02
From latent beliefs to observable data.
Trinity Term · 2026
Measuring
Expectations.
Surveys, markets, central-bank projections, text, and the wedges that make each measure useful.
Content
From latent beliefs to market prices, policy surprises, and causal identification.
Three empirical steps.
Start with fundamentals: define the expectation object, the instrument, and the wedge. Then read policy expectations from market prices and use high-frequency timing for identification.
02A
Fundamentals
Latent beliefs, surveys, market-implied measures, central-bank projections, text, and measurement wedges.
\[m_{k,t}=g_k(\theta_t)+w_{k,t}+\varepsilon_{k,t}\]
02B
Futures and asset prices
Fed funds futures, meeting-level probabilities, Kuttner surprises, target versus path news.
\[f_{t,m}=100-F_{t,m}\]
02C
High-frequency identification
Event windows, asset-price responses, information shocks, and macro external instruments.
\[\Delta_{\mathcal W}x_e\]
02A
Latent beliefs, observed instruments.
Fundamentals
Fundamentals.
Latent beliefs, measurement instruments, probability measures, and validation.
Agent, variable, horizon
Moment, probability measure, and wedge
Survey, market, central-bank, and text measures
Monetary Policy Works Through Expected Future Rates
Every core equation of modern macro is an expectations equation
Consumption Euler Equation
\[ u'(c_t) \;=\; \beta\,(1+r_t)\,\mathbb{E}_t\!\left[u'(c_{t+1})\right] \]
Households postpone spending based on what they expect consumption to be worth tomorrow. Current saving behaviour depends entirely on expected future real returns.
Fisher Relation
\[ r_t \;\approx\; i_t \;-\; \mathbb{E}_t[\pi_{t+1}] \]
The real rate — which drives investment and borrowing — is the nominal rate minus expected inflation. A central bank that cannot observe \(\mathbb{E}_t[\pi_{t+1}]\) is flying blind.
New Keynesian Phillips Curve
\[ \pi_t \;=\; \kappa\,\widetilde{mc}_t \;+\; \beta\,\mathbb{E}_t[\pi_{t+1}] \]
Today's inflation is partly driven by inflation expected tomorrow. Price-setters are forward-looking; anchored expectations limit inflation persistence after shocks.
Term Structure of Interest Rates
\[ i^{(n)}_t \;=\; \tfrac{1}{n}\sum_{j=0}^{n-1} \mathbb{E}_t\!\left[i_{t+j}\right] \;+\; \tau^{(n)}_t \]
A long rate is an average of expected short rates plus a term premium \(\tau^{(n)}_t\). Forward guidance moves \(\mathbb{E}_t[i_{t+j}]\) for \(j \geq 1\) — without touching the overnight rate. The language is the policy.
Why Measurement Is Hard: The Latent-Variable Problem
Expectations are latent distributions; data are instrument-specific traces
Fundamental obstacle
The belief is hidden.
\[
\theta_{a,t}^{(h)}(X)
\]
Agent \(a\)'s belief about \(X_{t+h}\) is a subjective distribution. We observe only traces left by surveys, prices, or language.
Observed object
\[
m_{k,t}^{(h)}
=
g_k\!\left(\theta_{a,t}^{(h)}(X)\right)
+
w_{k,t}^{(h)}
+
\varepsilon_{k,t}^{(h)}
\]
\(m_{k,t}^{(h)}\)
Number produced by instrument \(k\).
\(g_k(\theta)\)
Moment or transformation captured.
\(w_{k,t}^{(h)}\)
Structured wedge: not random noise.
\(\varepsilon\)
Sampling or measurement error.
01
Survey responses
Useful because they ask agents directly. Wedge: wording, framing, rounding, priming, numeracy.
02
Market prices
Useful because they update continuously and are traded. Wedge: risk premia, liquidity, collateral, risk-neutral pricing.
03
Textual traces
Useful for salience and tone. Wedge: selection, strategic language, model extraction error, language drift.
Lucas (1976) makes the point sharper: if agents revise expectations when the policy regime changes, then measurement is not a technical detail. It is the identification problem.
Survey Measures — Households
The general public's inflation beliefs — measured but imperfectly
University of Michigan Survey of Consumers
Point forecast
US · since 1978 · Monthly
Asks: "By what percent do you expect prices to rise over the next 12 months?" Longest-running household series. Mass spikes at 0, 5, 10% reflect rounding as a signal of uncertainty (Binder 2017). Also collects 5-year expectations.
NY Fed Survey of Consumer Expectations (SCE)
Distributional
US · since 2013 · Monthly, panel
Respondents assign probabilities to inflation bins — recovers individual means and uncertainty. Panel design tracks belief revision over time. Validated against spending data (CGW 2022).
BoE/Ipsos Inflation Attitudes Survey
Qualitative
UK · since 1999 · Quarterly
Asks about "prices in the shops generally." Qualitative balance statistic converted to a quantitative measure. Key input to the Monetary Policy Committee's deliberations on public credibility.
ECB Consumer Expectations Survey (ECB-CES)
Distributional + RCT
Euro area · since 2020 · Monthly, panel
Newest major household survey. Panel structure and embedded information experiments (RCTs) allow causal identification. Distributional elicitation with HICP framing. Benchmark for ECB communication research.
Key design choices: wording (aggregate prices vs own costs), format (point vs distributional), horizon framing (cumulative vs average annual vs point-in-time). These determine what you measure — they are not interchangeable.
Survey Measures — Professional Forecasters
Expert predictions with distributional elicitation and long track records
Survey of Professional Forecasters (SPF)
Philadelphia Fed / ECB · US since 1968
Longest-running professional survey in the US. Forecasters assign probabilities to inflation bins — the distributional format recovers uncertainty and disagreement. ECB SPF mirrors the structure for the euro area (since 1999).
Blue Chip Economic Indicators
Wolters Kluwer · US since 1976
Compiles monthly forecasts from ~50 business economists at major financial institutions. Widely tracked by markets and policymakers as a near-term consensus gauge.
Livingston Survey
Philadelphia Fed · US since 1946
The longest-running continuous expectations survey in existence. Bi-annual; economists at banks, industry, and government. Historical depth is essential for studying belief formation across monetary regimes.
BoE SEF / Consensus Economics
UK · ongoing
BoE SEF polls external forecasters ahead of each MPC meeting. Consensus Economics collects projections from 30+ UK institutions — broad cross-section of professional opinion.
Why professionals differ from households
Incentive alignment
Professionals are paid to be accurate. Households are not.
Informational advantage
Access to real-time data, econometric models, and market intelligence.
Herding risk
Reputation incentives push forecasts toward consensus — a bias opposite to households' limited-attention bias.
Forecast accuracy
Ang, Bekaert & Wei (2007): Michigan and SPF both outperform the US term structure at forecasting inflation at 1-year horizons.
