The Macro Cycle
A release moves price by the part of it nobody knew, and most of a headline number is not that part. Eleven of the twelve months inside an annual inflation rate were published before the release, so the arriving month can shift the headline across about a tenth of the range the headline itself covers, and the change in the headline is one new month minus one month printed a year earlier. On the sixty months below the annual rate falls 3.37 points across half a year, four fifths of that fall is carried by the months leaving the window rather than the ones arriving, and in the first row of the table prices do not move at all while the rate drops 0.38 points. The part that is genuinely new is quoted, and can be read out of a price rather than guessed: a contract at 95.615, with thirteen of the month’s thirty-one days falling after the decision, is quoting a 52.5 per cent chance of a move, where the same subtraction done without the day count gives 22 per cent — wrong by a factor of 2.38, every time. What is left over is the hard part, and it turns on one inequality: the same figure lifts the index in one year and sinks it in the next, depending on whether the policy response to a unit of growth news is more or less than one for one.
Prerequisites: Lesson 43, which established that a dated event already carries a quoted price, lesson 45, whose sign identity is why one figure moves one market both ways, and lesson 39, which priced what a filter has to clear before running it beats not running it.
Eleven twelfths of the number are already public
An annual inflation rate is not a measurement of the last twelve months. It is twelve monthly measurements multiplied together, and eleven of them were published before the twelfth arrived. That single structural fact decides most of what the release can do, and almost nothing written about inflation prints acknowledges it.
Turn this module’s sixty closes into a monthly price series by a published rule, so the arithmetic can be checked rather than believed: the monthly change in per cent is the close minus 100, divided by ten. That gives sixty monthly prints running from -0.18 to +0.71 per cent, averaging 0.30, which compounds to 3.65 per cent a year, and from them fall forty-nine annual rates running from -0.68 to +8.07. One monthly print spans 0.89 points across the whole construction; the annual rate spans 8.75. So the number nobody has seen yet can move the headline across roughly a tenth of the range the headline covers, and the other nine tenths were settled a month ago.
The change is sharper still. Write the annual rate as the product of the twelve months in its window and take logarithms, and each step forward adds one month at the front and drops one at the back. The change in the annual rate is the arriving month minus the month twelve back, exactly rather than approximately: across all forty-eight steps in this series the two sides agree to fifteen decimal places, because it is an identity and not a model. In percentage points instead of logarithms it holds to within two hundredths of a point across the stretch below.
Here are eight consecutive months through the sharpest disinflation the series contains.
| Month | The month arriving | The month leaving | Annual rate | Change in points |
|---|---|---|---|---|
| 22 | +0.00% | +0.37% | +3.31% | -0.38 |
| 23 | -0.09% | +0.67% | +2.53% | -0.78 |
| 24 | -0.18% | +0.46% | +1.87% | -0.65 |
| 25 | -0.09% | +0.30% | +1.48% | -0.40 |
| 26 | -0.05% | +0.57% | +0.85% | -0.63 |
| 27 | -0.12% | +0.22% | +0.51% | -0.34 |
| 28 | -0.08% | +0.49% | -0.06% | -0.57 |
| 29 | -0.04% | +0.08% | -0.18% | -0.12 |
Start with the first row, which is the cleanest demonstration on the page. In month 22 prices do not move at all: the arriving month is 0.00 per cent. The annual rate falls 0.38 points anyway, because the month leaving the window was +0.37. Nothing happened to prices, and the inflation rate fell by a third of a point.
Then read the second column against the third down the rest of the table. The annual rate falls from +3.31 per cent at month 22 to -0.06 at month 28, which is 3.37 points, and every arriving month across those six steps is negative, so the arriving months look like the whole story. They are not. Across the six steps the arriving months sum to -0.61 and the departing months sum to +2.71. Four fifths of the collapse in the headline was settled a year before any of it was printed.
The last row is the control. Month 29 arrives at -0.04, barely different from the -0.08 before it, and the annual rate moves 0.12 points instead of 0.57 — because the month leaving is +0.08 rather than +0.49. Nothing about the incoming data changed between those two rows. The window did.
