looking to calculate probability of a central bank rate hike… (not just US Fed).
I’m guessing it has to do with the term spread and market option premium??
I’m not a fixed income guy but I have done macro stuff. My understanding is that the implied probability of a rate hike comes by looking at the forward rate curve. If you assume that rate changes are going to be 25 bps, it’s fairly straightforward to back out a probability.
^ This. +1
example please good sir
Looking at the daily yield curves from the treasury:
I took Sept 14, 2015 data as an example, because the Sept 30 data is trickier to work with because you’re right up against the zero bound (actually, it would work, but it is easier to misinterpret the data).
My excel sheet might not translate to AF’s post pattern right, but I’ll try:
Sept 14, 2015 US Treasury Yield Curve Tbill Maturity Days Cur Spot Rate Imp Fwd Rte Delta Fwd Rate Prob of 25bps 1m 30d 0.02% 0.02% 0 0.00 3m 90d 0.07% 0.10% 0.08% 0.30 6m 180d 0.26% 0.45% 0.36% 1.42
Grr: Each “stanza” above seems to be one row of data, and each line of the stanza corresponds to a column (the header shows the order). What’s odd is that in my AF post area, I can format a table and it comes out right, but when I hit post, it throws away all the table structure info. 
Interpretation: Sept 14th prices imply a 30% chance of a 25bps hike between Sept 15th and Oct 14th (30 days), and a 100% chance of a 36bps or smaller hike between Oct 15th and Dec 14th (30 and 90 days).
This is a very simplistic model, but illustrates how you might do it. A more sophisticated model would try to estimate a liquidity premium (and perhaps others) for each of these securities, and discount it from the spot rates before computing the implied forward rates. There probably is not much of a liquidity premium for 30 vs 90 or 180 day securities however, so those effects are likely to be pretty small. Another improvement would be to try to create a continuous probability distribution around rate changes that is consistent with the data, but that requires further assumptions that I’d have to think about before going further.
The key idea is that the forward rate is an estimate of what interest rates would need to be like in the future for there to be a no-arbitrage opportunity between rates. It’s not a true arbitrage, because rates can go wherever the heck they like, but it does suggest that if you think rates are going to be somewhere other than where the forward rate is, you should be shifting out of one maturity and into another to take advantage of the arbitrage. Since some market participants are likely to do that, it suggests that this is where the average market participant (or at least the ones willing to try to do arbitrages like this) expects interest rates to be at these times in the future.
Pull out L1 books and draw out a probability tree via Bayes’ theorem.
Calculating the probability is easy. The Fed funds rate is perfectly negatively correlated to the amount of talking Fed officials do about raising rates.
The Fed is all bark and no bite on interest rates.
i would say its not nbegative 1 its 0
I just pull up the probability page on the Bloomberg terminal. It has it for several countries
Banks are more profitable when rates are higher and steeper.
This is not exactly a surprise, I don’t think, but here is a Bank for International Settlements working paper on “The influence of monetary policy on bank profitability”:
Overall, we find a positive relationship between the level of short-term rates and the slope of the yield curve (the “interest rate structure”, for short), on the one hand, and bank profitability – return on assets – on the other. This suggests that the positive impact of the interest rate structure on net interest income dominates the negative one on loan loss provisions and on non-interest income. We also find that the effect is stronger when the interest rate level is lower and the slope less steep, ie that non-linearities are present. All this suggests that, over time, unusually low interest rates and an unusually flat term structure erode bank profitability
Well, to financial analysts who understand that the archetypical bank model is to borrow at short term rates and lend at long term rates, this seems blindingly obvious. But to policymakers and others, it isn’t necessarily that obvious, so it’s good that there’s a paper to explain it.
It is surprising that it took this long for a paper like that to be researched and published as if this is news, though.
^ lol i know right
Specifically, you want to look at the forward curve for Fed Funds, or more conveniently the Fed Funds futures prices. When Bloomberg or other news sources say “probability of rate hike is X%”, they derive this estimate from Fed Funds futures.
The reason is that generic yield curves are affected by market structural risk premium, which creates a basis between the base rate (libor, fed funds, OIS) and the “market interest rate”. So, you want to directly refer to markets on the base rate.
CME has a very good description on their homepage.
http://www.cmegroup.com/trading/interest-rates/countdown-to-fomc.html
raising rates a good idea
This seems like a lot of hand waving. If banks want to make more net interest margin, they can increase the spread on their loans. How is that going to be improved by the fed raising their cost of capital.
Higher rates increasing confidence? Tell that to everyone whose on margin? Tell it to the people who are going to have to lower their home sale prices when mortgages are more expensive.
I get that rates close to zero for this long is unknown territory and that there are some dangers about hanging out here too long, but let’s not fool ourselves that higher rates pose some sticky issues.
Generally, it’s hoped that economic growth and hiring is robust enough that raising rates is not going to dampen it by more than just a little. That’s the main reason that rates aren’t rising now.
It’s not as simple to increase the spread on loans. But your right, deposits and other short term funding is expected to rise with the Fed funds rate. This doesn’t mean the longer term rate loans are priced off of would increase, which could actually make the curve less steep. It directly and immediately benefits the excess reserves and other cash balances held at the Fed. Not sure I agree it raises their cost of capital as much as their cost of funding.
Right, but if they can’t increase the loan spread, how are banks going to be more profitable with a higher fed funds rate?
Honestly I think most investors don’t actually understand the investment thesis they are deploying funds behind. What investors will do is take various disclosures to determine what company benefits from rising rates and they just determine this group of banks will benefit, this group won’t. I think you are thinking about it correctly that it probably won’t be that big of a deal outside a huge shift in sentiment (which will matter in the short term). But I don’t think the eventual fundamentals will reflect what people are expecting and I wouldn’t be surprised if most banks suffer. A 25 bps movement here and there in federal funds rate is inconsequential if the long end remains low.
The other, less talked about problem, is how the Fed decides to reduce the money supply. A lot of the 3 trillion in money created ended up on the balance sheets of banks. This could be a real challenge if that money supply starts to decline (from what i read, the Fed isn’t planning to suck it back out but time will tell)
I could see that rising rates might change the competitive position of banks, depending on the net duration of their assets, but if fewer people borrow money because (fed funds + spread) is now higher and the spread doesn’t change because banks don’t currently have pricing power, that sounds like a reduction in future bank interest income, and by extension 1) the present value of future earnings for that bank, and 2) a reduction in the overall money supply and thus (barring an unlikely change in money velocity) GDP.
Banks also tend to do well when the yield curve is steep, because lending long brings in money and borrowing short costs less, but the increase in the fed funds rate is likely to flatten the yield curve.
These articles that say “higher interest rates will increase confidence, and confidence will make money fall from the sky because people love to spend more when borrowing costs increase” just make me want to barf up froot loops in rainbow colors. It’s like saying, “if you smash your foot with a sledgehammer, it means you’re more confident that you can still run the marathon, so you should definitely do it if you’re worried about finishing.”
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I just think that a lot of people feel uncomfortable with rates close to zero and want to cash in on “being willing to say that we should take some pain” by pushing rates up to more normal levels (about 350-400 bps higher than where they are now). But when this moment actually comes, they’ll be squirming just like the rest of us, and if tighter money means we slide back into recession, well, let’s just hope they don’t own any assets other than cash.