# Lowered Expectations, part 2

When is a fixed payment not a fixed payment?

When it is in nominal terms.

Suppose you and I enter into an inflation swap contract where you offer to pay me $1.10 five years from now, while I offer to pay you CPIthen / CPInow dollars. It is true that one of us is offering a fixed value known today, while the other is offering an unknown value based on future events. But which is which? Rational investors do not think in terms of dollars, or yen, or Euros, or even ounces. Rational investors think in terms of purchasing power. After all, dollars are just ink on a page (or pixels on a screen); they are only interesting to the extent that they can buy stuff. This is why long-term price comparisons are always done using “real”, aka. “constant”, aka. “inflation-adjusted” dollars. And this is why risk aversion is always about real wealth. For many contracts, the distinction is irrelevant. For example, suppose we negotiated the following contract today: “In 2015, you will pay me N cents, while I will flip a coin and give you$1 should it come up heads.” Since any inflation over the next five years would affect both sides of this contract identically, you would be offering the fixed payment and therefore would be entitled to the risk premium. And so N would be somewhat less than 50 cents.

But inflation swaps are special because one side is perfectly correlated to inflation itself. In my hypothetical inflation swap above, you are offering me 1.10 nominal 2015 dollars. But I am offering you one constant 2010 dollar. What we know today is the real, inflation-adjusted value of my future payment. What we do not know is what your $1.10 will be worth. Therefore I am the one offering the fixed payment; therefore I am the one entitled to the risk premium; and therefore the break-even rate on inflation swaps overstates the market’s true expectations for inflation. Score one for Dr. Haubrich. How much do inflation swap rates overstate inflation expectations? According to the paper: The inflation-risk premium averages around one-half of a percent for most of the period. It also varies only between 29 and 61 basis points, effectively keeping between one-third and two-thirds of a percent over the 27-year period. Such a low and steady level means that outside of special periods, such as the present, break-even inflation rates provide a reasonable measure of expected inflation. What determines the inflation risk premium? From the other paper: The risk premium can move about for two very different reasons. First, the amount of inflation risk may change. Inflation may become more variableâ€”higher highs and lower lows, and the stakes of misjudging become higher. Secondly, the stakes may stay the same, but people may become less tolerant of risk. In other words, the price of inflation risk gets higher. Which means you need to a be a little careful interpreting inflation swap rates during times of increasing risk aversion or uncertainty. But generally, the bottom line is: The inflation risk premium fluctuates around half a percent. (See figure 2.) This gives a rule of thumb for adjusting the break-even inflation rate to get a better estimate of true inflation expectationsâ€”take half a percentage point off. If you just cannot get enough of this stuff, head over to the Cleveland Fed. There were several good comments on the previous post. Congrats to jesse for nailing the puzzle immediately; I hid his comment until now to avoid spoiling it. ### 30 comments to Lowered Expectations, part 2 • Nemo – does it have to be related to who is on the fixed side? can’t the risk premium depend on which party “needs” to hedge/trade? ie, if you are the one initiating the trade and eager to do it, YOU will pay the premium… no? -KD • Nemo Hey, KD. Can you give me an example of what you mean? Because I think we may be saying the same thing. If you “need” to hedge/trade, then by the definition of “need” you are exposed to some risk. (For example, you need fire insurance on your house because you are exposed to the risk of a fire.) An equivalent way to define “risk premium” is “what you have to pay somebody to transfer your risk to them”. • jesse After reading the comments in the last section I thought the answer was some fifth order effect of a complicated hedge swap derivative thingy. Turns out it was pretty simple after all! Great point that “risk aversion is always about real wealth” • Hi Nemo – let me talk about equities… in 2008, people panicked and sold stocks with abandon. The sellers drove the price action and the embedded risk premium (which the buyers of stocks essentially received as expected return) spiked. When everyone wants to sell, buyers demand and receive a big premium in their expected return. On the other hand, since then, stocks spiked – buyers drove the price action, and sellers were able to sell stocks with a much lower embedded risk premium (alternatively, buyers bought stocks and accepted a much lower premium to do so). get what I’m saying? isn’t it possible that sometimes inflation swaps overstate inflation expectations (probably when everyone is worried about inflation, and wants to hedge accordingly – sellers of “inflation,” aka the market makers, will sell it at a higher price), and sometimes inflation swaps understate inflation expectations (probably when everyone is worried about DEflation, and wants to hedge thusly – buyers of “inflation” will pay less for it). I may very well be mis-using the risk premium concept in my equities example, but my point is basically about price takers vs liquidity providers (price makers). thoughts? • Nemo KD — What you are describing will affect the magnitude of the risk premium, not its direction. At least, that is what the academics will tell you… “Risk aversion” applies even when you are losing money. Given the choice between a certain loss of 50 cents and even odds of losing$1, if you are “risk averse” you