# Dynamics of interest rates, exchange rates and bond prices within the UIP

There are already a few questions about the workings of the UIP and the exchange rate. What I have basically taken from those discussions is that one always has to distinguish between the spot rate and the expected future rate. Let's take the UK as our domestic country and the US as a foreign one, making the exchange rate E_t = X \$/£. If the UK increases its interest rate, the spot rate will, ceteris paribus, increase due to capital flows into the UK. Now, since the UK interest rate is still above the US interest rate, one would expect the pound to depreciate versus the dollar, i.e. the future expected exchange rate would decrease. This was just to establish my understanding of the UIP, in case my reasoning is flawed in some way.

The point that after the capital flow into the UK and the spot rate increase, there is still an interest rate differential, is crucial for my reasoning that follows below.

What I don't understand is how the future expectations part of the UIP can be reconciled with the relationship between interest rates and bond prices. Let's take again the above example. If the UK increases its interest rate above the US interest rate, there will be a flow of capital from the US into the UK, because UK bonds promise higher returns. This, in turn, will drive those bond prices up. On the other hand, because people will sell US bonds, the prices of US bonds will go down. Now, since interest rates and bond prices are inversely related, the flow of capital into the UK and the increase in bond prices will drive the interest rates on those bonds down. At the same time, the flows of capital out of the US and the decrease in bond prices will drive the interest rates on US bonds up. This will cause both interest rates to equalize again. What I fail to understand now, is why we would still expect a future depreciation of the pound / appreciation of the dollar, if the interest rate is already equalized in the first place due to the relationship with bond prices. Because in order to use the UIP, there must be an interest rate disparity that will cause the currency of the country with the higher interest rate to depreciate in the future.

Somewhere there must be a flaw in my reasoning, but I fail to see where. My guess is that it has something to do with the time dynamics involved. However, in the usual understanding of UIP dynamics that I have described in the first paragraph, the spot rate adjusts immediately after the increase in the interest rate due to capital flows into the UK. So if these capital flows are taken as an "immediate action" after the interest rate change, bond prices would have to adjust immediately likewise, and the interest rates would have to be equalized again. This would also make sense as the UIP assumes perfect capital mobility.

Can someone see where I fail to consider something?

## 1 Answer

One possible flaw in your reasoning is your assumption about what happens to bond prices when there are capital inflows. For example , suppose that the Bank of England has fixed short term interest rates at 1%, and that the yield of 5yr gilts is also 1%. Then there is a sudden unexpected rise in the Bank of England rate to 1.5%, resulting in capital inflows to Sterling investments and thus a rise in the FX value of the pound. However, the short term interest rate is still 1.5% because it is fixed by the BoE, and the 5yr gilt yield is likely to settle at a yield much higher than 1%, depending on the reason for the interest rate raise. If the BofE says there will be a series of hikes, this yield could settle at 2% or higher. If the BofE says it is a ‘one and done’ hike, it could settle lower, say 1.25-1.50%. These numbers are all made up, the point being that it is unlikely that the bond yields stay at 1% when the BofE has raised its short term rate, which appears to be an assumption you made.

• Thank you so much for the quick answer! This already clarifies a lot. Just to see if I fully understood your comment: I think the fact that interest rates decrease when bond prices increase (due to foreign capital buying UK bonds) is well established. So what you're saying is that the BofE would hold the 1.5% rate fixed, i.e. it would somehow have to counteract this downward pressure on the interest rates from the bond price increase? And it would do this through a series of hikes? – Luca Dec 26 '20 at 13:41
• Yes the BofE would hold the 1.5% overnight rate fixed. Bond market participants would not let the yields on longer dated bonds fall back to 1% , given that the overnight rate is 1.5%. – dm63 Dec 26 '20 at 14:32