Mankiw, Reis & Wolfers (2003): Households, firms, and professionals differ on inflation by percentage points; the gap widens significantly in high-inflation episodes. The disagreement is systematic, not noise.
Market Measures — Inflation Expectations
Financial prices reveal risk-neutral expectations — not physical beliefs
BE
TIPS breakeven
\[
\mathrm{BE}_t^{(n)}
=
i_t^{(n)} - i_{t,\mathrm{TIPS}}^{(n)}
=
\mathbb{E}^Q_t[\pi_{t,t+n}] + \lambda_t + \ell_t
\]
Difference between nominal Treasury and TIPS yields. Available at 1y, 5y, and 10y horizons. Limitation: TIPS liquidity can distort the signal in stress episodes; the liquidity wedge \(\ell_t\) is often countercyclical.
ILS
Zero-coupon inflation swaps
\[
\mathrm{ILS}^{(n)}_t
\approx
\mathbb{E}^Q_t[\pi_{t,t+n}] + \lambda_t
\]
Fixed-rate payer receives realised CPI or HICP growth. Swaps avoid the TIPS liquidity premium and are central for anchoring assessment; the ECB tracks the 5y5y HICPxT swap. Cleaner than breakevens, but less liquid in thin markets.
What the price contains
Q
Risk-neutral expectation
The market-implied distribution, not the average household or firm belief.
λ
Inflation risk premium
Compensation for holding payoffs exposed to inflation states.
ℓ
Market-friction wedge
Liquidity, collateral, segmentation, and balance-sheet constraints.
Instruments by jurisdiction
US
United States
TIPS breakevens; CPI-U swaps.
UK
United Kingdom
ILG breakevens; RPI swaps with CPI/RPI wedge.
EA
Euro area
HICPxT swaps; OAT/Bund breakevens.
Market Measures — Interest Rate Expectations
Futures and swaps price the expected path of the policy rate
FFF
Fed funds futures
\[
F_{t,m}
=
100
-
\mathbb{E}^Q_t\!\left[\overline{r}^{\,EFFR}_{m}\right]
\]
Settles against the arithmetic average effective federal funds rate during the contract month. This is the cleanest market instrument for near-term Fed expectations and meeting-level target surprises.
OIS
Overnight index swaps
\[
OIS_t^{(n)}
=
\frac{1}{n}\sum_{j=0}^{n-1}\mathbb{E}^Q_t[i_{t+j}]
+
\tau_t^{(n)}
\]
Fixed leg of a swap against a compounded overnight rate. OIS curves read out the expected path of policy rates across tenors, with a term-premium component \(\tau_t^{(n)}\).
Q
The object is a path
Not one rate: a sequence of expected future overnight rates.
Instrument by horizon and moment
0-3m
Fed funds futures
Current-month average EFFR; best for meeting probabilities and target surprises.
3m+
SOFR futures
Post-LIBOR instrument for longer dollar money-market expectations.
tails
Caps, floors, swaptions
Recover the risk-neutral distribution: \(\Pr^Q(i_{t+n}>\bar{i})\), not only the mean.
Whose Beliefs? Three Populations, Three Jurisdictions
"What do people expect?" has no single answer until you say which people, in which jurisdiction
Population
United States
United Kingdom
Euro Area
Households
Public beliefs
Michigan MSC (1978)
NY Fed SCE (2013, panel)
NY Fed SCE (2013, panel)
BoE/Ipsos Attitudes
(1999, qualitative)
(1999, qualitative)
ECB-CES
(2020, panel, RCT-embedded)
(2020, panel, RCT-embedded)
Firms
Pricing margins
Atlanta BIE (own costs)
Cleveland SoFIE
Cleveland SoFIE
BoE DMP
(2016, about 10,000 firms)
(2016, about 10,000 firms)
Bundesbank; Bank of Italy SIGE; Ifo
Professionals
Expert forecasts
Philadelphia SPF (1968)
Blue Chip; Livingston (1946)
Blue Chip; Livingston (1946)
BoE SEF; Consensus Economics
ECB SPF (1999)
Markets
Q-measure prices
Fed funds / SOFR futures
TIPS breakevens; CPI swaps
TIPS breakevens; CPI swaps
SONIA OIS; ILG breakevens
RPI inflation swaps
RPI inflation swaps
€STR OIS; HICPxT swaps
OAT/Bund breakevens
OAT/Bund breakevens
Each cell is a different population, instrument, and sampling frame. Michigan, ILG breakevens, and ECB-CES do not measure the same economic object.
Three Sources, Three Wedges
Each family of measures has a characteristic error structure — endogenous to the instrument, not classical noise
Source 01
Survey Responses
\[
\begin{aligned}
s_{i,t} &= \theta_{i,t} + b(q_k,z_i)\\
&\quad + r_{i,t} + \varepsilon_{i,t}
\end{aligned}
\]
Wording and framing
"Prices in general" and "inflation in the economy" do not elicit the same belief.
Bin design and priming
Bins centred near target can create artificial clustering around 2%.
Rounding as signal
Responses at 0, 5, and 10% often reveal uncertainty, not simple error.
Source 02
Market Prices
\[
\begin{aligned}
\mathbb{E}_t^Q[X]
&= \mathbb{E}_t^P[X] + \rho_t^X\\
\rho_t^X &= \lambda_t + \ell_t + \chi_t
\end{aligned}
\]
Risk premium \(\lambda_t\)
Compensation for bearing inflation or rate risk; time-varying, not a constant offset.
Liquidity wedge \(\ell_t\)
Thin trading, stress episodes, and collateral constraints distort prices.
P versus Q
The gap between physical and risk-neutral beliefs is itself economically informative.
Source 03
Textual Traces
\[
\begin{aligned}
T_t &= f(\theta_t,\text{strategy}_t)\\
&\quad + \nu_t^{extract} + \nu_t^{select}
\end{aligned}
\]
Extraction error
NLP scores depend on language, corpus, dictionary, model, and domain shift.
Selection bias
The people and institutions producing text are not a random sample.
Real-time advantage
Text can reveal attention and narrative shifts before surveys update.
Do not average blindlyThe wedge is structured by the instrument, so more observations do not make it disappear.
Sometimes the wedge is the objectRisk premia, disagreement, salience, and attention are themselves macro-finance variables.
TriangulateUse surveys, markets, and text together to separate belief movement from instrument movement.
Which Horizon? Level vs Forward Rate
Two datasets can both report "5-year inflation expectations" and mean completely different things
What years are being averaged?
Same label, different object
today
year 5
year 10
spot 5y: years 1-5
5y5y forward: years 6-10
Spot average
5-year level
\[
\pi_t^{0,5}
=
\mathbb{E}_t\!\left[
\frac{1}{5}\sum_{h=1}^{5}\pi_{t+h}
\right]
\]
Average expected inflation over the next five years. It includes near-term energy, food, tax, and supply shocks.
