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Treasury Market Pricing

Published by Anonymous (not verified) on Tue, 21/06/2022 - 10:09pm in

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bond market


The Fed surprise 75 basis point hike last week blew Treasury yields out, with a small reversal at the end of the week. Such a reversal is typical after large moves. In this article, I just want to discuss the big picture of Treasury pricing.

The figure above shows the post-2000 history of the 2-year Treasury yield. What we see is that the rise in yields in 2020 has been extremely violent when compared to previous behaviour. This fits in with market commentary pointing out that Treasuries have seen the worst short-term drawdown in decades.


The figure above shows the history of the 10-year yield over the same period. In this case, we can see that the recent move is still large, but its past history shows more volatility.

Risk-free rates are literally the simplest instrument to price in finance, and so the rates market ends up being closer to the theoretical ideal of “efficient markets”: rapidly changing price as new information comes in. If we eyeball the 10-year yield, we see that there are periods of range-trading that end with rapid movements to new levels. This behaviour is the worst possible behaviour for technical analysis, since mean-reversion trades are punished during the violent moves, and trend-following is punished when range-trading. This is somewhat different to commodity, equity, and foreign exchange markets — since “fair value” is somewhat nebulous, we quite often run into trending behaviour.

If we go back to the 2-year yield, it does appear to follow trends, with the recent experience being an outlier. This was the result of “gradualist” interest rate policies. The Fed used to be in one of three modes: on hold, hiking by 25 basis points per meeting, or cutting rates in a panic. As such, most of the time, market pricing for the Fed tended to be correct — it was only transition between “modes” that changed pricing dramatically. As such, most profits/and losses versus forwards were concentrated in short period when the mode being priced shifted.

The current rise in the 2-year rate was more rapid since the market pricing was wrong-footed from two directions: the terminal rate was rapidly revised higher, and the pace of race hikes is double (or triple!) that of recent cycles.

In other markets, the tendency to get increasingly bearish as prices fall can be rewarded at times. Should we extrapolate past losses forward? The issue here is that we need to keep in mind the simplicity of rates pricing. To keep moving the 2-year, we need to keep pushing up the Fed’s terminal rate. Is this plausible?

Recession Calls Everywhere

I do not follow street research, but I am seeing a drumbeat of recession calls on economics/finance Twitter. I certainly have sympathies for a recession call — but I remain cautious about the United States/Canada (as opposed to other countries with worse energy supply outlooks). Recession risks are the main obstacle for bond bearish positions: it is hard to see the Fed hiking to 4-5% if the global economy implodes in the next couple of quarters.

The 2-/10-year slope snapped back on Friday, but it is flirting with inversion. Although economists love to discuss the 2-/10-year slope as the result of the bond market pricing recession odds, it is the spread between two pricing benchmarks. Bond investors get paid based on trading profitably, not whether recessions are declared.

The current situation is a bit hard to interpret. The reason for a near-run inversion is that the 2-year is pricing another slug of rate hikes. If we are to take pricing at face value, all that is expected to happen is that there would be a small reversal of rate hikes in a couple of years.

Such an outcome is not impossible, but I believe it is only consistent with a “soft landing” scenario: the Fed hikes rates to around 3%, inflation is tamed, and there is no recession over the next year. Otherwise, one benchmark or the other is wrong: the Fed keeps hiking rates to contain inflation, or we have a hard landing and they are forced to cut. The bond bears are attracted to shorting the 2-year, and the 10-year is attracting the bulls.

One theoretical wrinkle on the “yield curve predicts recessions” debate is a scenario of a very rapid meltdown in activity. If it happened soon enough, it could take out a lot of the priced rate hikes — steepening the curve ahead of a significant inversion. I am not convinced that this will happen, but it is clear that it could happen.

War and Commodities?

The situation on the ground suggests that there will not be a rapid end to hostilities, as the Ukrainians have indicated multiple times that they intend to counter-attack on a greater scope towards the end of the year. Until the fate of that counter-offensive is known, there will be no serious peace talks.

Even once fighting reaches a lull, it would take time to formulate a peace deal — assuming that both sides are interested in a deal (which could easily not be the case). As such, the commodities markets will be disrupted for some time.

