"The purpose of the current paper is threefold. First, we document an intriguing empirical regularity that investors in countries of low interest rates tend to earn substantially higher returns on popular carry strategies than investors in countries with high interest rates. Second, we propose a simple procedure to construct country-specific stochastic discount factors (SDFs) to price carry trades and other assets in FX markets. Third, we evaluate the constructed discount factors in their ability to price stock market and macroeconomic risks. Below, in the same order, we elaborate on the merits of these findings."

"First, dierent countries price an identical risk unequally, because the same risk covaries differently with each country's marginal utility process (or SDF). For instance, the Japanese business cycle does not completely synchronize with the US cycle, and an investment strategy paying well when the Japanese economy's output is low (a hedge for the Japanese economy) is not necessary a hedge for the US economy. Consequently, the same strategy offers a higher return in USD than in Japanese Yens (JPY). For the same reason, a hedge fund's Tokyo office boasting a local 70%-Sharpe ratio does not necessarily outperform its New York office delivering a 50%-Sharpe ratio, if these statistics are risk-adjusted in their respective currencies. This observation does not arise because the strategy's return has a higher volatility when it is denominated in USD. While a change in volatility resulting from a change in the currency denomination is a possible contribution to the risk profile, our observation holds true for strategies with identical volatilities across currency denominations. Speciffically, we focus on net-zero investments, which have identical volatilities across all currency denominations – a property we refer to as diffusion invariance."

"Second, in a complete market setting, all risks in FX markets (all fluctuations in exchange rates) are priced by at least one country's SDF. This is in contrast to stock or other asset market fluctuations, part of which are idiosyncratic and not priced. FX markets are special because an exchange rate between two currencies is the ratio of the two countries' SDFs and the loading of an exchange rate on a risk source is equal to the difference in the two involved countries' prices of risk. Any shock to an exchange rate must be a shock to at least one SDF, and thus, all exchange rate risk must be priced by at least one SDF. FX markets offer an ideal setting to estimate market prices of risk and study how exchange rate risks are priced. In the context of a diffusion model, we employ a principal component analysis (PCA) to characterize the principal exchange risks in the market. Our PCA explains return differentials across currency denominations on the same carry trade strategy. Building on the PCA results, we construct a time-series of the SDF for every country by minimizing the carry trade pricing errors incurred by these SDFs. Our estimation is non-parametric and only uses observable price data as inputs. This is in stark contrast to other papers that either require strong assumptions on preferences and wealth distributions, or need noisy macroeconomic data as inputs. "

"There is an important limitation to our approach. While all exchange rate risk is priced, we cannot guarantee that all priced risk sources affect FX markets. Consider every country's SDF assigns an identical price to a risk source. The risk is clearly priced, but it is impossible to detect it in FX markets because there is no exchange rate with a non-zero loading on the risk source. Global and undetectable risks exist, and in our view are a crucial factor responsible for the observed "disconnection" between currency and stock markets. We quantify the "connection" between FX and stock markets using our constructed SDFs to price stocks. Our estimated SDFs generate about half of the equity premium, which demonstrates that the prices of risk inferred from FX markets price a nontrivial portion of stock market risks. Our constructed SDFs are also able to single out important events such as the market turmoils in the early 2000's and 2008-2009."

"Third, we look beyond the price data into macroeconomic factors to understand which fundamentals of the economy influence the pricing in FX markets. If a macroeconomic factor is important to a country's economy and currency, its fluctuations should affect the country's marginal utility and exchange rate. We examine the volatility as well as the covariance of macroeconomic factors with innovations in our constructed SDFs. In the cross section, we find strong evidence that fluctuations in output gap, which measures the difference between an economy's realized and potential (optimal) output, is a prominent macroeconomic risk which is priced in FX markets. Output gap volatilities and cross-country correlations exhibit significant and positive relationships with volatilities and cross-country correlations of our constructed SDFs. Because output gap is an important macroeconomic indicator inherent in business cycles, our findings lend supports to the basic economic intuition that the pricing of carry trades across currency denominations are intrinsically related to marginal utilities of the economies involved."

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