---
title: "Short-Term Interest-Rate Futures"
book: "Markets II: Rates, FX and Credit"
subject: quant
language: en
chapter: 8
exercises: 8
source: https://one-course.com/books/quant/2/en/chapter/8-short-term-interest-rate-futures
---

# Chapter 8 — Short-Term Interest-Rate Futures

A trader looks at the December 2026 one-month SOFR future. It trades at 96.040, which says that the overnight rate will average 3.960% over the month. The Federal Reserve meets on 9 December; the November contract says the rate will be 3.8975% going into the meeting. Nine days of December at 3.8975% and twenty-two at an unknown rate must average 3.960%: the unknown rate is 3.986%, 8.8 basis points higher, and if the only choices are to hold or to raise by a quarter point, the market is pricing a 35% chance of a hike. The trader’s desk thinks the chance is lower, but before selling the contract it has to ask one more question, about the last day of December, when the overnight rate is usually higher for reasons that have nothing to do with the Federal Reserve. The prices in this chapter are illustrative; the meeting dates and the contracts’ rules are real. It shows how futures on overnight rates turn a central bank’s calendar into prices, and how to read them back.

## 8.1 Overnight-rate futures

**Definition 8.1 (Overnight-rate future).**

An *overnight-rate future* is a cash-settled futures contract whose final price is 100 minus a rate computed from the daily fixings of an overnight benchmark ([Definition 1.13](https://one-course.com/books/quant/2/en/chapter/1-central-banks-and-the-short-rate#def-m2-central-banks-and-the-short-rate-rfr)) over a reference period: their arithmetic average over a calendar month for one-month contracts, their compounded rate over a quarter for three-month contracts. Before expiry the price is the market’s expectation of that settlement, adjusted for convexity ([Section 8.4](#sec-8-4)).

Quoting $100 - R$ makes the future behave like a bond: it rises when rates fall. Each contract has a fixed value per basis point, so a position’s interest-rate risk is simply its number of contracts times that value, and gains and losses are paid daily as variation margin (One Quant Book 1, chapter 5).

**As of September 2026 — Contracts on overnight rates.**

**CME three-month SOFR** (`SR3`): USD 2 500 times the index, USD 25 per basis point; 100 minus SOFR compounded over the [reference quarter](#def-m2-short-term-interest-rate-futures-imm), which runs from the third Wednesday of the third month before the delivery month to the third Wednesday of the delivery month; tick a quarter of a basis point for the nearest contracts, half otherwise; 39 quarterly contracts, nearly ten years. **CME one-month SOFR** (`SR1`): USD 4 167 times the index, USD 41.67 per basis point; 100 minus the arithmetic average of SOFR over the calendar month. **ICE three-month SONIA**: GBP 2 500 times the index; compounded SONIA from the third Wednesday of the delivery month to the next quarterly one; 25 quarterly contracts. **Euribor**, the euro’s surviving interbank rate, is published at 11:00 CET for five tenors by its administrator, and futures on three-month Euribor trade alongside those on overnight rates.

## 8.2 IMM dates, packs, bundles and strips

**Definition 8.2 (IMM date and reference quarter).**

An *IMM date* is the third Wednesday of March, June, September or December. A three-month contract’s *reference quarter* is the period between two consecutive IMM dates over which its rate is compounded.

The dates are used beyond futures: forward-rate agreements and swaps are often dated to them, so that their hedges line up with the [futures strip](#def-m2-short-term-interest-rate-futures-strip).

**Definition 8.3 (Futures strip, pack, bundle).**

A *futures strip* is a sequence of consecutive quarterly contracts, whose rates together describe the path of the short rate. A *pack* is four consecutive quarterly contracts traded in equal amounts as one instrument, a year of the strip; a *bundle* is the first $n$ years of consecutive contracts traded together, from the front.