We should see greater rail transport of Ukrainian wheat going forward, but that will take time to organise. Russian oil appears to be making its way to market via third countries. As such, it is possible that the oil situation has entered into a new steady state. Natural gas piped into Western Europe seems to be the main uncertainty in the near run. Over the longer term, if Russian supply is shut it, their long-term production capacity needs to be revised lower.

As such, it is hard to see too much relief for global energy prices in the absence of more meaningful demand disruptions. 

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(c) Brian Romanchuk 2022

Where Are Supply/Demand Curves?

Published by Anonymous (not verified) on Sat, 09/04/2022 - 12:22am in

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bond market

The reduction of the Fed’s balance sheet is coming, and so we are likely to be involved in debates about how much this will affect bond yields. I am in the camp that the quantities involved do not really matter (which some qualifications). I just want to explain my logic, which involves discussions about “supply and demand” curves for bonds, which vary based on time frame. Although this discussion might appear obvious, my feeling is that there are some hidden assumptions that people make about market price determination.

Disclaimers

Since this was a popular area of debate during the QE era, I will just note three areas where central bank buying/selling of bonds will move prices.

  1. Central bank buying/selling is a signal about future rate cuts/hikes. E.g., if the central bank is ramping up bond buying with the policy rate at 0%, it is a signal that they are not thinking about rate hikes any time soon, which should lower forwards. Although this effect exists, there is no reason to expect a stable sensitivity between quantities and yield movements — they can signal just with words, and no bond transactions.

  2. During the Financial Crisis, every major bond investor was at or over credit balance sheet limits. Central bank buying of toxic assets helped reduce those balance sheet strains, and thus would presumably have a major effect on spreads. However, if we do not have such strained conditions, fundamentals (e.g., fair value of a spread equals the default premium plus a liquidity premium) can re-assert themselves.

  3. We can expect a short-term effect and/or a squeeze in a market segment, as will be discussed in this article.

Instantaneous Supply/Demand Curves

If we look at a frozen instant of time, we can get well-defined supply demand curves — at least if we assumed the bond market followed a simplified screen-based trading structure.

Under this simplification, if we take a particular instrument, we have a list of firm bid/offers ordered by price. We will assume the “lot size” is $10 million, and each bid/offer is a whole number of lots. We can then break up each order into individual lots, and so we can label them bid 1, bid 2, … bid n, offer 1, offer 2, offer m. Note that each order book is instrument specific (although if there are spread markets, we then have order books on pairs of instruments).

Let us say that a “price insensitive” seller just dumps $100 million of a bond — their limit sales price is $0. The order will be matched against the first 10 bids (bid 1 - bid 10), leaving bid #11 as the new best bid.

What happens to the “market price” of that particular bond?

  • The best offer price is unchanged — remains at offer #1.

  • The bid price changes from bid #1 to bid #11, and so the new best bid is less than or equal to the original best bid.

The thing to note is that the fact that the seller had a selling price of $0, the market price is still determined by the remaining market participants — the seller just took out the most aggressive bidders. As such, it does not make sense to think of the seller as the “marginal” market participant.

We can look at the order book and map out a well-defined supply/demand curve: based on what your price limit is, you can see how many bond lots you can buy/sell. This is the only point at which we can define a “sensible” supply-demand curve.

Aside: Hydraulic Theory of Prices

This leads into one topic that I see that underlines a lot of popular commentary around markets: prices only change because of buy/sell orders. (One of my old bosses called this theory something like “The Hydraulic Theory of Prices,” but I have never seen the phrase used elsewhere.)

The reason why we have well-defined “supply curve” is that we “froze” the order book to be in its state before the order arrived. In the days before high frequency trading, order books were relatively static, and so it “feels” like how markets work. But this ignores what happens around information releases.

When “market-moving” news arrives, the immediately reaction of everyone is to move their bids/offers in response. In markets with market makers, moving the bid/offer is very easy to do. For markets with an order book, you either need fast algorithms, or you stop trading when the news arrives. (Equity trading has rules about news releases and trading for this reason.) The bids/offers move without any transactions. This flexibility of prices is what allows expectations-based pricing models to work.

Short-Term Supply and Demand

For reasons that I will discuss in the appendix, even if we have order book-based trading, investors generally do not dump all their orders into the queue at the start of trading and call it a day. Instead, they probably have decided upon some strategy (either formal or informal), and will enter orders during the day based on market action and news.