Forward window
5-year / 5-year
\[
\pi_t^{5,5}
=
\mathbb{E}_t\!\left[
\frac{1}{5}\sum_{h=6}^{10}\pi_{t+h}
\right]
\]
Expected inflation in years six through ten. It strips out the near-term shock and is the anchoring benchmark.
How to read 2021-22
Near-term measures surged because current CPI prints, energy prices, and supply disruptions entered the first few years.
5y5y measures moved less because they ask whether inflation is still expected to return near target after the shock.
Anchoring is a far-ahead statement. A high one-year or five-year level is not proof that the anchor has moved.
5y5y benchmarks by central bank
Fed
US: 5y5y TIPS breakeven and CPI inflation swap.
BoE
UK: 5y5y RPI swap, adjusted for the RPI-CPI wedge.
ECB
Euro area: 5y5y HICPxT swap, central to anchoring assessment.
Which Moment? The Mean Can Hide the Tail
Anchoring is a property of the full distribution, not of the mean alone
Same mean, different shape — same policy rate, different economy
Agent A: anchored
\(\mathbb{E}[\pi]=2\%\)
Uncertainty\(\sigma=0.4\) pp
Right tail\(\Pr[\pi>4\%]<1\%\)
Beliefs remain concentrated around the target; pricing and wage demands stay anchored.
Agent B: tail risk
\(\mathbb{E}[\pi]=2\%\)
Uncertainty\(\sigma=1.8\) pp
Right tail\(\Pr[\pi>4\%]\approx13\%\)
Same mean, but much more mass in high-inflation states; policy faces credibility risk.
Mean-only measurement gives the wrong comfort.
Both agents report the same expected inflation. But Agent B has higher uncertainty and a visible right tail. Anchoring is therefore a statement about the distribution, not only its centre.
Two tail episodes in recent history
Euro area, 2014–15: deflation risk
Option-implied \(\Pr^Q[\pi<0]\) on HICPxT rose sharply while the mean 5y5y inflation swap moved only modestly. The tail probability was the early warning signal.
US / UK, 2021–22: upside inflation risk
Option-implied \(\Pr^Q[\pi>4\%]\) surged before survey means fully adjusted. The distribution moved first; point forecasts lagged the risk signal.
Practical implication: point forecasts are incomplete. Distributional surveys and options-implied densities are needed to measure anchoring.
Central Bank-Based Measures
Official projections are measurement objects, conditioning assumptions, and communication tools
01
Federal Reserve “Dot Plot”
SEP · US · since 2012
\[
\tilde i_{t+h}^{CB}
=
\operatorname{median}_j
(i_{j,t+h}^{*,CB})
\]
SEP reports each FOMC participant’s fed-funds forecast for the next three years and the longer run.
Median dot is the focal summary; dispersion is internal disagreement.
Individual reaction functions, not a committee forecast. Strategic reporting matters.
02
ECB Survey of Professional Forecasters
EA · since 1999
\[
P_{t,h}(\pi\in B_b)
=
\frac{1}{N_t}
\sum_i p_{i,b,t,h}
\]
Quarterly survey for HICP inflation, GDP growth, and unemployment.
Collects point and distributional forecasts at 1y, 2y, and 5y horizons.
Data infrastructure, not central-bank beliefs; 5y horizon tracks anchoring.
03
Monetary Policy / Inflation Reports
BoE · ECB · other major CBs
\[
\widehat X_{t+h}^{staff}
=
E_t^{staff}
[X_{t+h}\mid\text{paths}]
\]
Staff projections are conditional on assumed paths for rates, exchange rates, fiscal policy, energy prices, and the model.
A gap versus market expectations reveals committee-market disagreement.
Different conditioning assumptions can explain different forecasts.
Projection as signal and instrument
The forecast can change the outcome it forecasts.
\[
\theta_{a,t+}^{P}
=
(1-\alpha_a)\theta_{a,t-}^{P}
+
\alpha_a \widehat X_{t+h}^{CB}
\]
Central-bank projections do not merely describe committee or staff beliefs. They can move private-sector expectations toward the policy-consistent path. The central bank is both forecaster and actor.
How to use these measures
1
Forward guidance effectiveness
Compare market-implied rate paths with the dot-plot median before and after press conferences.
2
Internal disagreement
Dispersion of dots or SPF forecasters reveals the distribution of policy or expert beliefs.
3
Communication errors
Persistent MPR or Inflation Report errors reveal model or reaction-function biases.
Dot Plot and Market-Implied Policy Path
FOMC dots show individual policy-rate assessments; futures prices summarize the market-implied path.
December 2021 SEP
December 2023 SEP
The dots are individual FOMC assessments of appropriate policy; futures prices are market-implied policy paths. Gaps between them reflect disagreement about the reaction function, risk compensation, or both.
Alternative & Composite Measures
Use them to triangulate the latent signal, not to replace surveys or markets
Common signal extraction
Composite indices filter many noisy measures into one latent expectations component.
\[
m_{k,t}
=
\lambda_k f_t
+
u_{k,t},
\qquad
f_t=\rho f_{t-1}+\eta_t
\]
The Fed's Common Inflation Expectations index is the canonical example: a principal-component composite of 21 survey and market-based indicators across agents and horizons.
Why?
No single measure is wedge-free. Cross-series correlation identifies the signal shared across instruments.
Limitation
High-variance series and structural breaks, including COVID and the 2021 inflation surge, can distort loadings.
Policy use
Distinguish idiosyncratic movement in one series from a broad shift in inflation anchoring.
Best practice: alternatives do not replace surveys or markets. They are leading indicators and cross-validation tools when surveys lag or market prices are distorted by liquidity and premia.
Text-based measures
Salience, tone, source, and narrative
NLP applied to central-bank minutes, news articles, earnings calls, and social media can extract high-frequency inflation attention.
\[
\frac{\#\{\text{inflation terms}\}}
{\#\{\text{all terms}\}}
\]
Central-bank text
Beige Books and FOMC minutes can be classified as supply-driven or demand-driven inflation language.
Earnings calls
Frequency of “inflation” and “costs” tracks firm-side inflation pressure and survey-based firm expectations.
News sentiment
Baker-Bloom-Davis EPU and inflation-specific newspaper indices are high-frequency but extraction-model dependent.
Google Trends analysis
Real-time public salience
\[
Google_t(\text{``inflation''})
\]
Search intensity for “inflation,” “price rises,” and “cost of living” can lead survey releases and correlate with Michigan or SCE at weekly frequencies.
Risk: attention, not beliefs.
Model-based decompositions
Separate expectation from premium
\[
BE_t^{(n)}
=
E_t^P[\pi]
+
IRP_t
+
LP_t
\]
No-arbitrage and factor models combine yields, swaps, surveys, and inflation data to split expectations from premia.
Risk: model-dependent.
