This article is somewhat loose, I am collecting my thoughts as I start delving into my report on inflation-linked bonds. I am picking up a train of thought that started in this earlier article on market efficiency. As can be seen, there is a lot of overlap with the discussion of the term premium. Unfortunately, this article only introduces the problem, and later article(s) will fit in other pieces of the puzzle.
Breakeven Inflation DefinitionI have an earlier primer on breakeven inflation, which gives a longer definition. The usual definition of breakeven inflation is that it is the spread between a conventional (nominal) bond, and an index-linked bond of the same maturity. For example, if a 10-year conventional bond yields 3%, and the quoted yield on a 10-year index-linked bond is 1%, the breakeven inflation rate is 2%. (The breakeven inflation rate is quoted in percent, not in basis points, unlike other spreads.) Unless circumstances are very unusual, this spread is extremely close to the rate of future inflation that results in the conventional bond and the inflation-linked bond having the same total return, for bonds with a maturity of five years or beyond.
Shorter maturity bonds -- particularly under one year -- can have an economic breakeven that markedly differs from the spread. For short-dated bonds, the seasonality of CPI can cause an impressive movements in the annualised breakeven rate. A 0.5% seasonal adjustment factor on 2 months turns into roughly 6% annualised.
(My report will have a long, drawn-out analysis of this aspect of breakeven inflation. Economists and market strategists use this spread a lot, and they should have an idea of how good -- or bad -- the approximation of the economic breakeven the spread represents.)
For the purposes of this article, I am referring to the true economic breakeven rate.
Hating On ExpectationsAnyone who has to write about markets loves synonyms. Since you are typically writing variations of the same thing every working week for a good portion of your brief life, you want to at least be able to change up the wording.
In many cases, people use "expectations" and "forecasts" interchangeably (I certainly do so myself sometimes). However, the connotations are very different in finance. In financial mathematics, expectations refers to the definition in probabilistic mathematics, which is a probability-weighted average of a random variable.
For example, if we are betting $1 on a fair coin toss, our expected return is $0., since we have a 50% chance of winning $1, and a 50% chance of losing $1. (I'd like to thank my reader Jerry Brown for pointing out that my initial draft of this example was wrong; my numbers were for a lottery ticket, not a bet.)
If we are indifferent to taking risks, the fair value of an instrument is equal to the expected value of its cash flows. (This is referred to as being risk neutral). In which case, an instrument is trading at fair value if its expected value matches our forecast. And if we are looking at forward interest rates, we see that the forward rate has to match the expected rate if we want to price options without arbitrage possibilities.
Many heterodox economists have issues with the notion of market efficiency and rational expectations. One can easily debate the wisdom of market pricing. That said, trying to operate as a market maker in fixed income options is going to be a debacle without some version of market efficiency embedded in your pricing algorithm.
This carries through to (economic) inflation breakevens. Although inflation option trading was not particularly active when I was involved in the markets, the breakeven rate is going to match the (risk neutral) expectations for future inflation. Using the mathematical definition, the breakeven rate has to match expected inflation.
However, this does not have to equal what anyone is forecasting, for reasons I discuss next. This is why I try to avoid the use of expectations in this context.
Forecasts Not Matching Expectations?The economic breakeven does not have to match any market participant's forecast for inflation. All that we need is for some factor to drive observed prices from the risk neutral expectation.
- There could be something like a term premium (an inflation risk premium).
- There could be a liquidity premium for one bond.
- (Related to the previous.) It may be possible to finance one bond more cheaply in the repo market. (Since this effect is quantifiable, we could adjust the economic breakeven to take it into account.)
- The tax treatment of index-linked bonds is at a disadvantage versus conventional bonds in most markets. This was a concern in the early days of the index-linked market in the United States. However, the trading of these bonds is dominated by tax-exempt investors, and so the observed tax effects seem to small in practice. (A taxable investor would need to take them into account when calculating the economic breakeven.)
- There can be institutional factors that create an imbalanced demand in the inflation-linked bond market. (There is a wider participation by borrowers in the conventional bond market, and so it is generally possible to sidestep demand imbalances. However, it is still possible, as seen in the U.K. gilt curve after the pension reforms of the 1990s.) Market participants will push their estimate of fair value away from the economic breakeven rate based on their estimate of this supply effect. In practice, this ends up looking like a term premium.
- Market pricing can be gosh darn dysfunctional, as was seen in the Financial Crisis. During the crisis, it was clear that there were many forced sellers of index-linked bonds, and no buyer was willing to take them out of their positions at a "fair" price. Once again, this might be thought of as something like a term premium.
As can be seen, many of these factors might be thought of as a "term premium" (as that phrase is used within finance, which may not match economic intuition). We have two alternative formulations:
- there is an inflation premium, (which might be either positive or negative); or
- there are term premia embedded in both the conventional bond and the index-linked bond, and the breakeven inflation rate is biased by the difference in term premia.
In my view, it is a lot easier to think of the differential in term premia rather than an inflation premium.
Why Are We Asking This?
The topic of the term premia (and inflation risk premia) has been the recipient of a large amount of academic research. I am not a particular fan of the affine term structure model estimates of the term premium; they are prey to the garbage in-garbage out syndrome.
In my view, the complexity of the analysis takes us away from a more fundamental question: why do we care? If we return to first principles, our attitude towards the term premium depends upon who is asking the question.
- If you are a long-term investor, you should look at the raw economic breakeven. You want to decide which type of bond offers a better return, and you should have your own assessment of risk premia. Subtracting a random term premium from the true economic breakeven biases your subsequent analysis.
- If you are an active fixed income investor, you may need a good estimate of where the market should be trading (conditional on an inflation forecast). You can make an estimate of what the term premium should be based on the current trading environment. Your methodology may change over time.
- If you are an observer of the bond market, you may just want to see what the market is pricing in for inflation over various horizons. Usually, this is being done by economists who want to create a time series estimate of inflation expectations. An algorithm that is consistently applied over time is necessary.
As can be seen, analysis of the term premium is trickiest for observers of the market. The problem with many estimation techniques is that the term premium estimate is unstable, and it ends up absorbing most of the volatility of market prices. Instead of movements in the raw breakeven being interpreted as changes in inflation expectations, all that is happening is that the term premium is bouncing around for completely unknowable reasons.
Returning to the original subject of this article, it is clear that breakeven inflation may have a bias relative to the inflation forecasts of market participants. I will have to return to the discussion of the size of this bias in a followup article. My view is that the bias is relatively small out to the 5-year point of the curve, probably not worth worrying about at the 10-year point, and is wildly uncertain at longer maturities.
We need to very careful in distinguishing forecasts from raw economic breakevens (forward rates, inflation breakevens). I will return to the discussion of the magnitude of the bias in a later article.
(c) Brian Romanchuk 2017
Why isn't the expected return on a coin toss zero?ReplyDelete
Ouch. I mixed up a coin toss bet and a lottery ticket. Thanks.Delete
The Fed has several studies where lagged BEI (Break-even inflation) is tested against realized inflation measures (CPI, PCE, headline and core versions.ReplyDelete
The effect on current BEI in various tenors from the release of inflation statistics is also interesting.
More details can be found at https://git.io/infl which uses Jupyter notebook for data analysis and forecasting.
Thanks, that package looks interesting.Delete
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