will give up the 50 cents. In fact, you will be willing to give up somewhat more than 50 cents; this is the same as saying you will pay a premium to eliminate the risk of losing $1. (Compare this to buying insurance, for example.) Whether people behave this way in general is a different question. And how inflation swaps would look if everyone really did expect deflation is an interesting thought experiment. But I am reasonably certain an academic economist would say that even then, the “risk premuim” should cause the break-even rate to overstate inflation expectations, on the grounds that markets in general prefer certainty to uncertainty and are willing to pay for it. • Nemo, you wrote “magnitude of the risk premium, not its direction” isn’t changing the “direction” of the risk premium just an extreme move in the magnitude? ie, when the magnitude goes from +2% to -2%, that’s just a 4% change in the magnitude, which crosses the boundary of zero… ??? I guess all I’m saying is that sometimes people pay too much while buying assets, and sometimes they accept too little when selling assets. Now, generally, people may be fearing inflation, and thus the implied inflation level priced into inflation swaps may be systematically too high. Right now, however, people may be fearing deflation, and thus the implied inflation inherent in the swap prices may be too low. It’s quite possible I’m on a different plane here and missing your point, but I don’t think so. Let me try one more analogy – options implied vols. They aren’t systematically too high or too low, right? In periods of panic, implied vols are too high (risk premium spikes). In periods of complacency, they are too low (risk premium plummets). • Nemo, I guess if I take my analogy directly to the topic of inflation swaps, you wrote: “But I am reasonably certain an academic economist would say that even then, the â€œrisk premuimâ€ should cause the break-even rate to overstate inflation expectations, on the grounds that markets in general prefer certainty to uncertainty and are willing to pay for it.” I’m saying that the “certainty” people want is that a change in inflation won’t screw up their portfolios. I don’t see why hedging this uncertainty should always result in an over or under pricing – it shouldn’t – it depends which scenario people are afraid of. If everyone is worried that high inflation will destroy the value of their savings, and thus wants to hedge against the uncertainty of high inflation, then inflation swaps will overstate forecasts. If everyone is worried about deflation and the value of their home eroding, then inflation swaps will understate. No? -KD • Nemo isnâ€™t changing the â€œdirectionâ€ of the risk premium just an extreme move in the magnitude? Well, yes, but that is not what I meant. I meant the risk premium will always be positive. So the magnitude may change, but never enough to make it cross zero. Assuming risk aversion + rationality, that is. People do play roulette, so of course they are not always rational. But the purpose of this sort of analysis is to infer a “market expectation” for inflation assuming the market is being efficient and rational. If you assume the market is just being random, then of course you can infer nothing. So the question is not whether rationality is a good assumption. The question is: If the market is being rational, then what can we infer about its expectations for inflation? Let me try one more analogy â€“ options implied vols. A perfect analogy, actually. They arenâ€™t systematically too high or too low, right? In periods of panic, implied vols are too high (risk premium spikes). In periods of complacency, they are too low (risk premium plummets). Yes, but they are never negative! Buying an option eliminates some risk for you; specifically, the risk of the underlying stock moving up or down. (Note: Up or down.) It does so by transferring that risk to another party. You will always pay that party for the privilege; they will never pay you. The premium you pay will certainly depend on how the market is anticipating the stock’s risk and how it is pricing that risk, but it will never, ever be negative. Nobody will ever pay you to give you an option, no matter how far in or out of the money it is or which way “everybody” expects the stock to be heading. If everyone is worried about deflation and the value of their home eroding, then inflation swaps will understate. No? No. If they are worried their house will lose between 10% and 50% (symmetrically distributed), they will actually have to pay a premium to insure it loses exactly 30%. • Nemo: I’m almost with you…expand on your last sentence, if you could…”No. If they are worried their house will lose between 10% and 50% (symmetrically distributed), they will actually have to pay a premium to insure it loses exactly 30%.” Won’t the price of the swap imply, say, 31% DEFLATION (and thus, understate inflation), in that scenario? If 30% deflation was “fair value” and everyone wanted to “sell inflation” so to speak? (the market makers extract a 1% premium here, as a charge to the people who are demanding the trade) Ie, the people who want to hedge against deflation will pay a premium – they will only earn returns on deflation of more than -31%… that’s understating inflation, not overstating it. ??? • Nemo Wonâ€™t the price of the swap imply, say, 31% DEFLATION (and thus, understate inflation), in that scenario? OK, I admit this one made me think for a minute. But the answer is still “no”. In an inflation swap, you offer to pay me a fixed rate y and I offer to pay you “inflation”. That is, after N years, you will pay me (1+y)^N, while I will pay you CPIN / CPInow, and what we negotiate today is y. In this scenario, you are the one paying a fixed nominal price (namely, (1+y)^N payable at year N) to get inflation protection, while I am paying a fixed real price ($1 in constant 2010 dollars) to provide it to you.