Which produces the result that reads as a paradox and is not one. Over the forty-eight steps the annual rate falls sixteen times, and in five of those sixteen the arriving month is positive: prices went up and the inflation rate went down. That is roughly a third of every fall in the headline, and each one will be reported as disinflation. The split also holds statistically rather than only in the example: the month leaving accounts for 38 per cent of the combined variance of the two terms, and the two are near enough uncorrelated to leave the split clean. If the monthly prints were independent and identically distributed it would be exactly half, and the only reason it is not is that this particular run is not stationary.
None of which requires forecasting anything. The month about to leave the window is already on the record, so the mechanical part of the next twelve headline changes can be written down today by anybody holding the last twelve prints.
An aggregate carries less news than its parts
The same subtraction runs through every aggregate assembled out of pieces already released, and there it is even easier to price. Suppose a quarterly figure is the average of three monthly ones and two of the three have been published. The entire surprise in the quarterly figure is the third month’s surprise divided by three, so its standard deviation is exactly a third of a monthly surprise’s. Three of four parts public leaves a quarter. One of three leaves two thirds. The rule is the fraction still outstanding, and it is not an estimate.
This is why the same reader can be moved by a monthly retail sales print and unmoved by the quarterly national accounts containing it. The advance estimate of a quarter’s output is assembled from monthly source data the statistical agency has already published — retail sales, the trade balance, construction spending, inventories — with estimates standing in for whatever has not arrived. The aggregate is not a new measurement. It is arithmetic on measurements you have seen, plus the gaps, and the gaps are the only part that can surprise anyone.
The same ordering holds between price indices. One agency’s monthly consumer and producer price indices are published roughly two weeks before another agency’s consumption deflator, and the second is built substantially out of the detail of the first two. Forecasters who map the components across get very close before the release, which is why the later print rarely moves much and the earlier one regularly does. Nothing about the second series is less important. It arrives second.
The releases that genuinely carry information are the ones built from a fresh measurement rather than an assembly. A survey of purchasing managers is a fresh measurement. A payroll survey of establishments is a fresh measurement. A weekly count of unemployment claims is a fresh measurement, small and noisy and immediate. So the question to ask of anything on the calendar is not how important the number is. It is whether its inputs were already on the wire.
The headline series is one of three
The clearest case of a published number being read as though it were the whole record is also the easiest to fix, and the fix takes two lines. A central bank’s balance sheet is published weekly and quoted as the measure of how much money is in the system. It is one term of three. Cash sitting in the government’s account at the central bank is not in the market; cash lent back to the central bank overnight is not in the market either. The quantity that reaches assets is the balance sheet minus those two, and all three series are public.
Run it on the two years that broke the rule everyone had learned. Across 2023 and 2024 the balance sheet fell by somewhere between 1.3 and 1.6 trillion dollars, which is the figure the headlines carried and the reason a great deal of commentary expected a bear market. Over the same stretch the overnight reverse repo balance drained by between 2.0 and 2.4 trillion. That term is subtracted, so a fall in it adds.
Take the corners of both ranges: -1.6 against -2.0 gives +0.4, and -1.3 against -2.4 gives +1.1. Every combination inside the two ranges is positive. The third term oscillated in the hundreds of billions around debt-ceiling episodes rather than trending, and at its least helpful takes the answer to roughly flat. The headline said a trillion and a half drained out of the system; the identity, on the same three public series, says something between four hundred billion and a little over a trillion went in. That is not a refinement of the headline but the opposite sign, and no precision was needed to reach it, because the conclusion survives the whole range.
The general condition is one line: the net figure disagrees in sign with the headline whenever the two subtracted terms move further than the headline does, in the same direction. Here the offsetting term moved between a quarter and five sixths again as far. And the forward-looking part is what most accounts of those two years leave out. The reverse repo balance fell from over two trillion to near nothing, and a balance already near zero cannot drain again. The cushion that absorbed two years of runoff was a stock being spent rather than a mechanism that renews. Nothing about the arithmetic changed; one of its terms ran out, which is something you can watch on the same three series.
A consensus is a survey; the expectation is a price
A release cannot move price by its level, because the level was expected. It moves by the difference between what arrived and what was expected, which puts the whole weight of the question on the word expected. There are two candidates and they are not the same object. The published consensus is a survey of forecasters, collected before the release and printed beside it: free, useful, and not the market’s expectation, because it is the average opinion of people under no obligation to trade on it. The market’s expectation lives in a price, wherever some instrument settles on the number in question. Where the two disagree, the price is the one the release will be measured against, because it is the one people have money on.
