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In the context of managing the risk of (non-fixed rate) debt where the interest rate is linked to a bank base rate, I want to understand how/where to get a sense of where a bank's base interest rate is likely to change in future, by looking at how the financial markets view the future.

Is it appropriate & correct to assume that, for example, a ten interest year swap rate is a prediction of what the bank base rate will be in ten years?

For example the UK Bank of England base rate is currently 0.5%, and if ten year swap rates sit at 2%, is it appropriate to assume from that that the market believes the UK base rate will be 2% in ten years time?

If not, can you direct me to where I can see what the market believes the base rate will be in the future? I assume this is traded in some form somewhere to hedge.

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  • You can take them as implying that the parties involved have opinions on this, I think. No guarantee that either of them guesses right, never mind that the compromise between their guesses is accurate.
    – keshlam
    Feb 10, 2023 at 5:05

2 Answers 2

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I believe the Bank of England base rate you reference is similar to the Federal Reserve Federal Funds Rate in the US. This rate, which I’ll refer to as the central bank rate, is the rate that certain banks can borrow from the central bank for an overnight loan. This rate is not a market rate. It is set by a group of central bankers. They can set the rate to any value they please since they have the ability to produce an unlimited amount of funds (i.e. print money).

Interest rate swaps are used to speculate or hedge against a change in interest rates. For example, if I am currently paying interest on a floating rate loan and I believe that rates are going to rise then I can enter into an interest rate swap with another party and swap my floating rate interest payments with fixed rate interest payments. Interest rate swaps are quoted in terms of the rate paid by the fixed interest rate side.

If rates do not change at all during the life of the swap then I do not receive or pay any additional money. If rates rise during the swap period then I will receive the difference between the floating rate benchmark, which is typically based on London interbank offered rate (LIBOR), and the fixed rate. If rates go down I will have to pay the difference.

So back to your question: Do swap rates determine future central bank rates? Maybe but not necessarily. Central bank rates affect market interest rates but market interest rates do not necessarily affect the central bank rate. Banks can borrow money at the central bank rate and loan it out at the market rate pocketing the difference. A larger spread between these two rates will encourage more lending by banks. The central bank does not have to raise the central bank rate even if market interest rates are rising. Remember they can provide an unlimited amount of funds at any given rate. Usually, however, the central bank will have to raise the central bank rate as the market rate rises in order to prevent massive borrowing by the banks which can result in significant inflation.

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  • This makes more sense to me. I appreciate there's no way to know what rates will be in future, my aim is to get a sense of what the market thinks they will be, and it seems that the best we have is swap rates, which I realise are fairly volatile. My goal is a practical one, to get input to my own estimates of where rates will be, as it has a very significant impact on my business and needs to be planned for, even if based on estimates and assumptions.
    – Ollie C
    Nov 30, 2012 at 12:44
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It is common practice to use OIS swaps (as well as futures if available) to compute implied probabilities of interest rate hikes, see for example:

It is not as simple as saying that the 10y rate is 2% and therefore the expectation is 2%. I will provide few explanations below. I will mainly base the idea on futures because it is simpler to compute and more intuitive.

For example, the price of stock futures is simply a function of the spot price, interest rates and dividends and as such contains no information that the spot market does not contain (it's a simple no arbitrage argument).

On the other hand, interest rate futures / OIS rates cannot be calculated from another. There is interesting information inherent in interest rate future prices because the future for March 2023 is completely different from Feb 2024 and price setting relies on market expectations.

The general idea is always the same and looks like this:

  • 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: ![enter image description here

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

enter image description here

It is reasonably close to the value Bloomberg shows (3.12) for this meeting date. Note, this is why the 2% is not simply the expectation as long as the (expected) meeting date does not fall exactly on the maturity date of the future / swap (the second bullet point above.

The CME offers a tool similar to WIRP on BBG - the so called CME FED Watch tool, which provides the probabilities just like WIRP.

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:

enter image description here

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.

Strictly speaking, you cannot solve this for a 10 year swap because you will have several rate decision dates in between quoted tenors, as well as a degree of uncertainty about the actual dates of rate decisions. That's why Bloomberg only provides values for about 2 years from today.

However, Bloomberg offers a second tool called MIPR, where this complication is assumed away and only a simple "basis" adjustment is done in case the policy rate and effective rate is not identical (e.g. Fed Funds mid vs Fed Funds effective rate). This is very much in line with your idea.

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