If we both know the expected compound 5-year inflation rate is -30%, and you offer me y=-0.3, that will be a “fair” trade in the sense that both of our expectations net to zero. But since you are getting the protection, you are reducing your risk, so you will need to offer me more than -0.3 for y. Maybe -0.29. So when someone looks at this transaction, they will know our expected inflation is less than the -29% you had to pay.

• “But the answer is still â€œnoâ€. In an inflation swap, you offer to pay me a fixed rate y and I offer to pay you â€œinflationâ€.”

but what if i want to take the other side of the swap? I’ll pay floating and receive fixed… perhaps i’m missing something SPECIFIC to inflation swaps, but I think you could make my exact argument about an interest rate swap. I think that I would argue that interest rate swaps do NOT systematically over or under price forward rates. Am I wrong?

Said differently, let’s pretend 5 year inflation swaps are pricing in 1% inflation. I can buy OR sell that rate, can’t I? I don’t have to act on one side of the market. Or do I? Is this an inflation swap quirk? Even so, I don’t think it matters. Maybe all the broker/dealers in the world want to sell the rate, so the rate gets artificially depressed until they attract “buyers” of the rate…

You are emphasizing the “paying a fixed price” side of the argument, but I don’t see why that needs to be the driver. The payer of the floating price could be the initiator/driver of price for the trade

• Nemo

but what if i want to take the other side of the swap?

Then you will be willing to accept a low risk premium. Possibly a desperately low risk premium. But never a negative risk premium. You will always demand more from the other party than what you expect inflation to be.

You cannot use an inflation swap to protect yourself against deflation, any more than you can use a call option to protect against a stock falling. You can buy a call or you can sell a call, but no matter how desperate anybody gets, the option seller will always collect the risk premium.

An inflation swap is a straight transfer of “risk” in the sense of “uncertainty”, not in the sense of “could lose money”.

perhaps iâ€™m missing something SPECIFIC to inflation swaps, but I think you could make my exact argument about an interest rate swap.