**Proposition 8.4 (A strip is a term rate).**

If consecutive reference periods of lengths $\delta_1, \dots, \delta_n$ (in years) have futures rates $R_1, \dots, R_n$ (convexity ignored), a deposit spanning them all has the rate

$$
R_{1\dots n} \;=\; \frac{\prod_{i}(1 + R_i\,\delta_i) - 1}{\sum_i \delta_i},
$$

and buying the strip locks in that rate for an investor who will roll a deposit through the periods.

**Proof.** One unit invested at each period’s rate grows to the product; the strip’s daily settlements replicate the difference between the realised and the locked rates, period by period, to first order. ∎

![Reference periods of the contracts of this chapter, September 2026 to March 2027. One-month contracts average their calendar month; three-month contracts compound from IMM date to IMM date, and are named after the month their period ends. The dashed lines are the Federal Open Market Committee’s decision days; each new rate applies from the next day.](https://one-course.com/images/onecourse/chapters/quant-2/m2-short-term-interest-rate-futures/fig-8f66413d1b04.svg)

***Figure 8.1.** Reference periods of the contracts of this chapter, September 2026 to March 2027. One-month contracts average their calendar month; three-month contracts compound from [IMM date](#def-m2-short-term-interest-rate-futures-imm) to [IMM date](#def-m2-short-term-interest-rate-futures-imm), and are named after the month their period *ends*. The dashed lines are the Federal Open Market Committee’s decision days; each new rate applies from the next day.*

## 8.3 Pricing a meeting

**Definition 8.5 (Implied policy path).**

The *implied policy path* is the sequence of policy rates the market expects after each scheduled meeting of the central bank, read from the prices of short-term interest-rate futures (or overnight index swaps) as if those prices were expectations, any risk premium neglected.

**Method 8.6 (Reading a meeting from a one-month contract).**

Let a month of $N$ calendar days have a decision on day $m$, the new rate applying from day $m + 1$. Let $\bar R$ be the rate implied by the month’s contract, $100 - F$, and $r_0$ the rate expected before the meeting (from the previous month’s contract or the current fixing). Remove any known [turn premium](https://one-course.com/books/quant/2/en/chapter/2-money-markets#def-m2-money-markets-turn) $\tau$ on $k$ days, then

$$
r_1 \;=\; \frac{N\bar R - k\tau - m\,r_0}{N - m},
\qquad
p \;=\; \frac{r_1 - r_0}{\Delta},
$$

where $p$ is the implied probability of a move of size $\Delta$ if the only outcomes are no move and $\Delta$. Chain the months to obtain the rate expected after each meeting.

**Example 8.7 (Three meetings).**

From a rate of 3.87% after the September 2026 decision, with illustrative prices of 96.1275 (October), 96.1025 (November), 96.040 (December) and 95.990 (January 2027): the November contract implies 3.8975% after the October meeting, an 11% chance of a hike; December implies 3.9856% after the 9 December meeting, a 35% chance; January implies 4.175% after the 27 January meeting ([Figure 8.2](#fig-m2-short-term-interest-rate-futures-path)).

**Remark 8.8 (Late meetings are fragile).**

The multiplier $N/(N - m)$ turns a price error into an error in $r_1$. The January meeting falls on the 27th, so only four days of the month carry the new rate: an error of one basis point in the January price moves the implied post-meeting rate by $31/4 = 7.75$ basis points, a third of a hike. The October meeting is worse (three days). For late meetings desks use the next month’s contract, in which the new rate applies all month, as the example did for October.