Applications Across User Groups
The same instruments serve different analytical purposes depending on who is asking
Central Banks
Monitor anchoring · Calibrate communication · Design forward guidance
Anchoring assessment
Track whether long-run 5y5y measures remain near target across populations. Divergence between household and market expectations signals a credibility gap.
Forecast conditioning
MPR projections use survey and market measures to discipline near-term paths and identify where private-sector views diverge from official forecasts.
RCT-based experiments
ECB-CES and BoE DMP embed information treatments to causally identify how communication moves expectations and subsequent decisions.
Financial Markets
Asset allocation · Hedging · Trading monetary policy
Rate path trading
OIS curves and futures imply the market-consensus expected rate path. Post-FOMC deviations drive fixed-income, FX, and equity strategies.
Inflation hedging
TIPS, ILG, and HICPxT swaps hedge real purchasing power. The breakeven is simultaneously a hedge instrument and an expectations signal.
Policy surprise extraction
High-frequency changes in futures prices around FOMC windows isolate policy surprises for event-study regressions.
Corporations
Borrowing decisions · Price-setting · Investment planning
Borrowing cost planning
Firms with variable-rate debt or upcoming bond issuance use OIS and SOFR futures to project funding costs over 1–3 year horizons.
Wage and cost indexation
Expected inflation informs multi-year wage bargaining and supply-contract pricing, especially for energy, food, and commodity inputs.
Capital expenditure decisions
Long-run real rate expectations, derived from Fisher decomposition, determine the hurdle rate for investment appraisal.
Academic Researchers
Causal identification · Model validation · Policy evaluation
Lucas-critique-robust estimation
Expectation measures replace model-implied expectations in structural equations, allowing identification without imposing rational expectations.
Disagreement and heterogeneity
Cross-sectional dispersion in SPF, SCE, and ECB-CES tests models of information frictions, sticky information, and rational inattention.
RCT causal chains
Information experiments in SCE, ECB-CES, and BoE DMP estimate how beliefs affect spending, hiring, and price-setting.
Should We Trust Surveys? Four Pillars of Validation
Forecast accuracy · Behaviour prediction · Administrative data · Randomised controlled trials
01
Forecast accuracy
Ang, Bekaert & Wei (2007) · UK and EA evidence confirms
Michigan consumer surveys and the Philadelphia SPF both outperform the US nominal yield curve and time-series models in out-of-sample 1-year inflation forecasting. Professional surveys dominate at short horizons; market measures add value at longer horizons.
Test: compare RMSE and out-of-sample predictive content against AR, VAR, and term-structure benchmarks.
Surveys are not dominated by financial prices; they contain independent information.
02
Stated plans predict behaviour
Coibion, Gorodnichenko & Kumar · Bunn et al.
In a large-scale NZ firm survey, 97% of managers who said they intended to change prices did so; 98% who stated no change made none. BoE DMP results are nearly identical. Household spending intentions also predict later purchases in scanner data.
Test: regress realised prices, purchases, hiring, or investment on prior stated expectations and plans.
Survey responses are not cheap talk; they predict costly, real decisions.
03
Alignment with administrative data
CGW · CGR · Albrizio et al.
Household spending plans align with scanner-data purchases. Firm employment and investment intentions match HR and capital-expenditure records. Earnings-call sentiment co-moves with survey-based firm expectations.
Test: link survey microdata to independent scanner, bank-account, HR, investment, or text records.
Survey measures gain credibility when they line up with hard external records.
04
RCT causal chain
CGR firms · CGW households · ECB-CES, DMP experiments
Information treatments randomly assigned within survey samples shift stated beliefs. Those shifted beliefs then change stated and realised decisions: hiring, investment, spending, and price-setting.
Test: identify the causal chain from information \(\rightarrow\) belief \(\rightarrow\) action without selection bias.
Beliefs are causally effective; moving them can move economic behaviour.
02B
Prices, paths, surprises.
Fed funds futures and asset prices
Futures and
asset prices.
Using fed funds futures and other asset prices as measures of expected policy, inflation, uncertainty, and risk.
Monthly futures contract to meeting expectation
Kuttner target surprise
Target, path, and market-wedge interpretation
Fed Fund Futures: What They Are
Derivative instruments whose settlement is uniquely tied to realised overnight Fed policy
Instrument
Cash-settled CME future
A tradable price today for a rate realised over a future contract month.
→
Settlement object
Monthly average EFFR
Average of daily effective federal funds rates across all calendar days.
→
Price convention
IMM index
\(F_{t,m}=100-\bar r_{t,m}^{\,Q}\)
Definition
Cash-settled futures contracts traded on the CME Group since 1988, formerly CBOT. Settlement is determined by the arithmetic average of daily EFFR values over the entire contract month — not by any single day's rate and not by the FOMC target range.
Primary uses in practice
Market expectations
Real-time window into where traders believe the Fed will set rates.
Interest-rate hedging
Banks, asset managers, and corporations hedge short-term borrowing costs.
Academic identification
Kuttner (2001) uses FFF to isolate the unanticipated policy component.
Unlike a standard interest-rate future that settles on a point-in-time rate, FFF settle on the monthly average. The timing of an FOMC decision within the month determines its settlement weight.
Contract essentials
Exchange
CME Group
Settlement
Cash only
Notional
USD 5m
Delivery
Monthly
Pricing
100 - R
Min tick
1/2 bp
Reading the price requires the meeting date
old rate
meeting
post-meeting rate
A futures price is not enough. To infer the expected policy move, we must know how many days in the contract month are governed by the old rate and how many by the post-meeting rate.
Effective Federal Funds Rate
Volume-weighted median of overnight federal funds transactions, computed daily by the New York Fed
Post-2016 rule: find the rate where cumulative transaction volume crosses 50%
$$\sum_{i=1}^{k-1} v_i \;<\; \frac{1}{2}\sum_{i=1}^{n} v_i \;\leq\; \sum_{i=1}^{k} v_i$$
Order transactions from lowest to highest rate. Accumulate volumes. The EFFR is the transaction rate \(r_k\) at which cumulative volume first reaches the half-way point.
Worked example: volume crossing
Total volume is USD 100B, so the half-way point is USD 50B. The third transaction pushes cumulative volume past that threshold.
5.30%
USD 10B
cum. 10B
5.32%
USD 15B
cum. 25B
5.33%
USD 30B
cum. 55B ← EFFR
5.34%
USD 20B
cum. 75B
5.36%
USD 25B
cum. 100B
EFFR = 5.33%, because this is the first rate where cumulative volume exceeds USD 50B.
