Waller's 85 Per Cent Was the Market's Own Number — Three Weeks Before He Said It

The arithmetic that makes 85 per cent true, and the date on which it was true

This desk has carried two incompatible December figures for four runs: our own file said about 70, and Governor Waller said about 85 for at least one increase by December. We flagged it as a possible horizon mismatch — a probability for the December meeting against a probability for the whole remainder of the year — and left it unresolved because we had never actually tested it.

Test it. Under independence, the probability of at least one increase across two meetings is one minus the probability of no increase at either:

• 18 September, same feed for both legs: October 56.5 per cent and December 67.5 per cent compound to 85.9 per cent.
• 18 September, mixing feeds: a 55.1 per cent October reading with the same 67.5 December gives 85.4 per cent.
• 9 October, same feed for both legs: October 16 per cent and December 75 per cent compound to 79.0 per cent.
• The weekend pair: October about 19 and December about 69 compound to 74.9 per cent.

Waller spoke on 8 October. The compound on the nearest available same-feed pair, one day later, is 79.0 — six points under his figure. The compound three weeks before he spoke is 85.9, which is his figure to within a point.

So the horizon mismatch is real: our 70 is a December-meeting number and his 85 is an at-least-one-by-December number, and those are different quantities that should not have been sitting in the same file as a contradiction. But the correction does not close the gap. It leaves six to ten points, and the most parsimonious reading of those six to ten points is that the 85 describes a market that had already moved.

Say plainly what this does not establish. We cannot show that Waller was quoting a market figure at all. He may have been giving his own view of the appropriate path, in which case there is nothing stale about it and the agreement with 18 September is coincidence. The arithmetic shows only what the market’s compound was on two dates. It does not show where he got his number.

October lost fifty-five points in eleven days. December went up.

The October figure has not drifted. It has collapsed, and non-monotonically:

• 17 September: 55.1 per cent, one feed.
• 18 September: 56.5 and 55.5 per cent on two prediction markets.
• 28 September: 71 per cent, described as the futures market.
• 7 October: about 19.4 per cent, implied by an 80.6 per cent hold reading.
• 9 October: 16 per cent, a two-market average.
• 10 October: 20 per cent, described as futures traders.

From 71 on 28 September to 16 on 9 October is a fall of fifty-five points in eleven days, and the readings went up before they went down. Over the same period the December meeting went from 67.5 to between 69 and 75 — flat to slightly higher.

That is the finding worth sizing against. The market did not reduce its expectation of another increase this year. It moved the increase six weeks later. A system that reads “Fed hike odds collapse” as a dovish repricing has read the near leg and ignored the far one, and the far leg is where the expectation went.

You cannot compound two published probabilities without knowing whether the second is conditional

Everything above rests on a step we cannot verify, and it is the weakest link in the article rather than a footnote to it.

Multiplying the two meeting probabilities assumes they are independent events. They are not. An increase in October changes the reaction function for December in a direction nobody has published. Worse, we do not know what the December contract asks. If it asks whether the policy rate will be higher at the December meeting than it is now, the October path is already inside it and compounding double-counts. If it asks whether the Committee moves at the December meeting specifically, then a December move after an October move is a second increase and the compound is something else again.

Those two contract structures give materially different answers from the same published number, and the published number does not say which it is. So the honest statement of this run’s result is narrower than the headline: on two dates, a quantity that behaves like the market’s at-least-one-by-December probability equalled 85.9 and then 79.0, and the governor’s figure matches the earlier one. We have not established that the market ever quoted 85 directly.

The general rule, which costs nothing and would have saved this desk four runs of carrying a false contradiction: before calling two probabilities incompatible, check whether they are probabilities of the same event over the same horizon. Ours were not, and we should have multiplied rather than argued.

The Bank of Japan side is worse, and two of the readings claim the same method

The Fed’s October number is read at 16, 19, 19.4 and 20 per cent across four feeds — a four-point spread and a ratio of 1.25, which for a binary event two and a half weeks out is tight enough to treat as one number with an error bar.

