Negative nominal interest rates have been a striking feature of the macroeconomic and financial environment since the Global Crisis. Switzerland, which has had negative nominal interest rates for more than three of the last five years, was the first economy to experience negative interest rates in a substantive way. It has also experienced the largest negative interest rates in absolute value. A number of other economies have also implemented negative nominal interest rates, both small countries like Denmark and Sweden and powerhouses like the Eurozone and Japan.

Negative interest rates have consequences for banks, the banking industry, and the broader financial sector (Arteta et al. 2016, Viñals et al. 2016). Our recent research focuses on the consequences of negative nominal interest rates for exchange rate behaviour. So far, the consequences appear to be negligible.

## Exchange rate volatility and negative interest rates

Our data set begins in January 2010. This reduces the effects of the Global Crisis and Great Recession, while including a period of comparable data before the onset of negative interest rates. It uses daily data, the highest frequency that is reliably available for a wide range of countries, so there is a large cross-section of data to analyse a problem with a limited time series. We used conventional spot and (one-month) forward exchange rates, and Bank of England effective exchange rates, for the 61 available currencies available. Our (annualised one-month) interest rates were also conventional (our series are more fully described in Hameed and Rose 2016).

Figure 1 shows time-series plots of the Swiss effective exchange rate and the (annualised 1-month Libor) Swiss interest rate. Swiss interest rates (the dashed line, labelled on the left axis) first went negative briefly in August 2011. This was shortly after a sudden appreciation of the Swiss franc (the solid line labelled on the right) caused the Swiss National Bank (SNB) to diagnose a 'massive overvaluation'.

This triggered a relaxation of monetary policy to protect competitiveness and reduce deflationary pressures. SNB policy innovations included quantitative easing, swap transactions, and most radically, the establishment of a floor on the euro/Swiss franc exchange rate on 6 September 2011. Swiss interest rates then fluctuated around zero until the dramatic events of mid-January 2015, when the SNB removed the exchange rate floor, lowered interest rates to substantially negative levels, and allowed the franc to appreciate.

**Figure 1 **Swiss interest and effective exchange rates, 2010-2016

The temporary spike of the Swiss franc in August 2011, and its jump appreciation in January 2015, are important features. But the volatility of the effective exchange rate seems unrelated to the interest rate level, with the exception of the events of August 2011 and January 2015. There is no theoretical reason to expect a relationship, either positive or negative, between exchange rate volatility and nominal interest rate levels. The question is whether there is a relationship in practice. Since bilateral exchange rates necessarily involve two currencies, and thus two interest rates, it is easiest to visualise the relationship between a single interest rate level and the volatility of an effective exchange rate. To measure volatility, we use the standard deviation of the first difference in the log of the daily effective exchange rate, calculated over the 21 business days that compose a month. Figure 2 scatters this monthly measure of Swiss effective exchange rate volatility against the level of Swiss interest rates. We also include a fitted least-squares regression line.

There are three outliers in Figure 2; each of these spikes in Swiss exchange rate volatility is clearly associated with the events that began and ended the Swiss exchange rate floor. But whether or not one ignores the outliers, exchange rate volatility does not seem to vary systematically as interest rates vary between small positive and substantially negative levels.

**Figure 2** Relationship between Swiss effective exchange rate volatility and domestic interest rate, 2010-2016

Figure 3 plots effective exchange rate volatility against the domestic interest rate for four major currencies (the US dollar, euro, yen and pound sterling) as well as for Denmark and Sweden, small economies that experienced negative interest rates. Least squares regression lines are also included. All of the major economies kept interest rates low during the entire period, while the two Scandinavian economies used wider ranges. There is no strong linkage between exchange rate volatility and the interest rate level for any of the currencies. In particular, negative nominal interest rates are not associated with more or less exchange rate volatility. More rigorous work in our paper bears this intuition out statistically.

**Figure 3** Relationship between effective exchange rate volatility and domestic interest rate for six economies, 2010-2016

## The relationship between ex post exchange rate changes and the forward premium

In theory, exchange rates and interest rates are tightly linked through interest parity conditions. Covered interest parity (CIP) is an arbitrage condition linking the forward premium – the spread of forward exchange rates over spot – to the interest rate differential. Uncovered interest parity (UIP) is a speculative condition that links expected or actual exchange rate changes to the forward premium (or equivalently, in the presence of CIP, the interest differential). Have interest parity relationships changed during the era of negative nominal interest rates?

Figure 4 is a scatter plot of the ex post one-month change in the bilateral euro exchange rate against the corresponding forward premium (the percentage difference between the 1-month forward and spot exchange rates). Since one-month exchange rate changes and forward premia are highly auto-correlated at the daily frequency, we graph only one bilateral observation for each business month (more on this below). Since bilateral exchange rate changes are correlated across economies, considerable cross-observation dependency remains (for example, when the euro appreciates against the Japanese yen, it is likely to appreciate against the Korean won).

We split our sample into four. The top-left graph plots exchange rate changes against the forward premium when euro interest rates are positive and at least 1.25%. The bottom-left graph shows the same relationship, but when euro interest rates are substantially negative – at least -.25%. Both graphs show a similar non-pattern.

The two graphs on the right are more interesting. Both scatter ex-post exchange rate changes against forward premia. The top-right graph shows observations where the euro interest rate is small and positive (between 0 and .05%), and the bottom-right graph when the same interest rate is small and negative (between 0 and -.05%). The pair of graphs on the right look similar.

**Figure 4** Ex post one-month change in the bilateral euro exchange rate against the forward premium, 2010-2016

## Unknown long-term effects

Negative nominal interest rates are a distressing and new feature of the economic landscape. While central banks manifestly think they are advantageous, the consequences for the financial sector are unknown, and may be larger in the long run than in the short run. We have ignored all such considerations in our short-run focus on exchange rate behaviour. Negative nominal interest rates have only affected a small number of economies for a short period of time, so it we should be conservative. But the data we have do not indicate that negative nominal interest rates have had substantive consequences for exchange rate behaviour.

## References

Arteta, C, M Ayhan Kose, M Stocker and T Taskin (2016), “Negative Interest Rate Policies: Sources and Implications” CEPR Discussion Paper No. 11433.

Hameed, A and A K Rose (2016), “Exchange Rate Behavior with Negative Interest Rates: Some Early Negative Observations” CEPR Discussion Paper No. 11498.

Viñals, J, S Gray and K Eckhold (2016), “The Broader View: The Positive Effects of Negative Nominal Interest Rates”, IMFdirect.