# Rate Cut Probabilities

When discussing upcoming rate cuts, you’ll often hear news services talk of the ‘probability’ of a cut or what the market has factored in. For the Australian market, here is how to calculate the probability.

The cash rate futures trades on the SFE settle at the end of the month at a price that equals the average cash rate for the month. As a simple example, if rates are 5% for half of the month and 4% for the other half, the futures will settle at a price of 95.50 (100 minus the rate).

We can use the current trading price to calculate the probability of a rate cut leading up to the RBA rate decision. Here we go:

The formula is:

TP = 100 – [[ (R1 * DB) + (R2 * DA * P) + (R1 * DA * (1-P)) ] / D]

Where:
TP = Trading Price for current month IB futures
R1 = Cash rate before the rate decision (and the value if it were left unchanged)
R2 = Cash rate should there be a cut
D = Total days in the month
DB = Days of the month before the rate decision
DA = Days of the month after the rate decision

This formula naturally only looks at two possible outcomes: a rate change of a defined amount (e.g. 25bps) or rates left unchanged

So for December 2011, the morning before the RBA decision, we have:

TP = 95.66
R1 = 4.5%
D = 31 days
DB = 6 days
DA = 25 days
R2 = we will set at 4.25% – implying a cut of 25bps, the general market consensus.

Plugging these numbers into the formula and working backwards, we can calculate the market expectations for a rate cut.

95.66 = 100 – [[ (4.50 * 6) + (4.25 * 25 * P) + (4.50 * 25 * (1-P)) ] / 31]

Using a little trial and error in Excel, we come up with a 79% chance of a cut.

So Where To Next?

After the rate decision, and assuming the only two possible outcomes are rates at 4.50% or 4.25%, the IB futures will either rally a fixed amount of sell off a fixed amount.

If we see no change, the IB futures will fall to 95.50, implying no change for the rest of the month (i.e. no emergency cut later on) and rates remaining at 4.50%.

If we see a cut, the IB futures will rally. To calculate where they will rally to, again assuming this cut will be the only one this month, we can use the formula above setting P at 100%.

100 – [[ (4.50 * 6) + (4.25 * 25 * 1.0) + (4.50 * 25 * (0.00)) ] / 31]

= 95.701

This means with a 25bps cut later today, the IB futures will rally to 95.70 or thereabouts. A trade at 95.705 or even 95.71 is the market factoring in the tiniest chance of another cut this month – this kind of thing is not unusual.

So How Do You Trade the Current Month?

1. Take a punt ahead of the data

The market is trading 95.66 right now. To take a punt on a 25bps rate cut would yield a 4pt gain if there is a cut, but potentially lose 16pts if there is no cut. If we say the approximate chance of a cut is 80%, then take a look at the mathematical expectation of the trade:

(4pts * 80%) + (-16pts * 20%) = zero

You could also do the opposite. That is, sell the futures at 95.66, gain 16pts if there is no cut and stand to lose 4pts if there is a cut. Given the higher chance of a cut, the mathematical expectation is the same – zero.

Either strategy is just a punt. You would be taking a position on what the RBA do behind closed doors.

Once on a while, the post decision price adjustment can overshoot what we might call fair value for the current contract. This happened in the Nov contract after the November rate decision. The Nov contract gapped up 16pts over (see below) where it should have been trading. The price lasted for a few seconds before the ‘overvaluation’ was hit with selling. So the trade would the pre-emptive trade to make be offering anywhere above 95.70 and bidding anywhere below 95.50? Absolutely – only on the assumption of no further cuts and no hikes this month. Nothing comes without risk of course.

Binary or not?

As mentioned above, all of that assumes only two possible outcomes – a 25bps cut or no change. In reality, they could cut by 50bps or there could be another cut later in the month. If Europe falls apart for example, an emergency cut is not that unrealistic.

So what does that mean for pricing? Quite simply, the Dec futures will maintain a small risk premium, perhaps just a couple of ticks. This premium represents the chance of additional action. So instead of falling to 95.50, the market might be a tick or two above. Instead of rallying to 95.70, again, the market might be a tick or two above.