States, inflation-adjusted and population-adjusted economic growth had been 1.9% from 1933–2011. This was based on average GDP growth of 7.5% (1933–2011), average inflation of 3.8%, and average population growth in the preceding 15–25 years of 1.6%.  [Note: The actual calculation is ((1 + 0.075) ÷ (1 + 0.038) ÷ (1 + 0.016) = 1.0193) – 1.]

Alternative Risk-Free Rate 3: Productivity Growth

The above measure is somewhat similar to productivity growth. I would argue that at a minimum, investors universally will want to capture the aggregate innovation of human ingenuity. After all, that is exactly what investing is about: Those with an excess of resources, but a deficit of innovation, seek to partner with those with a deficit of resources and an excess of innovation in order to grow the resources of both.

Yet the oft-reported productivity figure is just total output divided by the total hours worked by labor, so even this measure is incomplete. In the United States, a joint venture between the Bureau of Labor Statistics and the Bureau of Economic Advisors has created a “multifactor productivity” that seeks to be a comprehensive measure of innovation. For various 10-year rolling periods this number has averaged 1.1% for the non-farm private business sector.

Currently, the proxy for the bedrock required rate of return, constant maturity Treasuries, relies upon the strength of intelligence and character (creditworthiness) of an elected body and its monetary authorities for their performance. In other words, constant maturity Treasuries are an investment in a complex system that often reflects human frailty as much as, or more than, human virtue.

Thus one further advantage of using multifactor productivity growth as the “lowest-available-risk expected rate of return” is that unlike constant maturity Treasury securities, its performance rests on a seemingly innate, perhaps riskless quality of humanity that one can actually rely upon: The desire to make one’s life better through innovation.

If the essence of investing is about capturing the fruits of human productivity and innovation, then the bedrock required rate of return ought to be based on productivity and innovation, too.


Please note that the content of this site should not be construed as investment advice, nor do the opinions expressed necessarily reflect the views of CFA Institute.

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:

19 thoughts on “Rethinking the Risk-Free Rate: Offering Alternatives”

  1. Javier Gorriz says:

    Hi Jason,

    Your blog gave me some serious matter for thought, but I have to admit I am not convinced by the option of using productivity as a measure of interest rate. Irving Fisher in his Theory of Interest cautions precisely against using productivity measures as interest rates. Doing this presupposes that interest rates move forward in time, when in fact it is the inverse. The true nature of Interest rates is that they are a discount factor, the ratio of a future income to a present value of an asset. One should therefore think backwards, from future to present, with interest rates and not the other way around. Fisher did admit that productivity can play an important role in the evolution of the future income you would be discounting, but he argued that interest rates and productivity are not the same thing and taking one for the other a “pitfall” that should be avoided. He argued with bushels of wheat, and basically said that, if the yield of a piece of land where to suddenly be multiplied by 2, for instance, the increase in income potential from the yield would increase the value of the piece of land too, so it is not guaranteed that the increase in productivity would have at all an impact on the ratio of the flow of future income to the present value of the land; that is, the interest rate. I think you could safely extrapolate this example to the economy as a whole to discard productivity as an alternative measure of the risk-free interest rate.

    According to Fisher, the true nature of interest rates would have more to do with the inter temporal choices we make when sending resources back and forward in time and the value placed on present and future.

    I also have existential problems with the risk-free rate and the use of the T-Bill rate as an approximation to its measure. But it always makes me think of an engineering joke one friend of mine told me once. It’s “How would an engineer model a cow?” The answer was: “Let us assume the cow is a sphere…” My friend is an aerospace engineer, so if the people who build the planes we fly in can live with this kind of approximation to reality, I think I could live with the T-Bill as a proxy for the risk-free asset.

  2. Hello Javier,

    Thank you very much for: expanding the discussion, informing the piece with the writings of Fisher, and expressing your opinion so clearly. All of the preceding is met with appreciation.

    I have not read the Fisher discourse that you reference. However, I have spent a lot of time thinking about the risk-free rate of return and have several responses to what you have shared:

    * I am not certain whether or not you read my first piece on the risk-free rate of return, in it I expressed that to talk of “risk-free return” in the same framework that says that return is the inducement for taking on risk creates an oxymoronic situation.