If everyone was a value investor, we could argue that these are “implicit orders” and we could then trace out some “implied order book” with an associated supply-demand curves.

The problem is that investors are not all value investors. The most extreme counter-example would be trend followers that sell if prices fall, and buy if prices rise. In fixed income, the dreaded convexity hedgers in USD markets act this way — which helps turbo-charge moves. In such an environment, the path of prices matters, and so it is hard to define a supply/demand curve like we can for a frozen in time order book.

This “implicit order book” is deeper than what would be seen on a screen at any time, and so it may be hard to gauge the sustainable volume of daily transactions based solely upon a single order book snapshot. Nevertheless, the amount of risk that might be taken in a single day is still small relative to the total risk budget of investors, as discussed next.

Longer Term

Investment firms have risk limits for traders and portfolio managers — and if they do not, they tend to turn into ex-investment firms. If the market is smacked by a wave of large orders, there are limits to how far investors would react.

Those limitations on risk taking can be viewed as tactical — but the tactical risk limits may bear no resemblance to strategic risk limits.

  • It is fairly typical to sub-divide fixed income management to sub-teams by product. If a product class gets cheap, the fixed income portfolio can re-allocate its global risk budget to buy that product.

  • Fixed income issuers will adjust the maturities of their borrowings based on pricing. The standard mandate for treasurers is to “minimise the cost of funding over time” — which implies issuance based on rich/cheap analysis versus their expectations for the short rate (along with spread differentials).

  • Asset allocation risk budgets typically dwarf the risk budgets given to the asset class portfolio managers. For example, the bond allocation of a pension fund might be tightly constrained to follow its index/custom duration benchmark, and so bond managers cannot greatly change the DV01 of its portfolio versus benchmark. Conversely, the asset mix team can often move 10% of the portfolio into/out of fixed income.

Since these strategic shifts are necessarily slow, trend-following is not a great strategy. Instead, the considerations would be value, and so the “implicit strategic order book” would resemble that of the instantaneous order book — more buying as prices fall, selling as prices rise.

Since “bonds” compete with “cash” as an asset class, bonds need to be attractive versus the expected returns on cash. (Guess what the rate expectations theory says?)

As a final note, once we take into account this market structure, we can see that “event analysis” is a complete waste of time, and exists solely as a means for academics and central bankers to produce articles that fit their priors.

Central Bank And The Strategic Order Book

If the central bank seeks to influence bond prices with quantities of purchases, they need to overwhelm the strategic order book of all market participants. (If the central bank has a price target — like a yield cap in “yield curve control” — market participants have a price to take into account. They can then trade the targeted bonds like any other instrument that is pegged by the central bank — is the commitment to the peg credible?)

If the duration of the total fixed income market is small enough — or the central bank targets a small segment of the market, like linkers or ultra-longs — they can blow through the implicit order book and plant prices where they want. The usual question is whether the Fed purchases were large enough to do that? I don’t claim to have an answer, but my bias is that they did not. Although they previously took out the most aggressive bids, if the dispersion of views was not that great, the remaining bids may not have been much different than the aggressive ones.

Concluding Remarks

If the Fed decided to dump its holdings all at once, bond prices would collapse. That is not going to happen, and so it is much less clear what the effect of sales will be (other than the admittedly significant signalling effect).

Appendix: A Fossil’s Views on Fixed Income Market Structure

The first thing to note is that I was an analyst, not a trader, and I left finance in 2013. Although I interacted with traders, I was expected to doing important things like produce power points instead of looking over trader’s shoulders to see how they spent their day.

Even in 2013, the Canadian market was dominated by telephone trading, not screen trading. Screen trading was more advanced in the United States, and it is possible that inroads would come into the less liquid market.

I would describe telephone trading as follows. There is a screen based inter-dealer market — where “real money” investors could see pricing, but not trade. These prices are the “market prices” that are used as reference — but these are not all the transactions.

Sell side traders produced pricing runs with indicative prices that salespeople would send to buy side traders (like the ones at my ex-employer). The “indicative” qualifier is important — during a crisis, the sell side traders develop some amazing gastro-intestinal problems and are in the bathroom all day, unable to give firm prices.