Well, as I said in the post, inflation swaps are special because the nominal “floating” side is perfectly correlated with inflation and is therefore actually the fixed side (in real terms). Whether and how the same argument applies to interest rate swaps depends on how interest rates correlate with inflation… Which gets complicated. So let’s stick to inflation and/or “toy” examples.

Said differently, letâ€™s pretend 5 year inflation swaps are pricing in 1% inflation. I can buy OR sell that rate, canâ€™t I?

Yes, but in one direction you would have to offer fixed and receive floating, while in the other you would offer floating and receive fixed, and in either case the risk premium would always go to whoever is offering real fixed (nominal floating). To “buy” the 1% rate, you would take the nominal fixed (real floating) side; i.e., you would buy inflation protection. And whoever sold you that protection would demand more than his/her expectation for inflation. To “sell” the 1% rate, you would take the nominal floating (real fixed) side, and then you would demand more than your expected rate of inflation in return.

Whether the expected rate is positive or negative, whoever is paying “inflation” is assuming all of the risk and will therefore receive the risk premium.

You are emphasizing the â€œpaying a fixed priceâ€ side of the argument, but I donâ€™t see why that needs to be the driver.

It may not be the driver, but it does determine who collects the risk premium. Whoever is accepting the risk — regardless of who initiates the trade — will collect the risk premium. And it will always be positive.

• jaguaracer

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1364254

Abstract:
“Inflation-indexed securities would appear to be the most direct source of information about inflation expectations and real interest rates” (Bernanke, 2004). In this paper we study the term structure of real interest rates, expected inflation and inflation risk premia using data on prices of Treasury Inflation Protected Securities (TIPS) over the period 2000-2007. The estimates of the 10-year inflation risk premium are between 11 and 22 basis points for 2000-2007 depending on the proxy used for the expected inflation. Furthermore, we find that the inflation risk premium is time varying and, specifically, *******negative in the first half (which might be due to either concerns of deflation or low liquidity of the TIPS market), but positive in the second half of the sample. *****

• jaguaracer

an oft-referenced paper:
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1101513

pg. 23
Thus, using two versions of one and the same model, we were able to replicate the varying signs
of inflation premium that have been reported in the existing research. Hordahl and Tristani (2007)
provide a thorough discussion of this issue. In particular, the existing calibrations of various general
equilibrium models imply a positive inflation premium. On the empirical side, the sign of the inflation
premium depends on how inflation expectations are measured in a particular implementation.

• Nemo –
first off, thanks for the continued intelligent back and forth. The secret of my success throughout my educational and professional life had been repeatedly pestering intelligent people with questions until I understood what they were trying to explain to me. When you find someone who relentlessly responds to your questions without getting frustrated (as I have found in you), it’s a good thing.

I’m approaching this from the point of view of a trader. Thus, when you say

“You cannot use an inflation swap to protect yourself against deflation, any more than you can use a call option to protect against a stock falling,”

I’m kinda at a loss as to what you mean. By “Selling” inflation, you’re protecting yourself against deflation, are you not? You’re profiting if inflation is lower (or deflation is greater) than the implied level you sold.

By selling a call option (I don’t think this is the right analogy, which I’ll explain in a minute) – you profit from a falling stock price (I don’t want to argue semantics, but you protect yourself against a stock falling). I think the point with options pricing is in measuring the implied vol that markets are pricing in vs historical vol. It’s flat out wrong to say that markets always price implied vol at a premium (or a discount) to historical actual vol, isn’t it? It varies, with the sentiments of the market.