Same example in table form
| # | Rate | Volume | Cumulative |
|---|---|---|---|
| 1 | 5.30% | USD 10B | USD 10B |
| 2 | 5.32% | USD 15B | USD 25B |
| 3 | 5.33% | USD 30B | USD 55B ← median |
| 4 | 5.34% | USD 20B | USD 75B |
| 5 | 5.36% | USD 25B | USD 100B |
Pre-2016: volume-weighted mean
$$\text{EFFR}_{\text{pre-2016}}=\frac{\sum_{i=1}^{n} r_i v_i}{\sum_{i=1}^{n} v_i}$$
Why this matters for futures
The Fed switched to the median because the mean is sensitive to outlier trades. The EFFR is the settlement object for fed funds futures, so its construction matters before interpreting the futures price as an expectation of Federal Reserve policy.
Fed Fund Futures Contract Specifications
The IMM index convention and tick value — precision matters for hedging and P&L
Futures quote
94.50
IMM index price for a contract month
→
Decode the quote
100 − 94.50
subtract price from 100
→
Implied average EFFR
5.50%
market-implied monthly average rate \(R_{t,m}\)
IMM index price convention
$$F_{t,m}=100-R_{t,m}$$
\(R_{t,m}\) is the implied arithmetic average EFFR for month \(m\). A higher futures price means a lower expected rate; a trader expecting a rate cut buys futures.
Direction rule
F ↑ ⇒ R ↓
F ↓ ⇒ R ↑
Tick size and dollar value
Minimum fluctuation is \(0.5\) basis point. The \(1/12\) factor converts the annualised quote into roughly one month of exposure.
Tick value
USD 20.835
Full bp value
USD 41.67
Tick Value = (USD 5,000,000 × 0.00005) / 12 = USD 20.835
Price-to-rate conversion
| Futures price | Implied avg. EFFR |
|---|---|
| 94.25 | 5.75% |
| 94.50 | 5.50% |
| 94.75 | 5.25% |
| 95.00 | 5.00% |
| 95.25 | 4.75% |
Multiple contract months
Consecutive monthly contracts form a market-implied path. Adjacent months are the raw material for meeting-level extraction on the next slides.
May
5.50
Jun
5.35
Jul
5.20
Sep
4.95
Dec
4.70
More information: CME 30-Day Federal Funds futures
The Settlement Formula
Settlement is the arithmetic average of daily EFFR over all calendar days in the contract month
Input
Daily EFFR values
123...N-1N
One settlement input for every calendar day in the contract month.
→
Arithmetic average
\(\bar r_{\text{month}}=\frac{1}{N}\sum_{i=1}^{N}\mathrm{EFFR}_{i}\)
Every calendar day has the same weight, \(1/N\), even when the EFFR is carried forward from the previous business day.
→
Final settlement price
\(\text{Final}=100-\bar r_{\text{month}}\)
At expiration, the realised monthly average replaces the market expectation embedded in the futures price.
Calendar-day convention
Mon
5.33
published
Tue
5.33
published
Wed
5.58
published
Thu
5.58
published
Fri
5.58
published
Sat
5.58
carry Fri
Sun
5.58
carry Fri
Business days
Use the EFFR published for that date. The observation enters the monthly average once.
Weekends / holidays
No new EFFR is published. Settlement carries forward the previous business day's rate.
Why it matters
A rate change before a weekend can enter the settlement average several times. The futures price therefore depends on the calendar, not only on the policy decision.
Per-day settlement weight
1 / N
The contract does not weight business days only. It averages over all calendar days in the delivery month.
3.57%
one day in February, \(N=28\)
3.23%
one day in a 31-day month
Before final settlement
\(F_{t,m}\approx100-\mathbb{E}_{t}^{Q}[\bar r_{\text{month}}]\)
The traded futures price is a risk-neutral \(Q\)-measure object. The final settlement price is mechanical once all daily EFFR inputs are known.
Why Timing Within the Month Matters
The same 25 bp hike has a different settlement impact depending on the meeting date
General formula for a single rate change
$$\bar r_{\text{month}}=\frac{(d-1)r_{\text{pre}}+(N-d+1)r_{\text{post}}}{N}$$
Meeting on day \(d\) of an \(N\)-day month. Days \(1,\ldots,d-1\) run at \(r_{\text{pre}}\); days \(d,\ldots,N\) run at \(r_{\text{post}}\).
\(\omega_{\text{post}}=\frac{N-d+1}{N}\)
\(\Delta F=-\omega_{\text{post}}\Delta r\)
Old-rate days
d − 1
Calendar days before the meeting stay at \(r_{\text{pre}}\).
New-rate days
N − d + 1
Meeting day through month-end carry \(r_{\text{post}}\).
Sign: because \(F=100-R\), a positive rate surprise lowers the futures price. Reading a futures price as “the market expects \(x\)%” is only direct when there is no FOMC meeting in the contract month.
A 30-day month: where does the meeting fall?
Day 1Day 30
Day 5
86.7%
26 of 30 days carry the post-meeting rate.
Day 15
53.3%
Just over half the month is affected.
Day 25
20.0%
Only the final 6 days enter at the new rate.
Boundary cases
| Meeting day | \(\omega_{\text{post}}\) | Interpretation |
|---|---|---|
| 1 | 30/30 = 100% | Full month at new rate |
| 30 | 1/30 = 3.3% | Single-day effect |
Worked Example: Mid-Month Hike
FOMC hikes 25 bp on day 15 of a 30-day month; pre-meeting EFFR is 5.10%
Inputs
30
calendar days \(N\)
15
meeting day \(d\)
5.10%
pre-meeting EFFR
5.35%
post-hike EFFR
Calendar split
The meeting day itself is counted in the post-meeting block, so \(16\) of \(30\) days carry the higher rate.
Weighted-average calculation
Old-rate block
14 × 5.10 = 71.40
New-rate block
16 × 5.35 = 85.60
Total
157.00
$$\bar r_{\text{month}}=\frac{157.00}{30}\approx5.233\%$$
Result
Monthly average
5.233%
Settlement price
94.767
$$\text{Settlement}=100-5.233=94.767$$
Same hike, different meeting date
| Meeting timing | \(\bar r\) | Settlement |
|---|---|---|
| Meeting on day 1 | 5.350% | 94.650 |
| Meeting on day 15 | 5.233% | 94.767 |
| Meeting on day 25 | 5.133% | 94.867 |
| No meeting | 5.100% | 94.900 |
Implication: the policy action is the same \(+25\) bp hike, but the futures contract records a different monthly average because the calendar changes the weight on \(r_{\text{post}}\).
Source: CME FedWatch Tool
Extracting FOMC Meeting Expectations
Two contracts bracket a meeting; one weighted-average equation recovers the expected post-meeting rate
Extraction algorithm
1
Read the pre-meeting rate
Use \(f_0\), the contract ending before the FOMC meeting, as an approximation to \(r_{\text{pre}}\).
2
Use the meeting-month average
The contract containing the meeting gives \(f_1\), a weighted average of old-rate and post-meeting days.
3
Solve for the post-meeting rate
Invert the weighted-average equation to recover \(r_{\text{post}}\), then compute \(\Delta r=r_{\text{post}}-r_{\text{pre}}\).