![The path of the overnight rate implied by the illustrative one-month contracts of , stepping at each decision (dashed). The steps are expectations, averages over hold and hike, not forecasts of a quarter-point move: 35% of 25 basis points is the 8.8 of December. Data: the chapter’s tutorial.](https://one-course.com/images/onecourse/chapters/quant-2/m2-short-term-interest-rate-futures/fig-58147f7f386e.svg)

***Figure 8.2.** The path of the overnight rate implied by the illustrative one-month contracts of [Example 8.7](#ex-m2-short-term-interest-rate-futures-path), stepping at each decision (dashed). The steps are expectations, averages over hold and hike, not forecasts of a quarter-point move: 35% of 25 basis points is the 8.8 of December. Data: the chapter’s tutorial.*

![The December hike probability implied by the same price as the year-end turn assumed on the 31 December fixing grows: 35.2% with no turn, 33.4% with 10 basis points, 0.18 percentage points less for each basis point of turn. The turn is a money-market fact () that a policy reading must remove first. Data: the chapter’s weekend problem.](https://one-course.com/images/onecourse/chapters/quant-2/m2-short-term-interest-rate-futures/fig-450084672d7d.svg)

***Figure 8.3.** The December hike probability implied by the same price as the year-end turn assumed on the 31 December fixing grows: 35.2% with no turn, 33.4% with 10 basis points, 0.18 percentage points less for each basis point of turn. The turn is a money-market fact ([Chapter 2](https://one-course.com/books/quant/2/en/chapter/2-money-markets#ch-m2-money-markets)) that a policy reading must remove first. Data: the chapter’s weekend problem.*

## 8.4 The convexity adjustment

A future is settled every day; a forward rate agreement or a swap is settled once. The difference matters because the gains of a short futures position (which profits when rates rise) arrive when rates are high and can be reinvested at high rates, and its losses arrive when rates are low and can be financed cheaply. The short enjoys this, so it accepts a futures rate higher than the forward rate.

**Definition 8.9 (Convexity adjustment).**

The *convexity adjustment* of a short-rate future is the difference between its implied rate and the forward rate for the same period.

**Proposition 8.10 (The adjustment in a Gaussian model).**

If the short rate follows $dr = \theta(t)\,dt + \sigma\,dW$ (the Ho–Lee model), the futures rate for a period $[T_1, T_2]$ exceeds the forward rate by approximately $\tfrac12\,\sigma^2\,T_1\,T_2$. One Quant Book 6 derives it.

**Proof.** *Admitted here.* ∎

**Example 8.11 (Five and ten years out).**

With a normal volatility of 1% a year, the three-month contract starting in five years carries $\frac12 \times 0.01^2 \times 5 \times 5.25 = 13.1$ basis points of adjustment; the one starting in ten years, 51.25. At the front it is negligible; at the back of the strip it is larger than a typical move in a day, and a curve built from futures without it is wrong ([Figure 8.4](#fig-m2-short-term-interest-rate-futures-convexity)).

![The Ho–Lee convexity adjustment of a three-month futures rate by the start of its period, for three volatilities. It grows with the square of the horizon and of the volatility: negligible for the first contracts, tens of basis points for the last. Data: the chapter’s tutorial.](https://one-course.com/images/onecourse/chapters/quant-2/m2-short-term-interest-rate-futures/fig-25a716ed48d0.svg)

***Figure 8.4.** The Ho–Lee [convexity adjustment](#def-m2-short-term-interest-rate-futures-convexity) of a three-month futures rate by the start of its period, for three volatilities. It grows with the square of the horizon and of the volatility: negligible for the first contracts, tens of basis points for the last. Data: the chapter’s tutorial.*

## 8.5 Tutorial: extracting a policy path

**Goal.** Read the rate expected after each meeting from one-month futures, with and without a year-end turn, and compute strip rates and [convexity adjustments](#def-m2-short-term-interest-rate-futures-convexity). **End state:** Figures [8.2](#fig-m2-short-term-interest-rate-futures-path) and [8.3](#fig-m2-short-term-interest-rate-futures-turn) and the numbers of [Example 8.7](#ex-m2-short-term-interest-rate-futures-path).

