Negative interest rates don’t seem to make a lot of sense.
People value money now, more than potential money in the future. You need to pay people to deposit their money longer-term.

Think about it…

This means interest rates should always be positive. The lognormal distribution is often used for interest rate moves. This does not allow negative rates1. Besides, if it costs money to lend money, it seems likely that people will stop lending.

That’s the theory; what’s the reality?

Like a great many arguments this is reasonable, feasible, and provably false.

Here's why:

Short-end European and Swiss interest rates have been negative for a while, and the ECB’s deposit rate is now -0.2%. Whether it’s logical or not, whether it makes sense or not, it can happen and is happening. So it’s worth thinking a bit more about why and how this might come about. 

In theory there should be a floor on interest rates. At some point it is better to hold physical cash2. If nothing else, assuming investors like money, no-one will buy a 1-year bond at -100% interest. More immediately, for low enough rates physical cash would become an arbitrage opportunity. It would still have costs, including storage and insurance, inconvenience, and fraud and error.  Of these costs inconvenience could be the largest. Imagine the problems a large DB pension scheme would have posting cash to every member3.

As it turns out…

It is not clear how practical this arbitrage would be for the bulk of institutional funds. Most fund managers have operational and compliance requirements, and thus wouldn’t accept physical cash. There will be a floor somewhere, but it could be well below zero. Rates have gone negative, and so can go negative, but we have little sense of how much further they could go.

What does this mean for long term rates?


Source: Bloomberg, Redington

Swiss short-term rates have gone almost to -1%. There is no obvious reason why short-term rates may not fall lower than -1%. However, for long-term rates the picture is more complex. Long-term rates are just compounded short-term rates, so everything above holds. And while the yield curve slopes upwards (i.e. longer term rates are higher than shorter term rates) there will be some demand for longer-term bonds because of  carry and rolldown. As evidence, Swiss rates are negative up to 10 years out.

But that’s just part of the story…

The dynamics of long-term and short-term bonds are often different. There are many reasons why we might expect different behaviour. In particular, the motives for holding long and short term bonds are different. For example, flow is likely to be much less of an issue. Many of the arguments against replacing bonds with cash will thus be weaker. It may be that short-term rates have a much lower floor than long-term rates. Large negative long-term rates may not, in reality, be possible.

Are we close to the floor in rates?

One potential source of evidence is the size of rate moves down in a low rate environment. If rates are near the floor, we might expect rates to move by less as they approach it, and see a reduction in the size of short-term moves. If long-term rates cannot go below zero, then large falls from low levels should be extremely unlikely.

With a small data set we have to be cautious, but the findings are quite suggestive. Even in the long-end, the size of moves in rates has not shrunk as rates have fallen. This suggests any floor is still some distance away.


Source: Bloomberg, Redington


50-day Volatility GBP EUR JPY CHF USD
Current 0.61% 0.66% 0.50% 0.86% 0.74%
4Y Average 0.58% 0.66% 0.43% 0.57% 0.78%

Source: Bloomberg, Redington



Source: Bloomberg, Redington



It is not obvious whether long-term rates could go significantly negative. It is, however, quite easy to imagine rates being close to zero, or even marginally negative. What is clear is that GBP long-end rates are much higher than rates in comparable markets, and could still fall a lot lower.


[1] The CIR model is widely seen as an improvement on the Vasicek model for the same reason.

[2] Institutions could also hold deposits with central banks. The central banks could in extremis set their rates as low as they wanted, and the ECB rate is already negative.
[3] Credit card charges are another case in point. Most retailers are happy to accept credit card payments, despite the costs they incur, to avoid the inconvenience of only using physical cash. 


Author: Alex White

Alex joined Redington in 2011 as part of the ALM team. He is Head of ALM research, which involves projects such as: proactively modelling new asset classes and strategies, building and testing new models as needed for new business lines as well as a continuous review of current models and assumptions used. In addition to this, he designs technical solutions for clients who may require a bespoke offering to better solve the problem they are facing. Alex is a Fellow of the Institute and Faculty of Actuaries and holds an MA (Hons) in Mathematics from Robinson College, Cambridge.