A surprise also needs a unit, because a miss of 0.2 means nothing without the scale of past misses. Define a consensus that can be reproduced on this module’s series — the mean of the previous twelve months — and the forty-eight resulting surprises have a standard deviation of 0.21 points. On that scale a miss of 0.35 is 1.68 standard deviations and worth attention, while a miss of 0.05 is a quarter of one and is not a surprise at all. Exactly one of the forty-eight exceeds two standard deviations. Quote a surprise in points and you have said nothing; quote it in standard deviations of past surprises and you have said how unusual it was.
Why the same figure moves the same market both ways
A price is the present value of a stream, so a release reaches it by two routes: what it says about the cash flows, and what it says about the rate those cash flows are discounted at. Take the simplest form carrying both, a stream growing at one rate and discounted at another, worth the payment divided by the gap between them. The proportional move in the price is the change in the growth rate minus the change in the discount rate, divided by that gap.
The denominator does more work than anything else on this page. At a gap of 4 per cent the multiplier is 25, so ten basis points on the discount rate is two and a half per cent of the index. In the discount-rate channel an equity index behaves like a twenty-five-year zero-coupon bond, which is why a number about last month’s hiring can move it several per cent inside an hour.
Now put a growth surprise through both channels at once. It raises expected growth, and it raises the expected policy path, because the central bank responds to growth. Call the second response some multiple of the first. The index rises if that multiple is below one and falls if it is above one. That inequality is the whole of the sign, and nothing else here is needed to obtain it.
Put numbers on it. Take a print that revises expected growth up by twelve basis points. With the bank at the lower bound and unable to respond, the path does not move and the index gains 3.00 per cent. With the bank on hold and inflation at target, the path moves ten basis points and the index gains 0.50. With the bank fighting inflation and forced to remove twenty-five basis points of accommodation for every twelve basis points of growth, the index loses 3.25. Same print, same growth news, a spread of six and a quarter points with a change of sign inside it, and nothing different but a coefficient in somebody else’s reaction function.
Lesson 45 supplied the same result from the other side. When two shocks drive a pair of assets, the correlation between them is the difference of the two variances over their sum. When the rate shock dominates, stocks and bonds move together and good news is bad news; when the growth shock dominates they move oppositely and good news is good news. The stock-bond correlation and the sign of the equity reaction to a strong employment print are one quantity wearing two names, and both flip in the same place.
One asymmetry decides how usable any of this is. Of the two channels, one is quoted continuously and the other is in nobody’s price. The expected policy path sits in a futures strip, to the basis point, before and after every release. The growth revision sits nowhere. So the sign of a reaction is easy to explain afterwards and hard to call in advance, and anyone who tells you which way the market will take a number is quoting an estimate of a coefficient and calling it a forecast. What can be measured is the half that is quoted, and the next section measures it.
What the future was quoting, and what the print did to it
A thirty-day contract on a policy rate settles at a hundred minus the average of the daily effective rate over the calendar month. That averaging is the entire difficulty and the entire opportunity: a contract covering a month in which the decision falls part way through is a blend of the old rate and the new one, weighted by days.
Take a month of thirty-one days with the decision on the eighteenth and the new rate effective from the nineteenth, so eighteen days settle at the old rate and thirteen at the new. Suppose the effective rate is 4.33 per cent, the step under discussion is a quarter of a point, and the contract trades at 95.615, which is an implied average of 4.385 per cent.
Assume two outcomes only, no change or one step up. Then the implied average is the old rate plus the probability of a step, times the step, times the fraction of the month that follows the decision. Rearranged, the probability is the implied average minus the old rate, multiplied by 31, divided by a quarter point times 13. That is 0.055 times 31 over 3.25, which is 0.5246. The contract is quoting a 52.5 per cent chance of a move.
Now a release lands and the contract falls to 95.575, an implied average of 4.425 per cent. The same arithmetic gives 0.095 times 31 over 3.25, or 0.9062. The probability went from 52.5 per cent to 90.6. That release was worth 38.2 points of probability, or 9.54 basis points on the meeting rate, and unlike almost everything else that will be written about it, that is a measurement rather than an opinion.
Now do it the way it is usually done. Divide the implied average minus the old rate by the step, ignoring which part of the month the new rate applies to, and the answer is 22.0 per cent before and 38.0 after. Both are wrong by the same factor, 31 over 13, which is 2.38. The error is neither small nor random: the shortcut always understates, and it understates by more the later in the month the decision falls. Move the meeting to the twenty-fifth of the same month and the factor is over five.