1. **One month.** Remove the turn, then solve for the post-meeting rate. `def rate_after (c: MonthContract, rate_before: float ) -> float : """The post-meeting rate implied by the month's average (or the month's own rate if no meeting).""" turn = c.turn_days * c.turn_bp / 100.0 if c.meeting is None : return (c.average * c.days - turn) / c.days before = c.meeting.day # days 1..m at the old rate after = c.days - before return (c.average * c.days - turn - before * rate_before) / after` **Listing 8.1.** The rate after a meeting from the month’s average. code/firm/meetings/firm_meetings.py
2. **Chain the months**, and turn changes into probabilities. `def policy_path (contracts: list [MonthContract], start_rate: float ) -> list [tuple [str , float ]]: """[(label, rate expected after that month's meeting or over that month)] chained month by month.""" out, r = [], start_rate for c in contracts: r = rate_after(c, r) out.append((f " { c.year} - { c.month: 02d } " , r)) return out def move_probability (rate_after_meeting: float , rate_before: float , step: float = 0.25 ) -> float : """Probability of a move of `step` implied by the expected change, if only 0 or `step` are possible.""" return (rate_after_meeting - rate_before) / step` **Listing 8.2.** The policy path, and the probability of a move. code/firm/meetings/firm_meetings.py
3. **Strips.** `def strip_rate (rates: list [float ], fractions: list [float ]) -> float : """Term rate from a strip of consecutive period rates (percent), compounded: the rate of a deposit spanning them all.""" growth = 1.0 for r, d in zip (rates, fractions, strict=True ): growth *= 1.0 + r / 100.0 * d return (growth - 1.0 ) / sum (fractions) * 100.0` **Listing 8.3.** The rate of a strip of consecutive periods. code/firm/meetings/firm_meetings.py
4. **Run** `stir_demo.path()` and `stir_demo.december(10)` : 3.9856% and 35.2% without a turn, 3.9810% and 33.4% with 10 basis points.

**What to change next.** Replace the one-month contracts by three-month contracts compounding over IMM quarters, with two meetings inside one quarter, and solve for both ([Exercise 8.7](#exo-m2-short-term-interest-rate-futures-7)).

## 8.6 Build: the policy-path extractor

**Purpose.** The miniature firm’s rates traders, and its curve builder ([Chapter 9](https://one-course.com/books/quant/2/en/chapter/9-interest-rate-swaps#ch-m2-interest-rate-swaps)), need the market’s expected policy path: the traders to take views meeting by meeting, the curve to put its steps on meeting dates rather than smoothing through them.

**Interface.** `MonthContract(year, month, price, meeting, turn_days, turn_bp)`; `rate_after(contract, rate_before)`; `policy_path(contracts, start_rate)`; `move_probability(after, before, step)`; `strip_rate(rates, fractions)`; `convexity_adjustment(sigma, t1, t2)`.

**Rules.** Calendar-day averages; the new rate applies from the day after a decision; a [turn premium](https://one-course.com/books/quant/2/en/chapter/2-money-markets#def-m2-money-markets-turn) removed before solving; rates in percent.

**Acceptance tests.** `code/firm/meetings/tests/`: a month without a meeting returns its average; a constructed path is recovered exactly; a turn is removed; chaining; strip compounding; the adjustment’s value at five years.

**Stretch.** Three-month contracts (compounding, several meetings per quarter); the probability of 25 against 50 basis points from two adjacent contracts; the series of implied paths over time as a data product.

Sources and further reading

- CME Group, Rulebook Chapters 460 and 461 (three-month and one-month SOFR futures); ICE, *Three Month SONIA Index Futures* ; EMMI, *Euribor* .
- Federal Reserve, *FOMC meeting calendars* , 2026 and 2027.
- T. S. Y. Ho and S.-B. Lee, “Term structure movements and pricing interest rate contingent claims”, *Journal of Finance* 41, 1986.
- G. Burghardt, *The Eurodollar Futures and Options Handbook* , McGraw-Hill, 2003, for the market practice the SOFR contracts inherited.