Inflation should be the same way, and I apologize, but I still don’t understand why it’s not. I guess I’d ask you to explain this paragraph:

“Yes, but in one direction you would have to offer fixed and receive floating, while in the other you would offer floating and receive fixed, and in either case the risk premium would always go to whoever is offering real fixed (nominal floating). To â€œbuyâ€ the 1% rate, you would take the nominal fixed (real floating) side; i.e., you would buy inflation protection. And whoever sold you that protection would demand more than his/her expectation for inflation. To â€œsellâ€ the 1% rate, you would take the nominal floating (real fixed) side, and then you would demand more than your expected rate of inflation in return.”

my point is that if BUYERS of inflation swaps are the ones driving trading, then they’ll pay more than the 1% fair value – say, 1.05% – they’ll pay a risk premium. If sellers are the ones driving the trading, they’ll sell it for 95bps.. less than fair value. THEY will pay the risk premium. Right? Sellers wouldn’t still sell at 1.05%…

jaguaracer’s comment above seems to jive perfectly with what i’m saying – in the early 2000s, we were in a downturn and deflation was the fear, so the risk premium was negative, driven by SELLERs. In the second half of the decade, we had a recovery, and inflation was the fear, so buyers drove the risk premium into positive territory.

• Nemo

Thanks, jaguaracer.

Updated version of the same paper:

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1108401

That is interesting, but as they point out… (a) Their model for inflation expectations results in a risk premium lower than every other piece of literature they survey; and (b) TIPS are subject to liquidity risk relative to nominal Treasuries, which is easily sufficient to explain their “negative risk premium”.

Incidentally, since inflation swaps are derivatives, they are not subject to liquidity concerns. That is one reason I like them better than the TIPS spread for monitoring inflation expectations.

On the empirical side, the sign of the inflation premium depends on how inflation expectations are measured in a particular implementation.

This is the key quote. To these academics, the definition of “inflation risk premium” is the difference between the TIPS spread and the “inflation expectations” that their model spits out. That this “inflation risk premium” becomes negative says more about their model (and about the TIPS spread) than it does about actual risk premia.

Or perhaps these folks actually believe that people become “risk seeking” rather than risk-averse when faced with guaranteed losses, which would truly result in a negative risk premium for deflationary expectations. I wonder what Dr. Haubrich’s model says about inflation risk premia for the 2-5 year horizons in the fall of 2008, when the breakeven rate on inflation swaps became decidedly negative. (Of course, any derivations based on market behavior during that time are suspect, since the whole system was melting down.)

• Nemo,
what did you mean by this: “since inflation swaps are derivatives, they are not subject to liquidity concerns?”

again, I’m thinking like a trader, and I think the crux of what I’m saying is that everything is subject to liquidity concerns – you can only buy something (derivative or otherwise) that someone else is willing to sell, and vice versa of course.

I’m wondering if this whole thing is another example of the difference between economist’s theories and reality.

• Nemo

KD —

My option analogy was poor. So forget that.

If sellers are the ones driving the trading, theyâ€™ll sell it for 95bps.. less than fair value.

Ah, this is the crux. Let’s focus on this example.

Short answer: No, they will not. If you believe “fair value” is 1% — i.e., your inflation expectation truly has a mean of 1% — why would you sell (i.e., pay inflation) for only 0.95%? That would imply you are expecting to receive less than you pay (in real terms) and with more uncertainty to boot. This would be like betting 60 cents on a coin toss for $1; it would not be risk-averse. To say “fair value” is 1% is not the same as saying “the market price is 1%”. If someone is willing to sell inflation for 0.95%, that means that they think the real expected rate is 0.90% or something. No matter how badly they want to “drive the sale”, they cannot sell for less than their expected rate of inflation and still be risk-averse. For the buyer, it’s totally different… Even though the buyer expects 1% inflation, he is willing to pay 1.05% on the swap, because even though he expects to lose money in real terms, he gains certainty in real terms. Such willingness to give up expectation value in exchange for reduced variance is the definition of “risk aversion”. He is not paying a risk premium because he is “driving the purchase”; he is paying a risk premium because he is risk-averse, and the swap turns something uncertain for him into something certain for him. In short, the sellers will drive the price TOWARD but not all the way TO their inflation estimate, while the buyers will drive the price TO and BEYOND their inflation estimate. Deflation is a separate issue. *If* the risk premium actually does become negative in that case — which I do not believe, but apparently some academics do — then that just means the market becomes risk-seeking when facing a certain loss. (That would mean preferring to flip a coin for a$0 or $10 loss rather than accepting a certain$4 loss, for instance. Well, maybe.) But even here, it has nothing to do with who is initiating the trade; it has to do with who is taking on the risk and how much they are being paid (or are paying) to do so.

