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Monday, April 10, 2017

How To Approach The Term Premium

The term premium is an important concept in fixed income analysis. For our own analysis, there are a few ways of using the term premium. Unfortunately, there is no way of extending the analysis for an individual to the market in general, as there is no need for market participants to agree on the term premium before undertaking a transaction. As a result, we should not expect to be able to infer an average term premium implied by market pricing using any algorithm.

This article follows on from the article "The Term Premium Problem," which outlined my thinking about the term premium. I imagine that readers would be most interested in my criticisms of existing techniques to calculate the term premium. My argument is that the problem with those techniques is that they start in the wrong place; there is no technical fix as a result. Rather than attempt to criticise hundreds of complex algorithms, I will instead explain what I see as the best starting point. From that vantage point, the defects of the conventional approaches become more obvious.

Using the Term Premium as an Individual

I believe that investors that are making directional decisions in the fixed income markets, they should use the concept of the term premium. (Directional trades are positions that have risk exposure to the level of the interest rates across the curve. Conversely, in relative value trading, one normally attempts to hedge out the directional risk as best possible.)

(I assume that the reader is familiar with the concept; please see this primer for a definition of the term premium. But as a quick summary, the term premium for a bond is the additional yield it is expected to have versus rolling over short-term bills -- cash, in bond market jargon -- over the life of the bond. The expected return on cash is equal to the expected average of the short rate, modulo various small technical effects that I am ignoring for simplicity.)

Importantly, there are a number of ways of using the term premium; these different usages imply slightly different definitions for the concept. The reality that the definition of the term premium depends on how we are using it is a subtlety that I rarely see discussed.
  • How much extra return over cash do I demand in order to hold a bond instead of cash? This definition is purely determined by my preferences.
  • Given my expectations for the path of short rates, what level of term premium determines the fair value of a bond yield? That is, what is the fair value for the term premium. This fair value can be determined independently of the bond yield observed in the market; the objective is that we can buy or sell on a profitable basis when comparing the market yield to fair value.
  • Given my expectations for the path of short rates, what is the level of the term premium implied by the observed bond yield in the market? This market-implied premium -- relative to my rate expectations -- would presumably be an input into investment decisions.
  • What do I think other market participants believe is the proper level of the term premium for their own decisions? Why this is interesting may not be immediately obvious. As an example, if I am a market maker, I need to set my prices midway between other market participants, as I need to be have two-sided trading flows. I need to find what I believe is an "average" rate expectation and term premium so that my prices are roughly in the middle of market.
I can obviously determine what the level of the term premium I am using in each of these cases, since I can always ask myself.

Realised (Historical) Term Premia

One alternative way of approaching the term premium is to look at historical excess returns for bonds. The problem is that a bond's excess returns are baked in at issuance, and those excess returns are highly auto-correlated over time. More simply, we have been in a mega bond bull market, and so bond's excess returns have been huge.

I think we need to take into account historical excess returns when discussing the forward-looking term premium, but we have to accept that market participants have historically been quite wrong about the direction of interest rates, and these errors were persistent. However, if we are looking at maturities at 2 years and under, these errors should be less significant.

Should Term Premia be Positive?

Under the classical "returns volatility is bad" approach to finance, one would assume that term premia are positive. (That would certainly match the historical experience.) However, in a world where investors need to match actuarial liabilities, reinvestment risk can easily be less significant than the aversion to returns volatility. That said, it is hard to see how a negative term premium estimate on a 2-year bond is plausible.

The Moral Philosophy of Bond Pricing

I deliberately used the word "should" when I wrote: "they (investors) should use the concept of the term premium." I have made a weak normative statement: investors should be rational when pricing bonds. (I am using rational as it is usually used in economics and finance; and the rate expectations/term premium approach is what is typically implied by investor rationality.)

If everyone follows this prescription, all market participants would be trading bonds based on valuations derived using rate expectations and the term premium. Under this assumption, it appears to make sense that we could write about the average term premium amongst market participants.