    * In the previous piece I also said that the notion of a bedrock rate of return, as opposed to “risk-free” is an intelligent notion. That admission allows for discussion about what would serve as an appropriate proxy for bedrock return.

    * I agree with Fisher that productivity is not an interest rate, but neither is the “risk free rate of return” an interest rate. Instead, the risk-free rate of return is a concept. So that then shifts the context of the discussion to whether or not it is a valid concept. As I said above, I don’t think it is a valid concept. Instead I favor a bedrock rate of return. If this concept is agreed to be existentially valid then it makes sense to quantify the value of the bedrock rate.

    * I agree with Fisher’s example of the bushel of wheat. Recognition of this same issue is why I suggested two things: multifactor productivity, and multifactor productivity over long swathes of time.

    * Multifactor productivity recognizes the value of a new idea, as well as better use of land, labor, and capital.

    * “Multifactor productivity over time” recognizes that there are revolutionary ideas and inventions that can create short-term explosions in productivity, as well as productivity blind alleys during recessions and depressions.

    * I disagree with Fisher that his “bushels of wheat” example is scalable to the whole economy. First, bushels of wheat are a subset of the overall economy and its overall collection of ideas, inventions, businesses, use of factors (like wheat), willingness to work, etc. that compose the entire economy. Some factors see explosive growth in productivity, and some shrinking. This is why I began my discussion above with how to capture, at a minimum/bedrock, economic growth – the goal of investing. Yet, an economy, as measured, can also represent too much money supply, too many mouths to feed, and other distortions. Interest rates also reflect many of these same distortions. That interest rates fluctuate so massively over time is proof that they reflect distorting factors and therefore cannot be relied upon as a bedrock rate of return.

    At the end of the day, investing relies upon one fundamental transaction, those with a surplus of resources, but a deficit of ideas working with those with a surplus of good ideas, but a deficit of resources to find a way to get more from the same set of resources, or the same from a smaller set of resources. The economy at its core is the collection of all of the choices individuals make, both good and bad.Rates of return are call options on innovation. So rates of return are dependent on the economy expanding and not the other way around. When we invest we seek to capture the benefits of innovation for ourselves. Rates of return are contingent on this. Fisher seems to have framed it in the reverse. Put another way, the human desire to make one’s life better seems to be undistorted through time, and a more bedrock concept than interest rates which reflect the supply and demand of money. The supply and demand of money does reflect productivity/innovation, but it also reflects other factors such as monetary policy, irrational exuberance, and other distortions that create volatility.

    * Last, if I were asked to bet on a two horse race, where the winner would not be known for one hundred years, I would bet on the productivity horse every time, and not the constant maturity treasury horse.

    * Okay, second last, sorry…please feel free to reject any of the above, what matters is your opinions of the world working for your view of the world.


  3. Soumik Loha says:

    This is an excellent article. I have one confusion regarding excluding population growth effect from the GDP growth. We have assumed that new borne doesn’t contribute to the economy till the age of 15years. So we should take out the average population growth for those period of 15years, which is preceding 10 to 25 years. So time scale wise –

    1933…………..25th year …………10th year ………….2011
    from 2011 from 2011

    Please let me know if I am missing anything.

    1. Hello Soumik,

      I apologize for not being more clear. I have a spreadsheet in which I have the 15, 16, 17…25 year rolling average population growth. I calculated an average for each year’s effect on the economy, then calculated a final average. Note: if I were doing a time series analysis I would not have used this technique. But for the above piece I was trying to describe a general effect that population growth has on the economy, rather than a specific effect in one year. Does this make sense? Put another way, I was trying to relate a “rule of thumb” about the effect population growth has on the economy.

      I hope that helps…I am pleased that you liked the piece.

      With smiles,


  4. Richard Rosso says:

    I admire you Jason for taking this on. To reframe the discussion is most important now as what rate is truly risk-free after the financial crisis? Words mean everything, so bedrock is better and the willingness to examine this topic with some intelligent thought is so important. The risk free rate is indeed a concept and it requires a fresh look in the face of new normal. Looking forward to reading more.