Salespeople act as intermediaries between the two traders, since the negotiations are a zero sum game, and can get somewhat heated. (The usual description is that the difference between the buy and sell side is that the buy side yells “F%$# you a$$^*##!” and slams the phone down, while the sell side slams the phone down and then yells “F%$# you a$$^*##!”) (I only heard the hostilities second hand. I was only brought into these calls very rarely when there was some arcane disputes over pricing, and everyone acted polite when sensitive little analysts were in the room.)

Such trading was preferable done when the screen-based trading was quiet — since both sides used those prices as a reference. However, depending on the negotiations, the pricing on the telephone trade can be off the “market” price. Furthermore, only the two counterparties know about the transaction details — unlike public order books. The only way to know about the big transactions is via rumours.

Since I was not a trader, I am not the one to discuss trading techniques. However, it is safe to say that for anything other than a small (by fixed income trading standards) transaction, one needs a certain amount of ambiguity about intentions. The exact deal is only finalised after a period of negotiations. This is different than an (idealised) order book, where investors post binding orders with fixed sizes and prices.

For large transactions in the Canadian market (e.g., implementing an asset mix shift), the negotiations are a multi-day affair. Even though a large real money manager could transact quickly, the dealer counter-party needs to adjust their books to handle a huge slug of risk. For example, they need to source bonds to put into inventory to sell to the investor. If properly done, both sides have an incentive to keep the transaction quiet — they do not want the street front-running the transaction. Although the dealer looks like it has a huge informational advantage, if they move prices too much, the counter-party can walk away — and the dealer is stuck with the “wrong” position.

Old school transparent screen-based systems are not useful for less liquid markets where the on screen depth is not enough to absorb such large transactions. (The wider dispersion of investors in the U.S. dollar markets always allowed more screen-based trading.) Entering a buy/sell order (that will not be immediately filled) is the same thing as selling an out-of-the-money put/call option with an expiry of “how soon can I cancel the order?” for a premium of $0.

I am not an options trading guru, but I think it is safe to say that you do not want to sell options for $0. From this perspective, the rise of high frequency trading/”algos” was a way to recreate the cloud of uncertainty of intentions that telephone trading had. The order books jump around, and so nothing is truly firm. Furthermore, from a management perspective, you replaced the reliance on the fuzzily-defined notion of a trader’s “trading competence” with an allegedly measurable algorithm profitability. It is also a lot easier to hire programmers than experienced traders.

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(c) Brian Romanchuk 2022

Fed Flattens The Curve

Published by Anonymous (not verified) on Fri, 25/03/2022 - 2:39am in


I have been taking it easy for the past week, courtesy of dealing with a mild COVID-19 case. (It largely felt like a cold. However, some symptoms persist, and so I prefer to rest and let them clear.) During my down time, the Treasury market (along with other govvie markets) have been crushed. Fed policymakers have signalled that they want to ramp up the pace of hikes — which surprised me.

In my view, the only reason to hike 50 basis points in a meeting is if you expect that will be followed up 50 basis point hikes. I cannot guarantee that Fed policymakers agree with that assessment, but I would guess that they are lot closer to that position than they were to the idea of a one-off 50 basis point hike that was being floated. One possibility is that the Fed might alternate 50 and 25 basis point hikes. The inelegance of such a pattern suggests that they should take 12.5 basis point increments out of their monetary policy arsenal, so they can go 37.5 basis points per meeting.

If one wants to be a bond bear, I believe that the current setup has the most potential for reversing the trend in yields. I am skeptical about the effectiveness of rate hikes for slowing the economy, which implies that the faster the Fed hikes, the higher rates will end up. This is very different from the conventional belief that something will break within the economy solely because interest rates are “too high.” If we keep getting shocks raising consumer prices — very easy to see in war-strained supply chains — the length of time the Fed will be hiking will be long enough to allow a decent rise in rates. (Maybe I am complacent, Volcker-esque levels of rates do not seem to be in the cards.) My story is that the secular fall in interest rates is not telling us about r* (or whatever), rather the pace of rate cuts was very fast, while rate hikes were done slowly. As such, they never could return to previous levels across each cycle, and so the trend was down.

