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.
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20 Comments
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!
Jason
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!
Hi Martin,
Thanks very much for your comments. I feel that they are very poignant and relevant.
With smiles,
Jason
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.
Best,
Jason
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. http://blogs.stage.cfainstitute.org/investor/2012/03/20/rethinking-the-…
* 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!
Jason
One of my colleagues now refers to this as the "rate-free risk."
To Bob,
That is genius. I love that!
Jason
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.
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!
Jason
I think it would be much more interesting to use a personal rate that represents the highest return you could get on an almost risk free deal.
Let's say bonds give 2% for 20yrs, but if you could loan someone a lot of money with which he wants to buy a real estate portfolio, where he would pay 3% interest rate and the LTV is only 10%. Then I would think using 3% as your RFR would be more fair.
The more money and connections you have, the more opportunities to get into deals that are close to risk free and might give better returns than bonds.
And maybe there are different risk free rates per type of asset.
Because of the amount of money involved in some deals, 5% close to risk free deals can be done in buying/selling expensive art, while in real estate you can might be able to secure a 30 year loan for 2% on 500k which is perfectly high end and A+++ location, have it rented out. Sell 90% equity to someone who is willing to accept a 4% return (so 28k in costs in total) while renting it out for 30k. This would be a 4% ROE (just to give some examples).
I think using the risk free rated based on bonds is just a market practice because it's easy, convenient, uniform and understandable for everyone involved in the deal. But theoretically it's just a shortcut