    1. Hi Richard,

      Thank you for conveying your opinion about the piece. I hope that you read the other piece as well.

      It is my opinion that the “risk-free rate” is simply the intercept in the “slope-intercept” of line geometry we all learned in school in a reconstituted form. The concept still has validity if we want to use line geometry to describe expected rates of return, but the nomenclature is a poor one.

      With smiles,


  5. Jimmy Dotiwala, CFA says:

    Hi Jason,

    That is radical thinking and I enjoyed the article. I agree with you that concept of ‘risk free’ asset is indeed vague. I also think the concept of using GDP provides a good theoretical framework for capturing the minimum rate of return required for various asset classes. But I also see certain problems with this model:

    1. GDP is an ex post number. The forward GDP is know with little certainty. The spot RFR (I will use ‘RFR’ though I agree with your idea that it is not a risk free rate of return) is know with certainty and could be locked. This helps the investor to compare the spread over the opportunity cost of funds employed for a project/asset. GDP becomes a variable component in my equation and thus increases the noise related to the required return.
    2. RFR could be locked for a long term, maybe 10 years or above, disregarding the liquidity premium as the time frame increases. This helps in discounting a stream of cash flows far into the future. Again, GDP would be variable and known with little certainty for so many years.
    3. The RFR is a comparable proxy across borders. Often, GDP numbers may have some amount of noise or lag in the way different economies capture them.
    4. A big problem with real GDP is stripping out the inflation rate. The CPI/WPI seldom reflects the true level of inflation in an economy. The figure that flashes in the news reports is barely reflective of what I end up spending, year over year. On the contrary, The RFR seems more tangible in terms of what I would earn over an asset, say a G-Sec or any other proxy.

    These are merely opinions and I would like to understand if I am missing the big picture or perhaps your perspective. The GDP could be a better tool theoretically, but it lacks the pragmatic appeal of providing the right proxy to the RFR. I would love to hear if you have any thoughts on this.



  6. Hi Jimmy,

    Thank you for your criticisms…all of them valid. GDP is not my preferred proxy for a bedrock rate of return either. But then neither is productivity a perfect concept. But then neither is the “risk free rate” a perfect concept. Your comments, as well as Javier’s above, are exactly the type of dialogue I hope takes place about the concept of a bedrock expected rate of return.

    Several problems exist even with your suggestions. For example, when you say that the RFR can be “locked in” I am assuming you are talking about going long a bond or engaging in some sort of hedge. What about credit risk, reinvestment risk for the stream of coupons, and counterparty risk in the hedge? Certainly not risk-free.

    For me the discussion was best framed when I thought about what I can count on no matter the circumstances of a given market era or epoch. That thing I can rely on is the human desire to make one’s life better through innovation. While productivity cannot be directly bought, neither can the risk-free rate be directly bought. Instead bonds issued by a powerful economic and military power are used as a proxy for the RFR. The investor then holds her/his breath and hopes that it all works out and that budgets are balanced, countries are not invaded, climates continue in a predictible fashion, and so forth. So my criticism of the RFR is one of nomenclature and the proxies used for the RFR. The most important part is simply to recognize that as long as there is action there is risk and hence there is no such thing as “risk free.”

    It is my deeply felt preference that a continued, respectful, and intelligent dialogue be sparked about the RFR.

    With smiles,


  7. Jimmy Dotiwala, CFA says:

    Hi Jason,

    I now realize the direction of your argument and it seems perfectly valid. I think we approached the article from different perspectives but I am now clear of what you essentially want to highlight. I agree with you – there is no concept of ‘risk-free’. And truly, the long term yield is as speculative (or even adventurous) as any other proxy. These questions are important to redefine the way we look at investment valuation as a subject. Again, this was a very good article with deep insight!



  8. Mohammed Al-Alwan says:

    Hi Jason
    i found this article very useful and it certainly change the way i look to risk free rate.My question now is how this might affect my valuation.