The main potential spanner in the works for this bond bear story is a recession/inflation roll over that hits within the next year or so. I am not pretending to be a forecaster, but it is not hard to come up with such scenarios. (Inflation rolling over might raise eyebrows, but my feeling is that Russian energy will eventually make its way into global markets. The current spike will result in some demand destruction. Grain prices will be high, but the price effects on highly processed Western diets is buffered.)

Curve Shape

Rapid rate hikes mechanically flatten the curve. In a situation where rate hikes are being front-loaded, the resulting curve is quite flat. Yield movements then tend to be largely parallel moves. It is possible that an erratic Fed could raise term premia and inject some steepening, but that seems to be a scenario that is just wishful thinking by bears.

If we look at the late 1990s, the 2-/5-year curve was trading around 25 basis points or less for almost a half decade. (The inversion around 1998 was courtesy of the Asian Crisis.) We could imagine the curve reverting to similar behaviour going forward, even without immediate risk of recession.

War Uncertainty Peaking

My reading of the situation of the Ukraine war is that the combatants will not be able to sustain the fighting at current levels indefinitely, and we should see a pause of some sort within a month or so. Fighting may resume later, but the status will be somewhat more clear than is the case right now.

As such, I do not think that it will be enough to cause the Fed to stop rate hikes, unless the erratic Russian regime does something to escalate the situation elsewhere.
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(c) Brian Romanchuk 2022

Incoming Fed Rate Hikes

Published by Anonymous (not verified) on Thu, 17/02/2022 - 4:21am in


Inflation data in the United States came in surprisingly hot, and so rate hike chatter went off the charts. I think the idea of a “surprise” inter-meeting rate hike is silly in the context of modern Federal Reserve operating procedures, but I now see more chance of an initial 50 basis point rate hike in March as an attempt to assert dominance.

Unless inflation cools a lot, the base case has to be that we are looking at 25 basis points per meeting (plus the wild card of a starting 50) for forecast horizons going out a year. The pricing I have seen is consistent with this, so this should not be a surprise to anyone. After the one year horizon, far more uncertainty creeps into inflation/growth forecasts.

Since I do not think anything of interest happened, I will mainly repeat points that are not commonly appreciated.

  • What matters most for the rate hike cycle is the terminal rate pricing. Fed members can raise their estimates for long-term policy rates in the “dot plot” in an attempt to influence market pricing, but there is no particular reason for anyone to have much confidence in the Fed’s ability to forecast where they will decide to put rates years in the future. Unless they specifically target term yields, the Fed just reacts to historical data and sets the policy rate.

  • They can muck around with Treasury buying/selling (“Quantitative Tightening”). There is considerable uncertainty about the exact effects of Federal Reserve balance sheet expansion, so I expect caution in reversing it. I am skeptical about its effects, explained in more depth below. However, it is impressive that the army of Ph.D.’s at the Fed managed to develop a policy tool that is effectively slower to react to the cycle than fiscal policy.

  • The flattening of the curve (chart above) is coinciding with the inevitable “bond market is predicting recession!” stories. My view is that we have a market segmentation issue: bears are throwing all their risk at the front, bulls are buying long tenors, and relative value players are not going to jump in front of a steamroller to pick up nickels. Forwards are converging to the discounted terminal rate, and that terminate rate will move up and down as data hit.

Blow Up the Treasury Market?

We have seen some yappy comments from some of the more outspoken Fed hawks. Roughly speaking, they are mad that the discounted terminal rate is too low. However, the only way to do that is either by raising rate expectations, or the term premium (by definition of those terms). The ability of one Fed speaker to get market participants to change their rate forecasts is debatable. So, do crazy things to destabilise the Treasury market to raise the term premium?

Although that is a strategy, it is a rather bizarre one. Over the past couple of decades, I have been reading self-congratulatory missives by neoliberal economists regarding the reforms they made to lower term premiums. Now, some hawks want to raise them? Well, that’s the kind of consistency you expect from a highly mathematical science.

The problem with discussion of term premia and things like Fed balance sheet policy is that economists use toys models that just pick some economic variables at random. Given the number of crypto-Monetarists in the profession, they look at the Fed balance sheet (“money!”) and ignore literally everything else in the bond market.