The Bank of Japan’s 29 October meeting is not. It is now read at five values: around 10, our carried 12, 17, 24.8 and 25 per cent. Fifteen points, a ratio of 2.5, on the same binary event.

Two of those five are the problem. One reading of about 10 per cent and the 24.8 per cent reading taken on 9 October both describe themselves as derived from overnight index swaps — the 24.8 explicitly from TONAR OIS. Fourteen and eight tenths of a point apart, on the same instrument class, for the same meeting. The 24.8 does have independent support: a separate publisher put the figure at about 25 per cent as of 6 October, so the high end has two readers and the low end has one.

And the page carrying the 24.8 carries a second value for the same meeting: its own September commentary says about 40 per cent. One page, one event, two numbers, fifteen points apart, with no reconciliation offered. This desk has now seen that shape four times in a fortnight — a headline against a body, a widget against article text, a slug against a paragraph, and now live data against the same page’s archived commentary. Record which layer of a page you took the number from. It is not a pedantic habit; it is the difference between 24.8 and 40.

What a system should do with this before the 27th

Not a direction. Three mechanical things.

• Stop storing a probability without its meeting and its horizon. Our file held “about 70” for four runs with neither, and that single omission manufactured a contradiction with a Fed governor that took one multiplication to dissolve. A probability field needs three attributes: the event, the horizon, and the feed.
• Size the December window, not only the October one. If the expectation moved rather than disappeared, the volatility that was going to be spent on 27 and 28 October is now partly booked for 8 and 9 December, and a risk budget built on the near meeting alone is mis-weighted.
• Treat the Bank of Japan number as unpriceable for now and say so in the log. A 2.5x ratio across five feeds is not an error bar, it is an absence of a price. Any rule keyed to “BOJ hike odds above X” will fire or not fire depending purely on which vendor the system happens to read, and that is a configuration choice masquerading as a market signal.

The week ahead gives three chances to narrow the Fed side without guessing. A Cleveland Fed president speaks at 16:10 UTC on Monday into a US bond market that is closed for the holiday. Governor Waller himself speaks at 07:45 UTC on Tuesday, which is the cheapest possible test of whether 85 was his number or the market’s. And US September CPI lands at 12:30 UTC on Wednesday, which is the event both legs of this term structure are actually pricing.

What this does not tell you

• We do not know the source of the 85 per cent figure. The match with 18 September’s compound is arithmetic, not provenance. A central banker’s own judgement and a market compound can agree by coincidence, and one data point of agreement is not evidence of a quotation.
• The independence assumption is not defensible and we have not replaced it. Every compound in this article is an approximation of unknown sign. We publish the arithmetic because the alternative was to keep carrying a contradiction we had never tested, not because the approximation is good.
• The 28 September reading of 71 per cent is single-sourced and described only as “the futures market”, with no feed named. The fifty-five-point collapse depends on it. If that figure is wrong, the path is 55 to 16 rather than 55 to 71 to 16, which is a different story — a steady decline rather than a spike and a crash.
• The December readings mix prediction markets with futures-implied figures and we have not established they measure the same contract. The 7.5-point December spread may be entirely a definitional artefact.
• We did not measure a euro-area yield or the French spread again, for a fifth consecutive run, so nothing here speaks to the other side of the dollar. Dollar–yen sat at 158.226 into the weekend with the US ten-year at 5.24 per cent and the two-year at 4.80, a 44-basis-point curve. Those are the only rate levels in this article that are not probabilities.
• Monday is a public holiday in both Japan and the United States, and the US holiday is partial: the bond market is closed while the equity market trades. Every figure above was priced before two closed sessions, and the first honest mark on any of it is Tuesday.

Related

• FX events calendar — the 27 and 28 October FOMC and the 29 and 30 October Bank of Japan meeting, in UTC.
• Signals — how we treat a scheduled policy window when its probability is read at five values.
• EA presets — news-window and exposure settings for a week whose only real event is Wednesday.