    1. Hello Mohammed,

      Thanks for your feedback – much appreciated.

      You asked how this changes how you would conduct a valuation. I think this depends entirely on what you feel is a valid proxy for the lowest availalbe risk expected rate of return, and which financial asset you were trying to value. If you feel, as I do, that aggregate productivity is a valid proxy then that would be your starting rate. You would add on top of that the spread between a government bond with a duration/avg. maturity that matched your investment time horizon and that was issued by a low-risk sovereign (say Switzerland, Sweden, U.S., etc.). If your valuation is for a piece of fixed income then you would add any non-systemic risk spread you feel is appropriate to this base number. Now discount those anticipated cash flows and tweak for anything you anticipate happening in the intervening time frame (e.g. yield curve steepening). If you are valuing a piece of equity issued by this same credit then you would add the equity risk premium you feel is approrpiate to this number, and then discount those cash flows back to present value.

      One interesting thing about using productivity as your foundational cost of capital is that it highlights that bond yields of less than productivity strongly indicate, to my mind, a bubble.

      With smiles!


  9. Martin Pretty says:

    Hi Jason,

    I like the fact that you’ve looked outside the box for a better answer to what is clearly a sub-optimal basis for building return expectations. However, I struggle to see how economic statistics can be used as proxies for expected returns.As someone previously commented, they are not known in advance (whereas you know the yield on a 10 year bond today), but neither are they reliable as they are based on imperfect data collection, and neither do they reflect what investors expect (which is really what we are talking about establishing here).

    Then there is the puzzle about equities. From what research I have read and the little I have observed myself, there is a correlation between bonds and GDP growth but a very messy relationship with equities that would imply the equity risk premium is sometimes negative regardless of whether you were using bonds or GDP as the base return rate.

    Which brings us to what I think is the bigger issue – how do you model return expectations when investors will often pay a premium to take risk (think mining exploration, biotech or lottery tickets and the valuations they can attract relative to a profitable, well-established industrial) AND a premium to avoid risk (as appears to be the case with bond markets currently).

    Another problem to grapple with!

    1. Hi Martin,

      Thanks very much for your comments. I feel that they are very poignant and relevant.

      With smiles,


  10. Jason Ball says:

    Interesting post on what, at first glance, seems to be a relatively straightforward topic. Clearly implementing the idea of a risk-free rate in building return expectations is much more complex in practice! However, I am struggling to make the connection between growth (be it productivity, GDP, or something else) and the concept of a risk-free rate.

    I have always thought of the risk-free rate as purely representing the time value of money. Government debt has long since been used as a proxy for that element and to be sure, the validity of that proxy is clearly questionable given the poor fiscal state of so many major economies today. Yet the connection to growth and a bedrock rate of return escapes me.

    In my mind, growth does not come without risk. Someone somewhere is putting capital at risk in order to achieve that growth. Further, falling back on the idea that the risk-free rate conceptually represents the pure time value of money, one can think of several examples in which growth and the time value of money become divorced.

    For example, in a stagflationary economy, productivity growth would be declining while inflation was increasing. Or perhaps a less extreme (and more desirable!) scenario representing the same disconnect would be the proverbial “goldilocks” economy whereby economic growth was being realized without creating undue inflationary pressures. A risk-free rate derived from a growth metric in both of those cases would appear to me to be unable to capture the essence of what a risk-free rate is designed to measure. I’d be keen to hear your thoughts on this point of view.



  11. Hi Jason,

    I am happy that the piece triggered a thoughtful process!

    Regarding your questions – and what follows is just my opinion of which we all have one – here are my thoughts:

    * You wrote, “In my mind, growth does not come without risk.” On this we are in total agreement. In fact, take a look at part I of this extended risk-free rate exploration and you will see that is the essential beating heart of the discussion.

    * As is made clear in the first piece I believe there is no such thing as “risk-free” in a universe with action. However, I also believe that the concept of a bedrock rate of return is a good one. Because you and I think about this core rate differently (you: time value of money, and me: the return that I can count on) we have different preferences for a proxy.

