Saw a tweet yesterday that said "The market has priced in a 100bps hike at a 25% chance".

How does one go about determining the % chance of different rate hikes being priced in?

Thanks

Movement of short term yields vs current fed funds rate.

Hmm I see how that might show you what the market has priced in as the expectation, but how do you know what the % chance is? Like if the market is pricing in a 25% chance 100bps, 50% chance 75bps, and 25% 50bps, how do you determine the chances of each expected hike?

Look at the price of an option of 10 year gvmt bonds

The price of the short is determined by two factors (a) pay-off and (b) prob. Of pay-off.

You know the pay-off so can work backwards from the price of the short and estimate the markets expected prob. of the short being in the money.

I m not sure tbh because I m in healthcare but given no one else has answered thought I d shoot

To be analytically correct, you should be looking at OIS swap spreads and/or fed funds futures. You can then use that pricing to assess probability.

for example, if SOFR is 2% and the OIS swap spread through next week is 2.83%, then 3+ hikes are priced for next week. And the market is saying there is a 68% chance of 75bps and 32% of 4 hikes (because 2.83 is 32% of the way from 2.75% to 3.00%).

Good comment. Indeed this is effectively the methodology used in the CME FedWatch tool linked above (https://www.cmegroup.com/education/demos-and-tutorials/fed-funds-futures-probability-tree-calculator.html) with a few variations (i.e., take the difference in fed funds futures, interpolate values as two nearest hikes).

The wrinkle (a friendly amendment!) that I would add is that it imperfectly captures real policy uncertainty, limiting the range of outcomes necessarily to at most two adjacent hikes.

Imagine, in your hypothetical, that the relevant difference was exactly 75bps -> the linear method makes it impossible to distinguish between "the fed is hiking 75bps for sure" and "the fed is 80% likely to hike 75bps, but 10% likely to hike 100bps (a la, e.g., Larry Summers), and 10% likely to hike 50bps (a la, e.g., Jeffrey Gundlach or Joe Stiglitz)" - so we shouldn't take the simple futures-based-probability model too seriously. Indeed, it is clearly not "analytically correct" taken literally. (To be clear, even at 83bps, it could be pricing some (small) probability of a 50bps hike.)

While it may be the case that, in this particular example applied today, following the elevated CPI print, we can safely rule out the 50bps hike case and conclude that it is either 3 or 4 hikes, as recently as Tuesday that was likely not true: we could have in good faith assigned probability mass to both 2 and 4 hike cases.

Excellent answers from both of you thank you I'm definitely learning. How would you go about predicting the probability of a hike that isn't adjacent to the OIS swap spread? (i.e. if it is between 75 and 100bps how do you calculate the odds of a 50bps since it is technically non-zero)

Agree but given the level of knowledge, wanted to keep the answer simple.

When you say 3+ and 4 hikes do you mean 1 hike = 25bps?

To get to 68% did you back in to that via 32% between 275 and 300?

Thanks.

When you say 3+ and 4 hikes do you mean 1 hike = 25bps?

To get to 68% did you back in to that via 32% between 275 and 300?

Thanks.

Yes. A hike is 25bps. And yes - if you assume there are only two options in my hypothetical, then you arrive at 68/32 by finding the weightings that arrive at a weighted average of 2.83%.

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