However, as I will discuss in the next section, we need to question this assumption. Once we take into account the various other factors that go into investment decisions, investors may no longer transact bonds based on rate expectations and term premium, even if they are not narrowly "irrational." In such a case, we no longer have an "average" term premium (I am using average in a loose sense, not necessarily the arithmetic mean) that describes aggregate market participant behaviour.

I have never run across any serious discussion of the aggregation problem for term premia (I never bothered searching for such discussions; as a non-academic, that's not my problem). One explanation is that the assumption of rationality is so ingrained that the possibility that people can trade bonds without a view on the term premia was never taken too seriously.

The Average Term Premium Does Not Exist

I will now give a simplified example that highlights the problem with believing that there is an "average" term premium.

Imagine that trading one day in the 10-year bond is dominated by four large fund investors (possibly intermediated by dealers that end up with no net positions); assume that all are transacting in roughly equal size. All four investors are behaving in an optimal fashion, based on their situation. For simplicity, we assume that all trades clear at 4%; we will not worry about the mechanism that determined the market clearing yield.
  • Buyer. One investor assumes that the term premium is 0.50%, and the expected average of the short rate is 3.00%. As such, this investor is buying the 10-year.
  • Seller. One investor assumes that the term premium is 1.25%, and revised up the expected average short rate to 3.25% as the result of new data released that day. This investor sells 10-year bonds.
  • Buyer. One fund was forced to buy bonds in order to lower the Value at Risk of its aggregate portfolio; the 10-year bond was assumed to have a negative return correlation with the fund's equity position.
  • Seller. A bond index fund was forced to sell to meet redemptions by households who invest in the fund. Although each household had its own reasons, many were selling to raise cash in order to make tax payments.
There is no way of going from the observed bond yield to the risk premium. Even for the market participants who had term premium estimates, there estimates did not agree. Of course, two of the funds transacted without a defined term premium in mind. The market is cleared on the basis of bond yields, not risk premia. (The equity risk premium is in a similar position, but there are some practical differences, as I discuss below.)

Pretending that there is an infinite number of investors that we can average out is not a realistic response. The fixed income market is a scale business; trading is dominated by a few entities.

Things get even worse for the idea of an "average" term premium if we bring in "irrational" investors.

"Irrational" Participants

There are many bond market participants that will transact in a way that cannot be interpreted based upon term premia and expected short rates. (The behaviour might be considered rational from the perspective of a more complex utility function; but it will appear irrational from our narrow perspective here.)
  • Are committees rational? Most funds make directional investment decisions using an investment committee; individual portfolio managers normally have limited discretion to take risk. There is no reason for committee members to agree on how to decompose bond yields; they invariably make decisions based on observed market yields. The complexity of the decision making for a group may make it unlikely that we can fit a portfolio allocation decision to observed behaviour.
  • Technical Traders. There may still be investors that trade bonds based on things like candle stick charts (although such manager seem to be increasingly rare). However, there do seem to be people who trade government bonds based on stories they read on the internet.
  • Behavioural Finance. <Insert behavioural finance anecdotes here.>
  • Balance sheet driven investors. Central bank reserve managers have been notoriously price insensitive. Many individuals have automatic investment plans; and it is a safe bet that most households do not have any views about the level of the term premium.
  • Borrowers. We cannot look at just the investors for determining how markets clear. Borrowers also adjust their issuance profile over time, and they have to take into account multiple factors for their choices.

Analogy to the Equity Risk Premium

There are similarities between the equity risk premium and the term premium. In my view, there is a key difference in their behaviour. In order to calculate the equity risk premium, we need a long-term earnings growth (or dividend growth) estimate, which only moves at a low frequency. The equity risk premium moves at a high frequency to bring the high frequency market data in line with low frequency fundamental data. (The discount rate also moves at a high frequency, but is largely inconsequential for valuation on a day-to-day basis.) Once we decide what earnings growth series we use, we have no difficulty in pinning down an equity risk premium -- if we assume that investors all agree on earnings growth prospects (which is unlikely). 