    * Regarding the ‘time value of money’ concept. To me this is essentially the minimum opportunity cost. That is, what rate of return will induce me to surrender my preferred asset (fungible cash) for an idea (illiquid, narrolwy defined) for how to invest this cash. At a base level I feel that I will not surrender my cash unless someone can earn for me a rate of return greater than my own ability to productively deploy my assets/improve my life.

    * One apparent difference in our thinking is that you seem to indicate in your writing that you think of rates of return through-and-through and top-to-bottom as undulating, dynamic, and reflective of current economic forces. I am inferring this from your example of, “…in a stagflationary economy, productivity growth would be declining while inflation was increasing.”

    Several points about this:

    1) I think of rates of return as a combination of systemic (undulating) factors, non-systemic (undulating) factors, AND permanent factors (bedrock).

    2) Inflation, stagflation, the current yield on a constant maturity 10-year Treasury, LIBOR, et. al. are all measures of state changes reflective of temporary (undulating) factors.

    3) Embedded in use of the preceding as proxies for a bedrock rate of return is what I feel is a hidden, and flawed assumption, namely, an assumed time-scale. Put another way, they assume the current state of undulating factors will persist into the future. Yet, as we know undulating states do not persist indefinitely; i.e. there is mean reversion. Not only that, but lurking in the background is what I will call a traders’ mentality. That is, a mindset that sees no alternative to buying the current state of the world. Whereas, an investors’ mentality allows someone to decline purchasing the current state of the world. That is, “I don’t like stagflation and will invest elsewhere, OR I will not invest at all.”

    4) Another possible hidden influencer is the dreaded investment mandate. That is, “I must invest in the assets dictated by my charter;” or “My clients hired me to manage equities, not cash;” or “Consultants expect me to generate alpha relative to a declining benchmark;” or…something else having very little to do with capital preservation and capital creation.

    5) If you allow for a permanent factor in your required rate of return – for me, long-term (25 years at least) multi-factor productivity – then it allows you to use your rate of return to assess ALL investments, not just liquid investments like stocks, bonds, ETFs, REITs, etc., but also farm land, art, a contract to build a new house, and so forth. That is, if I cannot expect a prospective investment to pay me the aggregate innovation of an economy over the long-term, I will decline the investment. I now have a measure, not just reflective of the current state changes, but a rate that is a bit more of a bedrock and reflective of a constant need for an inducement to exit a liquid state into an illiquid. Here is an example of an application: If I see a negative nominal yield German schatz I can say to myself, “That’s ridiculous and I will decline to invest because I know that the German people, or at least some people and in some economy on the planet will be working hard to improve/innovate their lives and that’s what I want to, at a minimum (i.e. bedrock) to capture by investing.”

    6) Because a world with action is a risky world and so long as there is fiat money the bedrock rate is always positive, regardless of its magnitude. This is to compensate me for moving from liquidity to illiquidity.

    Last, can you imagine a long-dated call option being created by an investment bank that tracks various time-scaled measurements of multi-factor productivity? If so, then this concept is investible, fungible, marketable, observable.

    Best to you, too!


  12. Bob Kopprasch says:

    One of my colleagues now refers to this as the “rate-free risk.”

    1. To Bob,

      That is genius. I love that!


  13. Per Kurowski says:

    Current bank regulations allow banks to hold “solid” sovereign debt against much less capital than when lending to “The Risky” like small businesses and entrepreneurs.

    That translates directly into an artificial lowering of the “risk-free-rate” and so in fact we have not the faintest idea what that rate would be, in the absence of the distortions or manipulations carried out by the regulators.

  14. Hi Per,

    I agree that there are many distortions and manipulations of interest rates and makes using a “market”-based proxy spurious, at best.

    From your comment above, I take it that you agree with what I wrote in the piece:

    “Currently, the proxy for the bedrock required rate of return, constant maturity Treasuries, relies upon the strength of intelligence and character (creditworthiness) of an elected body and its monetary authorities for their performance. In other words, constant maturity Treasuries are an investment in a complex system that often reflects human frailty as much as, or more than, human virtue.”

    Thank you so much for participating in the discussion!


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