Inferring Expected Fed Rate Changes from Futures and OIS

# Number of Fed Rate hikes prices in


# Number of Fed Rate hikes prices in












Could someone please explain to me how the calculation of the market expected FED rate hikes is done?

Thank you.

## Answer by AKdemy (score 3)

https://quant.stackexchange.com/a/81460

This screenshot is using data computed from Bloomberg's WIRP tool.

One can use futures or OIS swaps for this task. The latter even has central bank meeting dated tenors. The general idea is the same though:

- Under the assumption that only central bank actions will impact the effective interest rate of an economy, you can push the expected overnight rates forward and backward through the tenor structure.

- With futures, you get the chain (all tenors) and look at the individual dates. Some contract months will not span central bank meetings, others will. Therefore, you have the future representing the average rate over the period, where it could be higher/lower prior to the meeting date, lower/higher after the meeting date. You can carry the rate forward where there is no meeting - meaning you know the rate prior to the meeting date - and solve the equation $$days_{total}*Future_{meeting_{month}} = days_{prior_{meeting}}*Future_{prior_m} + days_{after}*r_{implied}$$

To provide a specific example, let's look at the FED Funds futures on Bloomberg. In case you have access to BBG, you can look at {WIRP} and {FFA Comdty CT} for the following screens:

Computing the above logic with the market data results in the following lines of

```
days_total = 31
days_prior = 2
days_after = days_total - days_prior
future_meeting_month = 3.13
future_prior_month = 3.225

r_implied_may = (future_meeting_month*days_total - future_prior_month*days_prior)/days_after
```

It is reasonably close to the value Bloomberg shows (3.12) for this meeting date. Maybe they use a slightly different logic but the general idea holds (e.g. settlement prices vs Last traded price vs a snapshot of prices at some given time or they adjust for the "basis" between the current rate and the mid between the upper and lower bound or the like).

You compare this number to the current ON rate to see the number of 25bp hikes as shown on the screen.

The CME offers a tool similar to WIRP on BBG - the so called CME FED Watch tool, which provides the probabilities just like WIRP (that's also something frequently looked at and discussed in the market).

Apart from futures, you can also look at OIS swaps, which for some countries even have directly quoted central bank meeting date swaps. If not, you can still rely on the following equilibrium: $$ 1 + \frac{r*n}{360} = \prod_{i=1}^n \left(1+ \frac{r_i*d_i}{360}\right)$$ where the left hand side is the fixed part (r is the quoted OIS price / fixed rate), and the RHS the floating part, with $r_i$ denoting the expected floating rate on the $i^{th}$ day, $d_i$ the number of days $r_i$ applies for (1 for weekdays, 3 for weekends) and n is the total number of days for the swap. Since r, n and $d_i$ is known, you can solve this.