## 8.7 Exercises

**Exercise 8.1 ★.**

A three-month SOFR contract trades at 95.965. What rate does it imply? It rises 3.5 basis points: how many half-basis-point ticks, and what is the gain on 200 contracts?

**Solution of Exercise 8.1.**

$100 - 95.965 = 4.035\%$. A rise of 3.5 basis points is 7 half-basis-point ticks; on 200 contracts the gain is $3.5 \times 25 \times 200 = \text{USD}~17\,500$.

**Exercise 8.2 ★.**

Give the four [IMM dates](#def-m2-short-term-interest-rate-futures-imm) of 2027 and the [reference quarter](#def-m2-short-term-interest-rate-futures-imm) of the June 2027 three-month SOFR contract.

**Solution of Exercise 8.2.**

17 March, 16 June, 15 September and 15 December 2027. The June 2027 contract’s [reference quarter](#def-m2-short-term-interest-rate-futures-imm) runs from 17 March (included) to 16 June 2027 (excluded).

**Exercise 8.3 ★.**

The November one-month contract trades at 96.1025. What average rate does it imply? What does a 2-basis-point rise in that rate cost a holder of 100 long contracts?

**Solution of Exercise 8.3.**

$100 - 96.1025 = 3.8975\%$. A long position loses when rates rise: $2 \times 41.67
\times 100 = \text{USD}~8\,334$.

**Exercise 8.4 ★★.**

The October meeting is on the 28th. By how many basis points does a 1-basis-point error in the October price move the implied post-meeting rate? Which contract would you use instead, and why?

**Solution of Exercise 8.4.**

Only three of October’s 31 days carry the new rate, so the multiplier is $31/3$: a 1-basis-point price error moves the implied rate by 10.3 basis points, 41% of a hike. Use November’s contract, in which the post-meeting rate applies every day (there is no November meeting): its price reads that rate directly.

**Exercise 8.5 ★★.**

Four consecutive quarterly contracts imply 3.95%, 4.05%, 4.10% and 4.12% over periods of 91 days each (actual/360). Give the one-year strip rate.

**Solution of Exercise 8.5.**

$[(1 + 0.0395 \times 91/360)(1 + 0.0405 \times 91/360)(1 + 0.0410 \times 91/360)(1 +
0.0412 \times 91/360) - 1]/(4 \times 91/360) = 4.1178\%$.

**Exercise 8.6 ★★.**

A trader hedges a sterling position with the “December” three-month SONIA future, believing it covers the same period as the “December” three-month SOFR future. What is wrong?

**Solution of Exercise 8.6.**

The two exchanges name their contracts differently. The three-month SOFR “December” contract compounds from mid-September to mid-December: the period *ending* in December. The three-month SONIA “December” contract accrues from the third Wednesday of December to mid-March: the period *starting* in December. The hedge is one quarter out: read the reference period in each contract’s rules, never the month in its name.

**Exercise 8.7 ★★★.**

*Coding.* With `convexity_adjustment`, give the adjustment of the three-month contract starting in five years and in ten years at 1% volatility. By how much does it change if volatility rises to 1.2%?

**Solution of Exercise 8.7.**

At 1%: $\frac12 \times 0.0001 \times 5 \times 5.25 = 13.1$ basis points at five years; $\frac12 \times 0.0001 \times 10 \times 10.25 = 51.25$ at ten. At 1.2%, both scale by $1.44$: 18.9 and 73.8 basis points, an increase of 5.8 and 22.55.

**Exercise 8.8 ★★★.**

*Find the flaw.* “The October contract implies a 10% chance of a hike on 28 October and the November contract 11%: the market is internally inconsistent, and the difference is an arbitrage.” Correct it.

**Solution of Exercise 8.8.**

The October contract has only three days at the new rate, so its implied probability carries ten times the price noise of November’s: a difference of one percentage point of probability is a fraction of a tick in October’s price. And the two numbers are not claims on the same thing: October’s average also contains three days of whatever the month-end turn is. Neither difference is an arbitrage; the November reading is the reliable one.

