One of the most robust findings in international finance is that interest differentials do not point in the right direction for subsequent exchange rate changes. This means that *dollar* returns on say one year certificates of deposit in the US and in the UK are not on average equalized. In Chinn and Meredith (2004), we show that this anomaly — if it is one — disappears as one goes to longer horizons. This finding was discussed previously here.

In this post, I discuss new results regarding this finding, basing the discussion on Chinn and Quayyum (2012). The sample examined in Chinn and Meredith ends in 2000. Since then, the global financial crisis has introduced a tremendous amount of volatility and default risk into international financial markets. In addition, short and long term interest rates have descended toward previously unplumbed levels. (In addition, several of the exchange rates previously examined, such as the Deutsche mark, the French franc and the Italian lira). It therefore makes sense to re-examine the question of whether at long horizons, the previous results prove durable when a new decade’s worth of data is included.

*Some Theory*

It’s helpful to consider under what conditions *expected* dollar returns should be equalized for securities denominated in different currencies. This is essentially a no arbitrage profits condition, so it would require (1) no barriers to the free flow of financial capital, and (2) the securities be treated as otherwise equivalent in terms of default risk, and risk associated with how returns correlate with wealth or consumption (formally, the exchange risk premium is zero). Then:

*i = *Δ*s ^{e} + i^{*}*

Where *i* is the interest rate, Δ*s* is the exchange rate depreciation, superscript ^{e} denotes (market) expectations, and the superscript ^{*} denotes foreign variables. This is equivalent to:

Δ*s ^{e} = *(

*i-i*)

^{*}Note that the condition states that *expected* returns are equalized, and equivalently *expected*depreciation equals the interest differential. Now, one can’t test whether these conditions hold, because one doesn’t observe the market’s expectation of exchange rate depreciation. Typical practice is to assume the actual, realized, exchange rate equals on average the expected (i.e., the rational expectations hypothesis).

Δ*s = *(*i-i ^{*}*) +

*u*

Where *u* is a random error term; under the joint UIP and rational expectations hypothesis (known as the “unbiasedness hypothesis”), the error term is a true innovation, that is an error term with mean zero, and is unpredictable on the basis of all information available at the time expectations are made. If one runs a regression,

Δ*s = α + β*(*i-i ^{*}*) +

*v*

this relationship (with a coefficient on the interest differential of unity) might not show up in the data, either because of risk or because market participants make biased forecasts of subsequent exchange rate changes.What do the data look like? In short, there is a voluminous literature saying at horizons of a year that indicates the β estimate is typically *negative*.

*Empirics*

We confirm that short-horizon result, but find that, as in Chinn and Meredith, interest differentials at the longer horizons point in the right direction. However, even at long horizons, the effect is more muted than in the earlier study. This contrast is shown in Figure 1.

**Figure 1:** *β* estimates from panel regression of depreciation on interest differential, at 3, 6 and 12 month, 5 year and 10 year horizons, for sample extending to 2000 (blue bar), and 2011 (red bar). Panels do not contain same currencies in blue bars versus red bars. Source: Chinn and Meredith (2004), and Chinn and Quayyam (2012).One can see why the results show up the way they do, by examining the correlations at the different horizons. I show the scatterplots at 1, 5 and 10 year horizons.

**Figure 2:** US-UK Ex post one year depreciation against one interest differential. Source: Chinn and Quayyum (2012).

**Figure 3:** US-UK Ex post five year depreciation against five year constant maturity interest differential. Source: Chinn and Quayyum (2012).

**Figure 4:** US-UK Ex post ten year depreciation against ten year constant maturity interest differential. Source: Chinn and Quayyum (2012).Notice the progression; as the horizon gets longer, the slope becomes more positive. There are a number of reasons why this might occur. It could be that expectations are biased (this is examined in this paper). The other possibility is that the covariation between the exchange risk premium and the becomes less negative or more positive as the horizon is extended. This is the mechanism inChinn and Meredith (2004), as the central bank responds to shocks to the within period exchange risk premium.

*Why Do the Results Differ between Sample Periods?*

Figure 1 indicates that the slope coefficient is lower in the more recent study than in Chinn and Meredith. There is a degree of noncomparability, as the currencies covered change from the early study (which includes the euro legacy currencies, e.g., French franc) to the late study. Nonetheless, it does seem that the coefficients at long horizon are lower when incorporating more recent data. However, rather than arising from the behavior of all the currencies, this phenomenon seems to be driven by the Swiss franc and in particular the Japanese yen. In Figure 5, I present the scatterplot for the five year horizon, for the Swiss franc.

**Figure 5:** US-Swiss Ex post five year depreciation against five year constant maturity interest differential. Pre-1996 interest rates (red squares), post-1995 interest rates (blue circles). Source: Chinn and Quayyum (2012).In other words, we might expect that the long horizon results that obtained in an earlier period of fairly high interest rates might be attenuated for other currencies as long term interest rates stay at historically low levels. After all, as of Monday, US, UK, Swiss and Japanese ten year benchmark yields at 1.65, 1.52, 0.55, and 0.81% (Source: FT, accessed 8/27).