• Nemo

what did you mean by this: â€œsince inflation swaps are derivatives, they are not subject to liquidity concerns?â€

I was thinking that the liquidity risk is symmetric. A swap is just a bet; at all times, there are an equal number of people on both sides of the bet. Any concerns about liquidity should affect both sides equally and therefore not influence the price. Put another way, there cannot be any “deep pockets” on one side of the trade without equally “deep pockets” on the other.

I mean, for example, an illiquid stock will trade at a discount to fair value just because it is illiquid. But the derivatives (options) on that stock will not trade at a discount to their fair value. They might trade with a wide bid/ask spread, but the prices themselves will not mysteriously overestimate or underestimate the stock’s implied volatility just because they are illiquid.

My intuition is that swaps are similar; liquidity concerns might result in a wide bid/ask spread, but it should not result in an overstatement or understatement of inflation expectations. However I admit I have not studied this very carefully, so I could be wrong.

• Nemo, you are losing me…

you agree that a buyer expecting 1% inflation can be willing to pay 1.05% because he’s risk averse. A seller can do the same thing in reverse – be willing to accept only .95% inflation even though he expects 1% inflation – because he’s risk averse. I traded Merger Arbitrage for a while. it’s probably a pretty good analogy here: when people are risk takers, spreads contract. When people are risk avoiders, spreads widen. But it’s impossible and incorrect to say that market prices always over or underestimate the true level of risk in the merger deals.

Basically, I disagree with your claim: “In short, the sellers will drive the price TOWARD but not all the way TO their inflation estimate, while the buyers will drive the price TO and BEYOND their inflation estimate.” ON the contrary – buyers may drive the price to and above their estimate, while sellers may drive the price to and below their estimate.

as for the second comment about derivatives – yes, a swap is a bet, and there are an equal number of people on both sides ONCE THE TRADE IS DONE (forgive the caps, I’m not savvy with HTML italics code), which is exactly what determines the price! If you’re trying to take the illiquid side of a trade, you are the one that has to sacrifice on price in order to get an equal number of people on the other side of your trade – which comes right back to my point about inflation swaps – sellers OR buyers could be the ones needing to be “equlibrated” by a counterparty.

I don’t want to get into semantic argument, but your claim:

“But the derivatives (options) on that stock will not trade at a discount to their fair value. They might trade with a wide bid/ask spread, but the prices themselves will not mysteriously overestimate or underestimate the stockâ€™s implied volatility just because they are illiquid.”

isn’t right. assuming mid-market is fair value, a wide bid ask spread means buyers pay more, and sellers receive less – again, this translates back to inflation swaps.

this all comes back to what “fair value” is – you and the professor seem to be saying that it’s always overstated by the market, which seems impossible. I know you tried to address this by saying “To say â€œfair valueâ€ is 1% is not the same as saying â€œthe market price is 1%,” but again, that’s kinda a circular argument.

Markets aren’t efficient, but they are efficient enough, which is why discussions about risk premiums can begin by assuming that markets correctly price expectations when risk aversion on either side is neutral.

finally. you wrote “I mean, for example, an illiquid stock will trade at a discount to fair value just because it is illiquid.” why? why do you say that? why won’t it trade at a premium to fair value if everyone loves it for some reason? it could easily be either, which is precisely my point. If buyers want the asset, the sellers collect a risk premium. If sellers want to unload the asset, buyers collect the premium –> Right back to inflation swaps…

• Nemo,

maybe it comes down to this: you wrote “it has to do with who is taking on the risk and how much they are being paid” – aren’t both sides of every trade taking a risk? i think that’s precisely my point – both sides are taking risk – who “pays” who depends on market sentiment. If I buy an SPX future that you sell to me, (or a stock, or an option, or a currency, or a house, or a bag of oranges that I intend to re-sell) I’m taking the risk that it might go down, and you’re taking the risk that it might go up. If I buy an inflation swap that you sell to me, I’m taking the risk that my estimate is too high, and you’re taking a risk that your estimate is too low.