## 8.8 Problem: Hike or Hold

**Problem 8.1.**

Weekend problem — the December 2026 meeting

The November one-month SOFR future trades at 96.1025 and the December one at 96.0400. The Committee decides on 9 December; the new rate applies from 10 December. The only possible outcomes are no change and a quarter-point hike. Each contract is worth USD 41.67 per basis point.

**Part I — The reading.**

1. What rate does the market expect going into the meeting?
2. How many December days are at the old rate, and how many at the new?
3. Give the post-meeting rate implied by the December price.
4. Give the implied probability of a hike.
5. How many basis points of December price does one percentage point of probability represent?

**Part II — The turn.**

6. The 31 December fixing is expected 10 basis points above the rest. Recompute the post-meeting rate and the probability.
7. And for 20 basis points?
8. By how much does each basis point of assumed turn reduce the probability?
9. Why does the turn fall in the December contract and not in January’s?
10. How would you estimate the turn from market prices rather than assume it?

**Part III — The trade.**

11. A desk that thinks a hike is unlikely buys 1 000 December contracts at 96.040. What is the final price and its P&L if the Committee holds?
12. And if it hikes?
13. What is the expected P&L at the market’s 35% probability?
14. At what probability does the desk’s trade break even, and why is that the market’s number?
15. What else, besides the decision, moves the December settlement?

**Part IV — Judgement.**

16. Why is “35% chance of a hike” an approximation even with no turn?
17. Why might the risk-neutral probability differ from the Committee members’ own projections?
18. How would a surprise hike in October change the December reading?
19. State the *named result* : the implied December hike probability, without and with a 10-basis-point year-end turn.
20. In one sentence: what does a one-month rate future price?

**Solution of Problem 8.1.**

**1.** $100 - 96.1025 = 3.8975\%$. **2.** Nine (1 to 9 December) at the old rate, twenty-two at the new. **3.** $(31 \times 3.96 - 9 \times 3.8975)/22 = 3.9856\%$. **4.** $(3.9856 - 3.8975)/0.25 = 35.2\%$. **5.** One point of probability is 0.25 basis points of the new rate on 22 of 31 days: $0.25 \times 22/31 = 0.18$ basis points of December price. **6.** $(31 \times 3.96 - 0.10 - 9 \times 3.8975)/22 = 3.9810\%$: 33.4%. **7.** 3.9765%: 31.6%. **8.** $0.10/22 \times 100/0.25 = 0.18$ percentage points per basis point of turn. **9.** A one-month contract averages the calendar days of its month; the 31 December fixing covers 31 December, which is in December. January’s first days use the fixing of the first business day of January. **10.** From contracts or deposits that straddle the year-end and others that do not, as in [Proposition 2.11](https://one-course.com/books/quant/2/en/chapter/2-money-markets#prop-m2-money-markets-turn); or from the history of past year-end fixings as a prior. **11.** On a hold the December average is 3.8975%, the final price 96.1025: $+6.25$ basis points, $6.25 \times 41.67 \times 1\,000 = +\text{USD}~260\,438$. **12.** On a hike the average is $(9 \times 3.8975 + 22 \times 4.1475)/31 =
4.0749\%$, price 95.9251: $-11.49$ basis points, $-\text{USD}~478\,869$. **13.** $0.648 \times 260\,438 - 0.352 \times 478\,869 = 0$, to the dollar: the market’s probability is the one at which the trade is fair. **14.** At 35.2%, because the price is exactly the probability-weighted average of the two settlements; the desk wins on average only if its probability is lower than the market’s. **15.** The spread of SOFR to the policy rate (repo conditions, reserves), month-end and year-end turns, and the realised fixings of the days before the meeting. **16.** The outcomes are not only 0 and 25: a 50-basis-point move or an off-meeting move are possible; the price mixes all outcomes, so the two-outcome split is a convention. **17.** Futures prices embed risk premia: investors pay to hedge a hike, so the price-implied probability can exceed the real-world one; and the Committee’s projections are forecasts, not bets. **18.** The rate going into December would be about $3.87 + 0.25 = 4.12\%$; the December price would have to be re-read against it, and markets usually reprice the whole path after a surprise. **19.** Named result: *the implied December hike probability* is 35.2% with no turn and 33.4% with a 10-basis-point turn on 31 December. **20.** The average of the overnight rate over a month, and so every decision and every turn that falls in it.