Weighted-average pricing relationship
$$f_1=\frac{d-1}{N}r_{\text{pre}}+\frac{N-d+1}{N}r_{\text{post}}$$
$$r_{\text{post}}=\frac{Nf_1-(d-1)r_{\text{pre}}}{N-d+1}$$
Numerical example
30
days in month \(N\)
15
meeting day \(d\)
5.10%
pre-meeting rate
5.23%
meeting-month rate \(f_1\)
Solve
$$r_{\text{post}}=\frac{30(5.23)-14(5.10)}{16}=\frac{85.5}{16}\approx5.34\%$$
Post-meeting rate
5.34%
Implied move
+24 bp
Special case: no meeting
$$\bar r_{\text{month}}=f_1\Longrightarrow f_1=r_{\text{expected constant}}$$
If \(r_{\text{pre}}=r_{\text{post}}\), no decomposition is needed.
Implied FOMC Probabilities
If markets price only discrete 25 bp moves, the implied rate change identifies a risk-neutral probability
Two-outcome model: hike versus hold
Hike
+25 bp
Occurs with risk-neutral probability \(P_h^Q\).
Hold
0 bp
Occurs with probability \(1-P_h^Q\).
\(P_h^Q=\dfrac{E_t^Q[\Delta r]}{25\text{ bp}}=\dfrac{r_{\text{post}}-r_{\text{pre}}}{25\text{ bp}}\)
Numerical example
Implied move
+24 bp
→
Hike size
25 bp
→
Probability
96%
Interpretation: the contract prices almost, but not quite, a full 25 bp hike.
Q-measure versus P-measure
$$P_{\text{hike}}^Q=P_{\text{hike}}^P+\lambda_t$$
The futures-implied probability is risk-neutral. During calm periods \(\lambda_t\approx0\); during stress episodes the gap between market-implied and physical probabilities can be economically meaningful.
When the discrete assumption breaks down
With three outcomes \((-25,0,+25)\), one futures contract gives one equation but multiple unknown probabilities.
Options
Recover a fuller \(Q\)-distribution from option prices.
Assumption
Impose a logit or trinomial tree structure.
More prices
Use SOFR options and contracts around FOMC dates.
Monetary Policy Surprise
Kuttner (2001): the workhorse measure of the unanticipated component of FOMC decisions
Definition in a tight announcement window
$$TS_t=\frac{N}{N-d+1}\Delta f_t=-\frac{N}{N-d+1}\Delta F_t$$
\(F_t\) is the futures price and \(f_t=100-F_t\) is the futures-implied rate. The scale factor converts a monthly-average price change into an overnight-rate surprise.
Observed move
\(\Delta f_t\)
×
Gross-up factor
\(N/(N-d+1)\)
\(TS_t>0\)
Surprise tightening: the Fed hiked more or cut less than priced in.
\(TS_t<0\)
Surprise easing: the Fed cut more or hiked less than expected.
\(TS_t=0\)
The action was fully anticipated by markets.
The surprise is not the policy action itself. It is the action relative to the market's prior expectation.
Why a narrow window identifies policy news
13:4514:15
In a narrow window around the FOMC statement, scheduled macro news is held fixed, the Fed cannot react to within-window market moves, and risk-premium changes are plausibly small.
Kuttner (2001)
Anticipated policy moves have little effect; surprises move bond yields strongly.
Gürkaynak, Sack & Swanson
Two factors: target surprise and path surprise. Guidance moves the path.
Nakamura & Steinsson
High-frequency surprises can instrument monetary policy in structural macro models.
Predictive Power and Limitations
Strong at short horizons; risk premia and structural breaks dominate beyond six months
Forecast-error test
$$FE_{t,h}=r^{EFFR}_{t+h}-f_{t,h}$$
If futures are unbiased risk-neutral forecasts, \(E_t[FE_{t,h}]=0\). Persistent errors reveal premia, bias, or regime shifts.
What the futures rate contains
$$f_{t,h}=E_t^P[r^{EFFR}_{t+h}]+\lambda_{t,h}$$
At very short horizons, \(\lambda_{t,h}\) is often small. At longer horizons, policy-risk compensation becomes part of the price.
Forecast performance by horizon
1-3 months
Mean absolute error: 5-10 bp
Strong
3-6 months
Mean absolute error: 15-30 bp
Moderate
6-12 months
Mean absolute error: 30-60 bp
Weak
> 12 months
Mean absolute error: > 60 bp
Very weak
Short-horizon strength
For the next few meetings, futures are usually close to the market-implied policy path because little time remains for new macro news.
Cycle asymmetry
FFF historically underpredict rate increases before tightening cycles and overpredict cuts before easing cycles. The 2022-23 cycle is the recent example.
Structural breaks
Beyond six months, risk premia and institutional breaks matter. April 2023 marks the Eurodollar-to-SOFR conversion break for long-run dollar-rate studies.
Summary: Key Equations
The six equations that turn a futures price into policy expectations and surprises
01
Quote to implied rate
$$F_t=100-\bar r_t^Q$$
The contract price is quoted as 100 minus the market-implied monthly average EFFR.
02
Settlement average
$$\text{Settle}=100-\frac{1}{N}\sum_{i=1}^{N}r_i^{EFFR}$$
Settlement is mechanical: the calendar-day average of realised EFFR in the contract month.
03
Meeting extraction
$$r_{\text{post}}=\frac{Nf_1-(d-1)r_{\text{pre}}}{N-d+1}$$
Use the day count to separate known pre-meeting days from expected post-meeting days.
04
Binary FOMC probability
$$P_{\text{hike}}^Q=\frac{r_{\text{post}}-r_{\text{pre}}}{25\text{ bp}}$$
If the only outcomes are hold or +25 bp, the expected move maps into a risk-neutral probability.
05
Kuttner target surprise
$$TS_t=\frac{N}{N-d+1}\Delta f_t=-\frac{N}{N-d+1}\Delta F_t$$
Scale the event-window futures move by the share of the month affected by the decision.
06
Expectation plus wedge
$$f_{t,h}=E_t^P[r_{t+h}]+\lambda_{t,h}$$
The futures-implied rate is closest to a physical expectation when the policy-risk premium is small.
Mechanics: price quote, settlement rule, and day count determine what the contract mechanically measures.
Economics: probabilities and surprises are useful only after interpreting the \(Q\)-measure wedge.
02C
Timing as identification.
High-frequency data and identification
High-frequency
identification.
Using event-time price changes to identify monetary-policy news and its asset-market effects.
Why low-frequency regressions fail
Event windows and contamination
Target surprises as empirical instruments
The Core Identification Challenge
Monetary policy and financial markets form a simultaneous system
Low-frequency structural system
$$\Delta i_t=\beta\Delta r_t+\gamma z_t+\varepsilon_t$$
policy reaction function
$$\Delta r_t=\alpha\Delta i_t+\delta z_t+\eta_t$$
market response function
\(\Delta i_t\) is policy news; \(\Delta r_t\) is the asset-price or yield response. The confounder is \(z_t\): macro-financial news that moves both policy expectations and markets.