• Nemo

you agree that a buyer expecting 1% inflation can be willing to pay 1.05% because heâ€™s risk averse. A seller can do the same thing in reverse â€“ be willing to accept only .95% inflation even though he expects 1% inflation â€“ because heâ€™s risk averse.

No, because the trade is not symmetric; the seller is always assuming the risk.

Let me try another example. Consider fire insurance. I assert: “The market price for fire insurance always overstates the market’s expectation for the loss of the house due to fire.” The relative supply and demand for insurance do not affect this assertion. Maybe you think insurance in your town is overpriced and decide to take “the other side of the trade”. But the difference between what you charge and what you expect to pay out will still be positive, always. While the person who buys insurance will be willing to pay more than his expectation for the event, always. That is because the seller of insurance is assuming the risk, and is therefore receiving the risk premium, and it is always positive. (Unless the insurer is being irrational and/or not being risk averse.)

You can never sell fire insurance for less than you expect your payout to be and still be risk averse.

An inflation swap is essentially insurance against inflation. As the seller, you are agreeing to compensate someone for the “fires” of inflation. And you will charge them a premium to do so, always. If you are risk averse, you must charge them more than you expect to pay them, by the definition of “risk averse”. And inflation swaps are the extreme example of this, because the fixed/known payment is truly fixed in real terms.

I have enjoyed this conversation, but unfortunately I am out of time. Some of us still have to work for a living :-). So if you reply again it may be a while before I reply. (I am serious about enjoying it, though. You have made some good points and caught some fuzzing thinking of my own. You don’t miss much. Very appreciated.)

• Nemo –
I am throwing in the towel for the night as well, but this will haunt my dreams 😉 and I hope to continue it tomorrow.

I think I just had an epiphany while watching Jonathan Paplebon fan the final Oriole to preserve a Sox win this evening: the examples you are using have a cap on one (or both) sides: the coin flip can’t be worth more than the $1, which is why it’s very very hard to find someone willing to pay 51c for it. Similarly the fire insurance writer can’t be liable for more than the home value, but more importantly, cannot receive more than the premium paid! Inflation’s distribution, on the other hand, is not constrained, which is why it’s different. The seller’s and buyers risks are indeed symmetrical! there’s a possibly irrelevant analogy to be made here to lotteries, or other games of chance with discreet outcomes with big positive tails (which might encourage risk TAKING, rather than risk AVERSION), but I’ll save that for another day. • jaguaracer About TIPS liquidity, I agree. TIPS are subject to supply and demand along with repo risk, etcs. Like the difference between a corporate CDS trade vs a corporate bond against gov’t bond trade. CDS trade is usually a purer bet on a name. Getting your hands on corporate bond to short isn’t easy. Same thing in TIPS. The huge glut of natural buyers gradually forces down real rates on TIPS so separating out that liquidity premium and the risk premium is difficult to separate. I’m a little confused about discussing inflation risk premium in linkers at all. Inflation risk premium is usually discussed in the context of nominal securities. Inflation risk premium is the risk in nominal bonds that, even though you expect 1% inflation, you demand a 50bp premium on top because, well, you’re giving money to the owners of a money-printing press. nominal yield = real yield + inflation + inflation risk premium. breakeven rate = linker less nominal breakeven rate = real yield – (real yield + inflation + inflation risk premium) = inflation + ***inflation risk premium**** So …. just subtracting tips less nominal ***still leaves that risk premium piece from nominal bond***. We have not extracted the real inflation expectation. I just went back to all the selected quotes (from original blog entry) and I gotta say, it makes a whole lot more sense. Nemo seems to be talking about it in the context of risk-neutral, risk-averse, etc context. A more abstract “risk premium” concept. • jaguaracer sorry last point. So measuring this inflation risk premium in nominal bonds is very important for central banks/treasuries (hence the research). It’s effectively a loss because (govt) bond buyers demand an extra premium on top of inflation expectation and real yield. If this inflation risk premium gets too high, it makes more sense to 1) issue more linkers, less nominal and 2) contain the fear in the market that you (central bank head) could let inflation run out of control. • midnitecowboy ” (Of course, any derivations based on market behavior during that time are suspect, since the whole system was melting down.) ” I would think that derivations based on market behaviour during that time would be applicable to markets in that particular mode. ” *If* the risk premium actually does become negative in that case â€” which I do not believe, but apparently some academics do â€” then that just means the market becomes risk-seeking when facing a certain loss. (That would mean preferring to flip a coin for a$0 or $10 loss rather than accepting a certain$4 loss, for instance. Well, maybe.) ”
I see you havent dealt much with clients