## 8.9 Interview questions

**Interview question 8.1 ★ trader, researcher.**

How do you read the probability of a rate hike from futures prices?

**Solution of Interview question 8.1.**

Take the contract covering the meeting’s month (or better, the month after if the meeting is late); infer the rate before the meeting from the previous month’s contract; solve the month’s average for the post-meeting rate; divide the change by the size of the move. Remove turns and the SOFR–policy spread first, and remember it is a risk-neutral, two-outcome approximation.

*What the interviewer is looking for: the day-weighting, the late-meeting problem, and the caveats.*

**Interview question 8.2 ★ trader, bank.**

Why do short-rate futures quote $100$ minus the rate?

**Solution of Interview question 8.2.**

So that the price moves like a bond price: up when rates fall. Buying the future is then a long position in rate-sensitive assets, like buying a bill, and exchanges can list prices, bids and offers in the usual direction; a fixed value per basis point makes risk the number of contracts.

*What the interviewer is looking for: the bond-like convention and the fixed basis-point value.*

**Interview question 8.3 ★★ researcher, trader.**

What is the [convexity adjustment](#def-m2-short-term-interest-rate-futures-convexity) between futures and forward rates, and which way does it go?

**Solution of Interview question 8.3.**

Futures are margined daily, forwards settle once. A short future gains when rates rise, and reinvests the gains at high rates; it loses when rates fall and finances the losses at low rates. That correlation benefits the short, so the futures rate exceeds the forward rate; in a Gaussian model by about $\frac12\sigma^2 T_1 T_2$, negligible at the front, tens of basis points at ten years.

*What the interviewer is looking for: the direction and its reason, and the scaling with horizon.*

**Interview question 8.4 ★★ trader.**

What is a pack, and why would a trader trade the second year’s pack rather than the front contracts?

**Solution of Interview question 8.4.**

A pack is four consecutive quarterly contracts traded together: one year of the strip. The second year’s pack isolates expectations for rates a year ahead, the policy path after the next few meetings, without the front contracts’ exposure to the next meeting and to money-market noise; it is the cleanest futures position on the medium-term path.

*What the interviewer is looking for: packs as a way to trade a segment of the curve.*

**Interview question 8.5 ★★ developer, researcher.**

You build a service that publishes meeting-by-meeting implied rates every minute. What goes wrong at month-ends, around meetings late in a month, and at the year-end?

**Solution of Interview question 8.5.**

Month-ends: turn premia in the fixings, weekends that make the last fixing cover several days. Late meetings: the post-meeting rate is estimated from a few days, so noise explodes; switch to the next month’s contract. Year-end: a large turn that, if not removed, reads as a probability of a move. Also: stale prices in illiquid months, holiday calendars, and the day the new rate takes effect.

*What the interviewer is looking for: concrete failure modes with their fixes.*

**Interview question 8.6 ★★★ researcher.**

Futures imply a 35% chance of a hike. Is that the probability you should use to decide a trade? What would you need to convert it?

**Solution of Interview question 8.6.**

No: it is a risk-neutral probability, containing the premium investors pay to hedge the outcome they fear; it also assumes two outcomes and a known turn and spread. To convert: estimate the risk premium (from the history of implied against realised decisions, or from surveys), compare with your own model’s probability, and trade only the difference net of costs.

*What the interviewer is looking for: risk-neutral versus real-world, and how to estimate the gap.*