Hi. I’m having a difficult time understanding the solution to the question below, specifically why they calculate the probability for a 25bps rate hike?
“Sarah Ko, a private wealth adviser in Singapore, is developing a short-term interest rate forecast for her private wealth clients who have holdings in the US fixed-income markets. Ko needs to understand current market expectations for possible upcoming central bank (i.e., US Federal Reserve Board) rate actions. The current price for the fed funds futures contract expiring after the next FOMC meeting is 97.175. The current federal funds rate target range is set between 2.50% and 2.75%”
In the solution they assume that the new range will be 25bps higher as follows;
"Ko should determine the probability of a rate change. She knows the 2.825% FFE rate implied by the futures signals a fairly high chance that the FOMC will increase rates by 25 bps from its current target range of 2.50%–2.75% to the new target range of 2.75%–3.00%.
Why do they make that assumption of 25bps? Its not in the question. Why not a 30 or 40 bps hike assumption?
25 bps is a convention for rate range widths, and also a common assumption the market uses when predicting target rate adjustments. This is because the FOMC makes moves in 25 bps increments or multiples thereof. Here the implied FFE is 2.825% so the expected new rate range would be 2.75% to 3% (capturing the 2.825% inside it). Because that is the 25 bps range covering the implied rate here.
That’s also why you see the original target range in the problem was 2.5%-2.75% (25 bps).
For a more detailed explanation you can read here:
https://www.cmegroup.com/education/demos-and-tutorials/fed-funds-futures-probability-tree-calculator.html#
On a mock exam they may ask, for example, whether it is likely or unlikely the Fed will adjust rates 25 bps. In that case you just run the formula to determine that probability. If the FFE implied rate from futures is greater than a 25 bps difference, then you can calculate the probability of the new change to that larger rate range up/down (which still will land at a range 25 bps in width regardless, by convention). The new target range will be whatever the 25 bps range is that encaptures the implied rate, and you can calculate the probability of that change happening by using the formula.
Folks often think of 25 bps adjustments up/down in typical scenario. But the width of the target rate range is always 25 bps regardless. So if the implied rate in futures is 2.8%, the predicted target rate range can be 2.75-3%. If the implied rate is 3.1%, the predicted target rate range can be 3-3.25%. To calculate the probabilities of that predicted target rate range happening, run the formula.
Cheers - you got this 
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Well explained. Thank you.
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