When we look at some estimates of the term premium generated by arbitrage-free yield curve models. both the rate expectations and the term premium are moving at a high frequency. It is going to much more difficult to untangle these time series.

I will discuss this frequency issue in greater depth when I comment on the arbitrage-free yield curve estimates of the term premium.

Even if You Have a Term Premium, What Do You Do With It?

It might be possible to commission a survey of investors of what term premium they are assuming in their investment decisions. (This is quite different from how some analysts are using existing survey data; a point I may return to in later articles.)

I would have serious doubts about the validity of such a survey; I certainly would not have offered outsiders any peeks at our proprietary investment analytics when I was with an investment firm. The most likely outcome that the responses would be filled in by junior economists, who would then just grab the latest data points off a term structure model that is in the public domain.

However, even if we have access to such data, how so we use it? In the examples of how an individual uses a term premium, the concept makes sense; it offers me guidance how I should act. It is unclear what information an aggregate term premium would give us -- who is acting, and why? Unless it can be related to some observable financial or economic outcome, there is nothing that distinguishes one term premium estimate from another.

Concluding Remarks

The term premium is a well-defined concept within our own analysis, although the exact definition depends on how you are using it. However, there is no way of looking at market data to determine an average term premium used by market participants. Therefore, when we look at a time series that is labelled as an average term premium, we should not expect it to be coherent with how any individual would price bonds.

(c) Brian Romanchuk 2017


  1. Actually, the ERP suffers from a worse flaw even given your framing of the issue: it requires a term premium estimate to get it off the ground.

    So even before you start considering the ERP in and of itself it must rest on the term premium foundation.

    It also doesn't seem to "do much" in reality. See:

    1. Sure. I just wanted to cover one obvious objection -- we can say roughly the same thing about the equity risk premium (ERP). That is, we cannot observe it directly, and people use it all the time. Whether or not they should be using the equity risk premium the way they do is yet another big question...

      I certainly have less objections to some uses of the equity risk premium (partly because I gave up on trying to understand equity pricing), which I may explain that in a different article. (You are explicitly focusing on either growth or the ERP, and pretending the other factor follows some simple rule.) Since I suspect many readers might feel the same as me about the ERP, I want to highlight this objection from the beginning. I do not want to make it look like I've missed an obvious point.

  2. How can u say negative term premia on 2y rates cant be negative. So how do you explain the 2y rate in Germany in ur framework. 2y schatz is well through 2y OIS, its well through any reasonable expectation of 2y rates.

    1. That's one particular instrument, which is in short supply, trading through the rest of the curve. Germany has the special status as the only major borrower without default (euro exit) risk. That is a situation that does not normally happen in the other developed markets, as the supply of central government bonds is normally large enough to avoid squeezes.

      In the euro area, I would treat swaps as the benchmark curve, and the term premium is with respect to that benchmark curve.

      I have no idea what the funding cost on the schatz is. If their funding is trading through the other sovereigns, that supports lower yields. The expectation is with respect to the funding cost, which may not reflect the euro average short rate.

    2. Its not one instrument. Whole german curve up to 30y is well through OIS. Thats the 2nd most important bond market in the world.

      I guess we see it differently. The fact that their funding cost is so low is a reflection of negative term premia. If the rates market normalises (Credit risks decline + large amount of ECB accomodation removed) in in euro area their funding costs will go back close to OIS.

    3. "There are many bond market participants that will transact in a way that cannot be interpreted based upon term premia and expected short rates. "

      2y schatz=China reserves

    4. There's a premium for German debt, sure. My objection is labelling that as a "term premium," as why does this not effect other instruments.

      Nevertheless, if the repo funding cost for German bonds below other short rates (which I assume is the case), then low German bond yields are not a mystery in any sense. I do not have a definition of euro OIS handy, but I assume that it is not German bond repo rates.

    5. yes short term OIS is 30bps higher or so than average german repo rates.


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