Object of interest
\(\alpha\)
The causal effect of monetary-policy news on asset prices. Low-frequency regressions do not isolate it.
Why OLS fails
$$\hat\alpha_{\text{OLS}}\neq\alpha,\qquad \operatorname{Cov}(\Delta i_t,\eta_t)\neq0$$
Simultaneity
Markets affect policy and policy affects markets.
Omitted variables
Macro news \(z_t\) drives both policy and markets.
Anticipation
Markets move before the announcement at daily or monthly frequency.
Identification move
Use a narrow event window around the announcement so that \(z_t\) is fixed, the policy decision cannot react to within-window market moves, and the observed price change is closer to monetary-policy news.
Quantifying the OLS Bias
The policy-rate regressor contains the very shocks we want to exclude
Matrix form of the structural system
$$\begin{pmatrix}1&-\beta\\-\alpha&1\end{pmatrix}
\begin{pmatrix}\Delta i_t\\ \Delta r_t\end{pmatrix}
=
\begin{pmatrix}\gamma\\ \delta\end{pmatrix}z_t+
\begin{pmatrix}\varepsilon_t\\ \eta_t\end{pmatrix}$$
\(\alpha\) is the causal market response to policy news. \(\beta\) is the policy reaction to market conditions.
Reduced-form policy regressor
$$\Delta i_t=\frac{1}{1-\alpha\beta}
\left[
\varepsilon_t+\beta\eta_t+(\gamma+\beta\delta)z_t
\right]$$
\(\varepsilon_t\)
monetary-policy news
\(\beta\eta_t\)
market shock fed back into policy
\((\gamma+\beta\delta)z_t\)
common macro-financial news
OLS estimand under independent shocks
$$\operatorname{plim}\hat\alpha_{\text{OLS}}=
\alpha+
\frac{(1-\alpha\beta)\left[\beta\sigma_\eta^2+\delta(\gamma+\beta\delta)\sigma_z^2\right]}
{\sigma_\varepsilon^2+\beta^2\sigma_\eta^2+(\gamma+\beta\delta)^2\sigma_z^2}$$
Desired variation
\(\varepsilon_t\) is the shock we want: unexpected monetary-policy news.
Market feedback
If \(\beta\neq0\), the policy-rate change contains \(\eta_t\), the market shock in the outcome equation.
Common news
If \(z_t\) moves both policy and markets, OLS confounds information effects with policy effects.
OLS Bias: Channels and Event-Window Logic
The estimator is close to causal only when monetary-policy news dominates market shocks and common news
OLS coefficient
$$\begin{aligned}
\hat{\alpha}_{OLS}
&=
\frac{\operatorname{Cov}(\Delta i_t,\Delta r_t)}
{\operatorname{Var}(\Delta i_t)}
\\[0.35em]
&=
\frac{(\beta\delta+\gamma)(\alpha\gamma+\delta)\sigma_z^2
+\alpha\sigma_\varepsilon^2+\beta\sigma_\eta^2}
{(\beta\delta+\gamma)^2\sigma_z^2+\sigma_\varepsilon^2+\beta^2\sigma_\eta^2}
\end{aligned}$$
Bias relative to the causal response
$$\hat{\alpha}_{OLS}-\alpha
=
(1-\alpha\beta)
\frac{\beta\sigma_\eta^2+\delta(\beta\delta+\gamma)\sigma_z^2}
{\sigma_\varepsilon^2+\beta^2\sigma_\eta^2+(\beta\delta+\gamma)^2\sigma_z^2}$$
Simultaneity
$$\beta\neq0,\qquad \sigma_\eta^2>0$$
Asset-market shocks enter the policy-rate regressor because the central bank reacts to market conditions.
Common News
$$\sigma_z^2>0,\qquad \delta(\beta\delta+\gamma)\neq0$$
Macro-financial news \(z_t\) moves both expected policy and the asset price, so OLS mixes policy effects with information effects.
Event Time
$$\sigma_\varepsilon^2\gg\sigma_\eta^2,\qquad
\sigma_\varepsilon^2\gg\sigma_z^2$$
A narrow FOMC window raises the signal-to-noise ratio: policy news is measured while other shocks are less likely to arrive.
$$\frac{\sigma_\varepsilon^2}{\sigma_\eta^2}\rightarrow\infty,\qquad
\frac{\sigma_\varepsilon^2}{\sigma_z^2}\rightarrow\infty
\quad\Longrightarrow\quad
\hat{\alpha}_{OLS}\rightarrow\alpha$$
The one-day window is usually too wide: CPI releases, labour-market news, growth announcements, earnings, and risk-premium shifts can all move asset prices. High-frequency event studies use timing to make the non-policy components small, rather than assuming they are small.
The High-Frequency Identification Approach
Policy decisions are announced at a known moment; narrow the window until only one arrow remains
Timing is the instrument
Event-time change
$$\Delta_{\mathcal W}A_{j,e}=A_{j,\tau^+}-A_{j,\tau^-}$$
Policy surprise
$$TS_e=\Delta_{\mathcal W}f_e$$
Regression and condition
$$\Delta_{\mathcal W}A_{j,e}=\alpha_j+\beta_j TS_e+u_{j,e}$$
$$\operatorname{Cov}(TS_e,u_{j,e})=0$$
What must be true inside \(\mathcal W\)
1
No new macro news
scheduled \(z_t\) is fixed inside the window
2
No policy feedback
the decision cannot react to within-window market moves
3
No fast wedge movement
risk and liquidity premia are approximately stable
Daily moves mix several shocks. Intraday windows work because information timing is sharper than confounder timing.
Choosing the Event Window
Narrower windows strengthen identification but amplify microstructure noise and require tick-level data
Intraday measurement
$$TS_d=\frac{D}{D-d}\left[-\left(ff_{\tau+\Delta\tau}-ff_{\tau-\Delta\tau}\right)\right]$$
\(\tau\) is the exact announcement time; \(\tau-\Delta\tau\) and \(\tau+\Delta\tau\) are just before and just after.
Daily measurement
$$TS_d=\frac{D}{D-d}\left[-\left(ff_d-ff_{d-1}\right)\right]$$
Daily prices are easy to obtain, but the close-to-close change includes every other shock on the announcement day.
Window trade-off
30 minutes
Best isolation
Gainsminimal contamination from other news
Costsmicrostructure noise; may miss delayed interpretation
2-3 hours
Digestion window
Gainscaptures statement, press conference, and interpretation
Costshigher chance of overlapping market news
Daily
Broad coverage
Gainseasy replication and more assets available
Costsweakest identification; includes all daily news
Practical rule
Use a 30-minute intraday window as the baseline, then report robustness for 60-minute, press-conference, and daily windows. Window choice is an identification assumption, not a formatting choice.