• Danny Black

Hi,

The idea that you will never pay someone to give you an option only works when the option is obvious. I can think of a number of cases in convertibles where the effective price of the embedded option was negative – usually for a regulatory or “madness of crowds”. The example that comes to my head immediately was an Israeli bond backed by the proceeds of housing built in Romania. It was an Israeli company building the houses the coupon was in ILS and it traded at a lower yield than the equivalent maturity Israeli government bonds – also paying out in ILS. Now there is an implicit credit protection option there, short the govvie and buy the corporate. Obviously you have manage the margin etc but modulo that and assuming you held to maturity – they were short-dated – you had a option that people were paying you to take. Retail and “sophisticated” investors regularly pay to sell an option, mainly because they don’t realise they are doing so.

I also am a little confused because you seem to be going back and forth between an academic model and real life. Arbitrage pricing says if my house is has a (risk neutral) uniform distribution between -0.1 and -0.5 over a year and the interest rate is zero ( duration and rate set to make the maths easy) then buying inflation protection on my 100,000USD home should cost me 30k. The spread you are talking about is surely a market making one – ie one of those real-life situations we normally assume away to make the maths easier. If we are talking real-life then risk aversion is most certainly not symmetric, we are most risk adverse when it comes to taking profits than we are to realising losses.

• Danny Black

Sorry 5:40am where i am, I meant short the corporate and buy the goverment bond…

• mcnai002

In my opinion the major reason Breakevens overstate inflation is not the risk premium but the LIQUIDITY PREMIUM. The best example of this is what happened at the end of ’08 begining of ’09 when TIPS traded insided Treasuries. This should never happen because the principal for TIPS are NOT adjusted down if CPI decreases like it adjusts up when CPI increases (In deflation they just become a defacto Treasury)… unless there is a liquidity premium – which became massive in ’08 – ’09.

• jamiebanurji

Sorry to revisit this after such a long time. I understand most of the arguments you’ve given for why the BEIs on zero coupon inflation swaps should overstate inflation, but why is it that looking at UK RPI zero coupon inflation swap rates (data from Reuters) and comparing them to observed inflation (12 months after the date the swap rate is given), the rates for the fixed leg (by this I mean the person paying the fixed nominal rate) are almost always lower than observed inflation?

For example, the monthly average 1y zero coupon swap rate (averaged from daily data) for July 2007 for UK RPI swaps is 3.19%. The floating leg corresponds to CPI inflation between May 2007 and May 2008 (there is a 2 month lag for the UK). Actual RPI inflation between May 2007 and May 2008 was 4.32%. If your comment about the bottom line is correct, this means that the market inflation expectation in July 2007 for May 07-May 08 was around 2.69% which was way off the realised rate. This is the case for most of the data I have between 2007 and 2013. Am I missing something here?