Two things about what has just happened. The number that came out is the market’s own expectation rather than a forecaster’s, and it cost nothing to obtain. And it is exactly one of the two channels from the previous section, the one that is quoted. The other is still in nobody’s price, which is why the sign of the reaction stays a judgement even after this arithmetic is finished.
What it does not buy you
None of this tells you what to hold, and the step from a macro read to a portfolio is where most of the damage in this subject is done. That step has a price, and the price can be computed before it is taken.
Rotating on a regime call is a bet whose three outcomes are already known. Get the call right and you hold that regime’s best asset. Get it wrong and you are stuck in its worst. Do nothing and you hold the index. Setting the first two against the third gives the accuracy the call needs: the index return minus the worst, over the best minus the worst. Below are four episodes with the conventional pair in each — a technology index against broad commodities through the long expansion, energy against a concentrated growth fund in 2022, long government bonds against financials in the crisis, gold against long government bonds in the 1970s in real terms — and the broad index as the do-nothing alternative in every row.
| Episode | Best asset | Worst asset | The index | Accuracy the call needs |
|---|---|---|---|---|
| Goldilocks, 2010-2019 | +400% | -40% | +255% | 67% |
| Inflationary boom, 2022 | +64% | -67% | -18% | 37% |
| Deflationary bust, 2008-09 | +20% | -83% | -57% | 25% |
| Stagflation, the 1970s in real terms | +600% | -30% | -13% | 3% |
The bar moves by a factor of twenty-five across those four rows, and it moves the wrong way for anybody who wants to be clever about it. In the benign stretch you had to be right two times in three before rotating beat holding the index, because a benign regime already puts the index near the top of the available range: the gain from being right is small and the loss from being wrong is enormous. In the crisis you needed 25 per cent, which is what blind guessing gives you on a four-box model. In the 1970s you needed 3.
So the rule the arithmetic supports is not the one usually printed. A regime read should move your size long before it moves your holdings. When conditions are good, a wrong rotation is the most expensive mistake available and the correct response to an ambiguous signal is to do nothing at all. When conditions are genuinely bad the rotation is close to free, and by then you are not forecasting anything, because the confirming series have already turned.
Lesson 39 asked the same shape of question about a filter and found two break-even points where the usual advice offers none. This is the third of that family. What decides whether a view is worth acting on is not how strong the view is; it is what acting costs when the view is wrong, and that number can be computed in advance from three returns you can look up.
What this does not settle
That the surprise is the whole of the reaction. It is not, and the correction has a name. Splitting policy announcements into factors turns up two rather than one: the decision, and the revision to the expected path that the accompanying language causes. A release can land exactly on consensus and still move the market several points, because the sentence after the number changed what the next four meetings are expected to do. The worked example prices the first factor exactly. Nothing prices the second in advance.
That the base-effect arithmetic bears on what a release does to price. It does not, and the two halves of this lesson sit beside each other for a reason worth stating rather than hiding. The month leaving the window carries 38 per cent of the combined variance of the two terms and none of the surprise, because it was published a year ago and everybody forecasting the release subtracted it long before the release. What the arriving month contributes to the change is its full weight and not a twelfth of it. So the first table explains why a headline can fall while prices stand still, and it explains nothing whatever about why a release moves a market: on the surprise, which is the only thing that does, the departing month is worth exactly zero. Both halves are true and they answer different questions, and running them together is how a reader talks himself into ignoring a print that genuinely did surprise.
That one price identifies the probabilities. The worked example assumes two outcomes, no change or one step. The moment a second step is genuinely live there are two unknown probabilities and still one price, and no algebra recovers both. What the contract quotes honestly is an expected average rate. Turning that into a probability means assuming away every outcome but two, and on a meeting that is actually open the assumption is doing more work than the arithmetic.
That the central bank will step in if the market falls far enough. It has, repeatedly, and once conspicuously it did not: in 2022 the index fell about a quarter from its high while policy went on tightening, because inflation was competing for the same instrument. A reaction function with two arguments cannot be summarised as a floor under one of them. When the two point the same way the floor looks real; when they conflict, the argument with the legal mandate attached wins.