The reality is that a Treasury bond is just a source of default risk free duration (DV01 might be a better term, but whatever). Although there are some managers that might be confined to only holding Treasury securities, asset allocators rarely have such restrictions. (The exceptions are entities like trusts, and smaller central banks.) If Treasurys get too expensive versus spread product (including mortgage-backed securities, which are more of a vol risk than a credit risk), they just move their assets to those asset classes to get their DV01 there. The stock of USD duration is large, and we have to keep in mind that issuers can change the duration of issuance.

In other words, a rapid change in Fed policy could move the curve a lot in the short run, but that just will result in asset mix and issuance shifts if the curve appears stupidly priced.

Postscript: Canada Crisis Update

The safest observation I can make is that everything you might read in the American media about the convoy protests is incorrect.

  • The Emergency Act is part of a legislative overhaul of The War Measures Act that was last invoked by Trudeau Senior in the 1970s in response to separatist violence in the 1970s. The overhaul was done by the Progressive Conservative Party (yeah, the name is funny, it was that for a reason), and explicitly is subordinated to The Charter of Rights and Freedoms that were brought in by Trudeau senior in the early 1980s. (From what I recall, conservatives viewed the Charter as a liberal-commie plot at the time.) The Emergency Act had not been invoked, but the act that might be considered “martial law” was invoked by the Progressive Conservative government (at the request of Quebec) during the Oka Crisis of 1990. That crisis was a border dispute between the Mohawks and Canadian governments, with roots in treaties pre-dating Confederation. In other words, what is happening is a constitutional nothingburger that bleeding heart “conservatives” are crying about.

  • The existence of “money laundering” tells us that governments have always frozen banking assets of criminal organisations. The only thing different is that it is easier to do it more quickly (and puts more burden on the banks to enforce).

  • At the time of writing, other protests are winding down, and the authorities are signalling a roll up of the Ottawa protest. The question remains whether the “nonviolent” protest (if we ignore the intimidation, criminal charges, weapons charges, and charges of a conspiracy to commit murder) gets ugly.

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(c) Brian Romanchuk 2022

Central Bank Confusion

Published by Anonymous (not verified) on Fri, 28/01/2022 - 3:04am in

The Fed and Bank of Canada announced that they were on hold yesterday, but signalled that rate hikes are likely hitting in March. From what I have seen of chatter on Twitter and various editorial pieces, this has caused some confusion. (I am not sure what street research is saying.) This article is a grab bag discussing what I saw as common (or at least popular) points of confusion, as well as some of my editorial comments.

Editorial: Yeah, That Stochastic Calculus Really Helps

Most people are quite reasonably not concerned about economic theory disputes most of the time. But one needs to keep them in mind when keeping up with the latest events.

Whenever you are reading commentaries about central banking outlooks, you need to ask yourself: are the people in the discussions using any of the mathematical models that the literally thousands of neoclassical doctorates employed by the central banks produced? If not, what exactly was the point of them? Why is it so important that MMT have lots of mathematical models of the economy (keeping in mind that critics ignore the ones that exist) when nobody even refers to the ones that are supposed to be relevant?

Admittedly, one might not expect equity or credit analysts (or gold bugs) to keep up with DSGE modelling, but rates analysts — the primary target for rates discussions, allegedly — almost all have science/mathematical doctorates from fancy universities. If the models worked, the technical audience to use them is there. However, the only people interested in those models are those whose credentials are tied to the production of said models, which is not encouraging.

(Probably) No Need For 50 Basis Point Hikes

I do not have access to a plot of the instantaneous forward rate, but the figure above is my best bet what the shape looks like for forwards up to ten years or so. (The instantaneous forward rate is the implied path of the overnight rate from a fitted discount or zero curve.) After the ten year point, you are fitting less liquid bonds, and there are various technical effects that impact the shape of the curve. For example, you typically see a hump in the curve due to the value of convexity, which implies an inversion of some forwards. See my earlier article on the long end inversion for more details. Bonds with maturities under ten years do not have a lot of convexity, so the hump is pushed out beyond that point.

As an aside, different sources will legitimately have different instantaneous forward curves. The instantaneous forward curve is determined by taking the derivative of the discount curve, and so different choices for parameterising the zero/discount curve will result in quite different forward curves. To price an instrument with a duration longer than overnight, you take the geometric mean of the instantaneous forwards over the life of the instrument. This “integrating out” of the forward curve will mean that different fits will end up with roughly the same fair value prices of traded instruments.

