Currency valuation and risk premia

Lukas Menkhoff, Lucio Sarno , Maik Schmeling, Andreas Schrimpf

30 June 2016



What is the appropriate way to assess currency valuation levels? And how can this knowledge be operationalised to improve economic decisions? Answering these questions is crucial for global investors and policymakers, who usually devote substantial resources – financial and human – to building tools for this purpose. In turn, these ‘currency value’ estimates trigger actual investment decisions and policy responses.

A core building block of any method to determine currency value is purchasing power parity (PPP) and the related concept of the real exchange rate (RER). Real exchange rates embed expectations about future macro fundamentals and currency risk premia, rendering them useful gauges of future currency excess returns (Engel and West 2005, Froot and Ramadorai 2005). They also play a major role in theoretical and empirical exchange rate models. Yet, the way in which currency valuation measures relate to future currency movements is far from being well understood.

Measuring currency value

In a new paper, we shed light on the question of how to measure currency value and how this knowledge can be used to obtain more precise estimates of currency risk premia (Menkhoff et al. 2016).

A useful model of currency value should display some simple basic properties, but above all a currency that is overvalued should underperform an undervalued currency going forward, and vice versa. This property implies that a currency value measure should have predictive power for variation in future exchange rate movements and excess returns in the cross-section of currencies. Hence, testing whether a specific value signal delivers on its promises involves measuring the economic value in the information embedded in the measure in out-of-sample prediction.

We tackle this question using data for a large set of currencies and by means of both panel regressions and portfolio sorts. Building portfolios to mimic the returns to a currency value investment strategy allows for a straightforward assessment of the economic significance of the link between real exchange rates, fundamentals, and currency risk premia.

Conceptually, the RER is driven by three components:

  1. Expected excess returns (currency risk premia);
  2. The expected real interest rate differential; and
  3. If long-run PPP fails to hold, the long-run expected RER.

Hence, adjusting the RER for macroeconomic fundamentals related to the latter two expectations should in principle result in a cleaner measure of risk premia. It is this basic, yet powerful idea that we study in great detail.

Which fundamentals drive the real exchange rate?

In the empirical analysis, the fundamentals we use to adjust real exchange rates for movements of expected macro variables are motivated by the international economics literature. We focus on (i) Harrod-Balassa-Samuelson (HBS) effects (measured as real GDP per capita), (ii) the quality of a country's exports, (iii) net foreign assets (a measure of net foreign wealth of a country), and (iv) output gaps.

Each of these variables bears a clear link to long-run expectations of the RER and/or expected real interest rate differentials. Most prominently, HBS effects capture the stylised fact that highly productive economies tend to have persistently stronger real exchange rates than less productive ones. Another key variable associated with RER variation is the quality of a country's exports. Differences in the quality of traded goods (i.e. a departure from the assumption of homogeneous tradable goods) will lead to persistent differences in price levels across countries such that PPP may be violated over prolonged periods of time. It has also been shown that net foreign assets (NFAs) capture global imbalances that require exchange rate adjustments as part of the mechanism that leads to sustainable current account positions (Gourinchas and Rey 2007, Gabaix and Maggiori 2015). NFAs thus likely play a key role as determinants of currency valuation levels. Finally, output gaps capture the different states of the business cycle across countries. Given their prominence in the reaction function of central banks, output gaps are key indicators of current and expected interest rate differentials across countries.

In fact, we find that all four fundamentals have predictive power for real interest rate differentials. This makes them useful devices to purge the effect of fundamentals from the RER, which in turn helps to obtain a cleaner risk premium measure for investment decisions, and allows for a better understanding of the information contained in the RER.

Currency value and prediction of currency returns

Indeed, we find that value measures computed from the RER generally display predictive power – countries with a weak RER against the US dollar (that is, their currency has become cheap in real terms compared to the dollar) have higher excess returns going forward than countries with a strong RER. Translating this predictability into a currency value investment strategy results in a Sharpe ratio of about 0.5 per annum, and this profitability of simple currency value strategies is in line with what has been reported in earlier work (e.g. Asness et al. 2012).

However, standard currency valuation metrics based on the RER should be appropriately adjusted for expectations about future macro fundamentals. Purging the impact of expected fundamentals from the RER boosts predictive power of the currency value measure and the resulting profitability of currency value strategies, generating Sharpe ratios in the range of about 0.8-0.9 per annum. The rise in Sharpe ratios largely stems from the lower return volatility of the proposed value strategy. A natural interpretation of this finding is that adjusting the RER for fluctuations in fundamentals (which are not necessarily related to future risk premia) yields a less noisy signal of what constitutes currency value. Currency risk premia will thus be revealed with higher precision.

This effect is also visible from simple predictive regressions of future currency excess returns on lagged RER with and without controls for macro fundamentals. The upper panel of Figure 1 shows the predictive coefficient of the RER for future excess returns over forecast horizons from one to 20 quarters based on panel regressions with time fixed effects. The lower panel shows the same coefficient estimate when controlling for macro fundamentals in the regression. As is evident from the figure, purging the effect of macro fundamentals yields stronger predictive power of the RER for future currency returns.

Figure 1. Impulse responses of currency excess returns to RER

Finally, one may wonder how measures of currency value, carry, and momentum are related. The answer is that they are largely unrelated. The returns of the value strategy accounting for macro fundamentals are not spanned by conventional currency strategies. In fact, our proposed currency value strategy receives a higher weight in the investors' ex-post optimal portfolio allocation than a classical carry trade strategy.


Determining ‘currency value’ is a century-old topic on which there is little consensus among economists. Our research suggests that one can derive useful gauges of currency value based on real exchange rates, which relate to exchange rate risk premia in the cross section of countries. This is especially the case when purging the real exchange rate of key macroeconomic fundamentals that are related to the real exchange rate but not necessarily to currency risk premia.


Asness, C S, T J Moskowitz and L H Pedersen (2012) “Value and momentum everywhere”, Journal of Finance, 68: 929-985.

Engel, C and K D West (2005) “Exchange rates and fundamentals”, Journal of Political Economy, 113: 485-517.

Froot, K A and T Ramadorai (2005) “Currency returns, intrinsic value, and institutional-investor flows”, Journal of Finance, 60: 1535-1566.

Gabaix, X and M Maggiori (2015) “International liquidity and exchange rate dynamics”, Quarterly Journal of Economics, 130: 1369-1420.

Gourinchas, P O and H Rey (2007) “International financial adjustment”, Journal of Political Economy, 115: 665-703.

Menkhoff, L, L Sarno, M Schmeling and A Schrimpf (2016) “Currency value”, CEPR Discussion Paper No 11324 (forthcoming in Review of Financial Studies).



Topics:  Exchange rates Global economy

Tags:  real exchange rates, currency valuation, risk premia, risk premium, productivity, export quality, foreign assets, output gap, exchange rate

Professor of Economics, Leibniz Universität Hannover

Professor, Associate Dean and Head of Finance Faculty, Cass Business School, City University London

Professor of Finance, Cass Business School

Senior Economist, Bank for International Settlements