That the four episodes in the second table are precise figures. They are approximate total returns over the stated windows, carried here because the ordering they produce is what matters and that ordering is robust. For the benign row to fall to a coin flip the index would have had to return +180 per cent over the decade instead of +255; for the stagflation row to reach even 25 per cent the index would have had to return +128 per cent in real terms instead of -13. No plausible revision of the inputs reorders the column.
That these sixty numbers are anybody’s inflation series, or that the liquidity identity forecasts anything. The months are the module’s closes rescaled by a rule printed above, so every figure in the first table can be reproduced; five years is a short record for a statistic built on a twelve-month window, and the run is not stationary, which is the only reason the variance share came out at 38 per cent rather than the exact half an independent series gives. The liquidity identity is accounting on three published series rather than a model: it fixes the sign of an input and says nothing whatever about the output.
Problems
- Split one headline into the month that arrived and the month that left. Take the last thirteen monthly prints of any published price index and compute the annual rate for the most recent two months. Then compute the newest month minus the month thirteen back. The two answers agree, and the second shows which part of the change was already on the record. Now run it forward: write down the twelve months due to drop out of the window over the coming year, and you have the mechanical part of the next twelve headlines before one of them is published.
- Read the expectation out of a dated contract, twice. Pick a contract that settles on a policy rate. Note which day of the month the decision falls on and how many days of the contract month follow it, convert the price into an implied average, then into a probability. Do it the day before a scheduled release and again the day after. The difference is what that release was worth, in basis points, and it is the only part of the reaction you can measure rather than argue about. Then run the same subtraction without the day count and see how far off it lands.
- Price the rotation before you make it. For whatever macro call you are inclined to act on, write down three returns: the asset you would move into if you are right, the one you would be stuck in if you are wrong, and the index you would hold by doing nothing. The accuracy the call needs is the third minus the second, over the first minus the second. Then write down how many of your last ten macro calls were right. If the second number is smaller than the first, the honest move is to change your size and leave the holdings alone.
Sources. Kenneth N. Kuttner, “Monetary Policy Surprises and Interest Rates: Evidence from the Fed Funds Futures Market” (Journal of Monetary Economics, 2001), for the method the worked example uses: splitting a decision into the part the futures had already priced and the part they had not, with the day-count correction that makes the split honest. Refet S. Gürkaynak, Brian Sack and Eric Swanson, “Do Actions Speak Louder Than Words? The Response of Asset Prices to Monetary Policy Actions and Statements” (International Journal of Central Banking, 2005), for the finding that two factors are needed rather than one, and that the revision to the expected path explains more of the reaction than the decision does. John Y. Campbell and John Ammer, “What Moves the Stock and Bond Markets?” (The Journal of Finance, 1993), for the decomposition that turns the question of sign into an arithmetic one: a price move is news about cash flows minus news about discount rates, and the two are separately measurable. David O. Lucca and Emanuel Moench, “The Pre-FOMC Announcement Drift” (The Journal of Finance, 2015), for a scheduled-event pattern documented across many meetings, and for the reason to read it as an average rather than as a plan for the next one. Bureau of Economic Analysis, the national accounts methodology papers and the source-data tables published alongside each advance estimate, for which monthly series a quarterly aggregate is assembled from and which of its parts are estimated rather than measured when it first appears.
A macro release is a measurement, and most of the measurement was already public when it arrived. What is left over is small, it is quoted, and it reaches price through two channels whose net sign is somebody else’s reaction function rather than your reading of the data. That closes this module: twelve lessons that began by measuring a regime off the tape and end by naming what moves every position inside one at the same time. Module 6 turns to the instruments people put on the chart instead. Lesson 48 opens it with what an indicator is, and the answer governs everything after it: every indicator is a function of prices you already have, so none of them adds information, and the only questions worth asking about one are what it discards, how long it takes to discard it, and whether it quietly rewrites its own history.
Scheduled Events
The quoted price of a dated event, which this lesson reads out of a different contract.
Read Lesson →Correlation
The sign identity behind one figure moving one market in both directions.
Read Lesson →Trading More Than One
The same question asked of a filter, with the same answer about what acting costs.
Read Lesson →Markets Have Modes
The regime this module opened by measuring off the tape, and here gives a cause.
Read Lesson →Educational only. Trading involves substantial risk of loss. Not financial advice. Past performance does not guarantee future results.
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