The figure shows the actual instantaneous curve, along with straight line approximation. I divided the straight line approximation into three regions, labelled A to C.

  • Region A is the “on hold” period. The forwards are relatively flat, possibly with a small term premium effect.

  • Region B is the “hiking period” which features the most rapid change in the forward rate per unit of forward time. In the modern era, it’s a good bet that the “slope” of that line will be a multiple of 25 basis points / (k × six weeks), with k in the set 1, 2, …. The six weeks is the number of central bank policy meetings per year, so that is 25 basis points every k meetings.

  • Region C is the “terminal rate” period where the forward rises at a very slow pace. One possible interpretation is that the observed forward is the “terminal rate” plus a term premium.

We can then write a the fair value yield of a bond as follows:

yield = f(length of on hold period, slope of hiking period, terminal rate, term premium).

Since the term premium is just going to generate arguments, we can replace the “terminal rate” with the “adjusted terminal rate,” where the adjustment is to add the average term premium.

We can then ask: what matters for bond yields? Well, if the hiking period is two years, eight years of a 10-year bond’s lifetime has the instantaneous forward rate equalling the “term premium adjusted” terminal rate. That is 80% of the observed yield is explained by the terminal rate. The rate of initial hiking does not matter too much, all that matters is that it reaches the terminal rate relatively quickly.


At 25 bps/meeting, the policy rate is rising at 200 basis points per year. That puts us at 4% in two years, which seems be hawkish enough when compared to past history (figure above). The only conceivable reason to go to 50 bps/meeting is that the policy rate needs to be 6% or so very quickly — which seems to be a bit of a stretch.

As was pointed out by Ben Bernanke (possibly the “Gradualism” speech), the Fed Funds rate (or any overnight risk free rate) is only of limited importance for the real economy. Non-financial entities borrow and invest quite often at term rates, and if rates are rising, they will be cautious about borrowing overnight.

The real battle between bond bulls and bears is where to plant the terminal rate. At current pricing, 25 bps/meeting is enough to vaporise the bulls.

Why Not One And Done?

The idea of doing one big hike and getting it over with recurs over time. Two cycles ago, Stephen Roach floated the idea in a op ed, which was answered by the Bernanke “gradualism” speech. (Although not a Bernanke fan, I think that speech was a very good explanation of conventional central bank thinking. It also referred to “bang-bang control,” which I ran into during my doctoral student days.)

The argument against it is very straightforward. Let us assume that we follow conventional beliefs about interest rates (higher policy rates act to suppress growth and/or inflation). But if we are faced with uncertainty, the safest course of action is to move the policy rate gradually, and then change direction/go on hold when the trend in the economy is changing. “Doing it all at once” relies on a belief that we know what the terminal rate is. The current set up frees central bankers from having to forecast the terminal rate: that’s the job of rates market participants. The central bank just ratifies spot overnight pricing.

Since the effect of interest rates is determined by levels along the whole curve, a higher implied terminal rate still has an immediate effect.

“The” Interest Rate Dial Does Not Exist

I ran into some comments by someone attempting to make a big deal about the flattening that occurs during a tightening cycle. The idea is that since other rates (allegedly) matter more than the overnight rate, then the market is counter-acting the policy rate rise.

I would argue that this is a symptom of using Economics 101 models with one “interest rate.” Any modern models tell us that the yield curve is a continuum, and the only way to make sense of pricing is that yields are primarily determined by expectations.

  • The curve does not move in parallel with the overnight rate. You cannot expect X basis points in hikes to translate into an X basis point rise in yields/rates across the maturity spectrum. If you are attempting to measure the effect of interest rates on the economy (good luck), you probably need to somehow capture the levels across the curve, and not use the policy rate as a proxy.

  • Since markets are forward looking, the timing of trend changes in yields will not match the timing of changes in administered rates. Given that markets with levered players invariably overshoot in both directions, it is completely unsurprising that bond bear markets happen before the first hike, and rally once it hits. You need to look at the yield levels, and the current 10-year yield is higher than it was during most of 2021 (figure above); hence the “interest rate tightening” has started already.

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(c) Brian Romanchuk 2022