Pre-Meeting Futures Rate: Decomposition
The current-month futures rate is a weighted average of known past days and uncertain future days
Pre-announcement futures rate
$$ff_{d_0-1,t}=\frac{d_0}{D_0}r_0+
\frac{D_0-d_0}{D_0}E_{d_0-1}(r_1)+\eta_{d_0-1,t}$$
Known calendar days plus the expected post-meeting rate for the remaining days.
Post-announcement futures rate
$$ff_{d_0,t}=\frac{d_0}{D_0}r_0+\frac{D_0-d_0}{D_0}r_1+\eta_{d_0,t}$$
The expectation \(E_{d_0-1}(r_1)\) is replaced by the realised post-meeting rate \(r_1\).
Calendar weights inside the month
The announcement only changes the uncertain part of the monthly average. The known part is already locked in by past calendar days.
Already happened
Days through \(d_0\) are governed by \(r_0\). This component is known and does not move at the announcement.
Still uncertain
Remaining days depend on the post-meeting rate. The announcement resolves this expectation.
Example: day 15 of a 30-day month
$$ff_{14,t}=\frac{15}{30}r_0+\frac{15}{30}E_{14}(r_1)+\eta_{14}$$
Exactly half the month is already determined and half remains in expectation. The FOMC announcement moves only the uncertain half.
The decomposition is not algebra for its own sake. It tells us why a mid-month surprise must be scaled up: the futures contract is a monthly average, while the policy surprise is an overnight-rate innovation.
Deriving the Target Surprise
Subtract pre- from post-announcement futures rates; the known component cancels
01
Difference pre and post
$$\Delta f_{d_0,t}=
\frac{D_0-d_0}{D_0}\left[r_1-E_{d_0-1}(r_1)\right]+\Delta\eta_{d_0,t}$$
The known component \(\frac{d_0}{D_0}r_0\) appears in both futures rates, so it drops out of the event-window change.
02
Isolate the overnight-rate surprise
$$r_1-E_{d_0-1}(r_1)=\frac{D_0}{D_0-d_0}\Delta f_{d_0,t}$$
This uses the event-window approximation \(\Delta\eta_{d_0,t}\approx0\): the risk-premium wedge is assumed not to move inside the window.
Cancellation
Only the remaining \(D_0-d_0\) days are affected by the announcement. The known part of the monthly average cannot move.
Step 3: Kuttner target surprise
$$TS_{d_0,t}=\frac{D_0}{D_0-d_0}\Delta f_{d_0,t}
=
-\frac{D_0}{D_0-d_0}\Delta F_{d_0,t}$$
\(TS>0\)
Surprise tightening: the futures price falls and the implied rate rises.
\(TS<0\)
Surprise easing: the futures price rises and the implied rate falls.
\(TS=0\)
The action was already priced before the announcement.
The Scaling Factor: Intuition and Limits
A mid-month hike shows up in only half the monthly average, so we gross up the signal
Scaling factor
$$\phi=\frac{D_0}{D_0-d_0}=\frac{1}{\omega_{\text{post}}}$$
The current-month contract averages over the whole month. A policy surprise affects only the remaining days, so the observed futures move is mechanically attenuated.
Intuition: day 15 of a 30-day month
Already priced
15 days
Affected by news
15 days
$$\Delta f=\omega_{\text{post}}\Delta r
\quad\Rightarrow\quad
TS=\frac{\Delta f}{\omega_{\text{post}}}=\phi\Delta f$$
Worked example
$$\phi=\frac{30}{30-15}=2,\qquad
TS=2\times 12.5=25\text{ bp}$$
A 25 bp post-meeting surprise moves the monthly average by only \(25\times15/30=12.5\) bp. The scale-up recovers the overnight-rate surprise.
Scaling factor by meeting day
| Day | Affected days | \(\phi\) | Reading |
|---|---|---|---|
| 1 | 29 | 1.03 | Tiny scale-up |
| 5 | 25 | 1.20 | Early-month meeting |
| 15 | 15 | 2.00 | Signal doubles |
| 25 | 5 | 6.00 | Noise amplified |
| 30 | 0 | Undefined | Switch contracts |
Limit
\(\phi>5\)
Late in the month, a small quote error or risk-premium move becomes a large measured policy surprise.
Use the next-month contract instead of amplifying current-month noise.
The Late-Month Problem and its Solution
When only one or two days remain, current-month scaling turns small quote noise into large fake surprises
Current-month contract
Only one affected day remains
φ=31
$$\phi=\frac{31}{31-30}=31$$
The announcement changes only one day in the current-month settlement average.
Next-month contract
The full following month is affected
φ=1
$$TS_{d_0,t}=-\Delta F^{1}_{d_0,t}
=-\left(F^{1}_{d_0,t}-F^{1}_{d_0-1,t}\right)$$
No gross-up is needed because the contract is already fully exposed to the new rate.
1 bp
quote noise, stale price, or risk-premium movement
×31
31 bp
false target surprise after current-month scaling
Operational rule: for late-month meetings, switch to the next-month futures contract rather than multiplying current-month noise by a large \(\phi\).
What the switch fixes: mechanical gross-up noise.
What it does not fix: liquidity and risk-premium wedges still have to be checked.
The Empirical Framework: Kuttner (2001)
A one-equation model with one clean result: anticipated moves have zero market impact; surprises do not
The empirical model
$$R_{i,d}=\alpha+\beta_1TS_d+\varepsilon_{i,d}$$
\(R_{i,d}\)
Yield change on asset \(i\) on FOMC day \(d\).
\(TS_d\)
Unexpected component inferred from fed funds futures.
\(\beta_1\)
Immediate asset response to a one-bp surprise.
Anticipated versus unanticipated
$$\Delta i_d=\underbrace{TS_d}_{\text{unexpected}}+
\underbrace{(\Delta i_d-TS_d)}_{\text{anticipated}}$$
Under efficient markets, the anticipated component is already embedded in yields before the meeting. The event-day movement should load on \(TS_d\), not on the expected part of \(\Delta i_d\).
Kuttner result: response per 1 bp tightening surprise
Anticipated move
≈ 0 bp
Short yield
≈ 1 bp
Long yield
0.4-0.6 bp
The regression rejects the idea that rate changes matter mechanically. What matters is the revision relative to market expectations.
Why later papers extend the framework
GSS (2005)
Adds target and path surprises; longer yields mostly respond to path news.
Nakamura-Steinsson
High-frequency surprises also shift macro forecasts, pointing to central-bank information effects.
Single-factor limit
A target surprise alone explains little variance in longer-maturity yields.
End · Lecture 2
Measuring
Expectations.
Fatih Kansoy
Macro-Finance · Trinity Term 2026
02/