Friday, 21 June 2013

The Short Rate, the Long Rate and the Exchange Rate

Reading about the market reaction to Bernanke's comments on a possible end to monetary stimulus, I was interested to note the appreciation of the dollar being generally attributed to associated expectations of a rise in dollar short rates.

Whilst this may indeed be the case in this instance, it's a good opportunity to highlight that there are two quite distinct reasons why we might expect an announcement on asset purchases to have this effect on the exchange rate.  It would be quite reasonable to expect an exchange rate impact, even if expectations of short term interest rates remained anchored.   The mechanics behind this are closely related to the way I have looked at Modelling QE.

For this type of analysis, it can be useful to think in terms of expected single period rates of return.  To simplify, we can think in terms of two asset classes: deposits, carrying a short rate of interest and bonds with a long rate.  For our single period, the return on deposits is known, but the return on bonds is not, because the latter depends on how the bond price changes in the period.  We therefore need to use an expected return, based on what the bond price is expected to be at the end of the period.

In the simplest models, the actual return on deposits and the expected return on bonds will be equal.  The assumption is that if they were not equal, investors would keep trying to switch their portfolios until the change in demand drove the expected returns into line.

This assumes that the two assets are perfect substitutes, but in reality there are plenty of reasons for believing they are not.  More sophisticated models will recognise that the two rates will typically be different.  The difference might be attributed to a liquidity premium or a term preference.  For convenience, I am going to call the excess of the expected single period return on bonds over the short rate the term preference (noting that this value could be positive or negative).

The important point here is that  the size of the term preference is a function of demand and supply.  For whatever reasons (often institutionally), there will be some investors that want exposure to long term rates and some that want exposure to short term rates. At the same time the relative supply of short term and long term assets may vary (through QE for example).  This is going to change the value of the term preference.

We can extend this analysis to the long term.  The expected long term return on bonds will be the compound of all the expected single period returns (that is, all the future returns expected now).  The expected long term return must equal the actual return (if a Treasury yields 2% to maturity and I expect it to yield 3% to maturity, I'm clearly mistaken).  In which case, the actual yield on bonds is equal to a compound of:

1. all the expected short term rates from now until the bond maturity; and
2. all the expected values of the term preference from now until the bond maturity.

where, in each case, expected means expected now.

So, when the bond yield changes, it may represent a change in expectations of future short rates, or it may represent a change in expectations of the term preference, or maybe a combination of both.  However, whilst it's possible that a change in asset purchases might not result in any changes to the actual short rate, it is highly unlikely that it will not lead to any changes in the term preference, as that would imply that investors were indifferent between long and short rate exposure.

Therefore, where the bond yield changes in response to an announcement on asset purchases, we know for sure that the expected value of the term preference has changed, but we don't necessarily know what it implies about the expected course of future short rates.

This has all been about changes in the domestic term structure.  How does this relate to the exchange rate?  The important point here is that what matters to the exchange rate is not just the short rate on deposits, but also the expected single period rate of return on bonds.  If investors with long-term rate preference invested exclusively in the domestic market, then this might not matter.  However, this does not appear to be the case; cross-border holdings of long-dated securities are substantial.  The demand and supply for these assets (which has immediate impact on the exchange rate) depends on the single period expected return on long assets, not on the short rate.

In conclusion, an announcement on asset purchases may do two things: it will definitely have an effect on the term preference; but it may also have an effect on expectations of short term interest rates.  These two effects are quite distinct, but both will have an impact on the exchange rate.

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