Currency Risk Premia

The daily trading volume of the foreign exchange market is over 7 trillion USD.

The daily trading volume of the foreign exchange market is higher than the daily trading volume of global stock markets (approximately $600 billion) and much higher than global GDP (approximately 101 trillion USD annually in 2022).

The foreign exchange market is characterized by over-the-counter (OTC) trading, an increasing share of FX derivatives, electronification of FX markets, concentration of trading in a few financial hubs, fragmentation across dealers’ proprietary platforms, relatively large size of individual transactions, low transaction costs, and settlement risk.

The most important currencies in global FX trading are the U.S. dollar (USD), Euro (EUR), Japanese yen (JPY), and Pound sterling (GBP).

A spot transaction involves the exchange of two currencies at a rate agreed on the date of the contract for settlement in two business days or less. A forward contract involves the delayed delivery of two currencies on an agreed future date, at an agreed price.

A foreign exchange swap involves the actual exchange of two currencies on a specific date at a rate agreed at the time of the contract, and a reverse exchange of the same two currencies at a date further in the future at a different rate.

The nominal exchange rate is the price of a base currency in terms of the quote currency.

The log excess return of a zero-cost strategy that borrows in USD and invests in foreign currency is given by: $$r_e^{t+1} = s_{t+1} - s_t + i^*_t,t+1 - i_t,t+1$$

Covered interest rate parity (CIP) implies that the forward rate equals the spot rate adjusted for the interest rate differential between two currencies.

Using CIP, the forward rate can be calculated as: $$f_{t,T} = s_t + i_t,T - i^*_t,T$$

Uncovered interest rate parity (UIP) states that the expected return from investing in USD and the foreign currency should be the same, implying that the expected change in the nominal exchange rate should exactly compensate for any difference in interest rates.

UIP does not hold in practice because currencies with high interest rates tend to appreciate rather than depreciate, contrary to UIP predictions.

The regression model used to evaluate UIP is: $$s_{t+1} - s_t = \alpha + \beta (i_t,t+1 - i^*_t,t+1) + \epsilon_{t+1}$$

Common risk factors in currency markets include country-specific and global risk factors that determine interest rates and exchange rates. Exposure to the global factor should be priced.

The HML FX portfolio is constructed by sorting currencies on their forward discount (interest rates) into portfolios and constructing a portfolio that is long high interest rate currencies and short low interest rate currencies.

The carry trade strategy involves going short in low-interest rate currencies and long in high-interest rate currencies.

The most popular currencies for the carry trade are CHF, JPY (short), and NZD, AUD, NOK, and emerging markets currencies (long).

The downside risk associated with the carry trade includes the potential for significant losses during market crashes, as high interest rate currencies tend to earn high risk premia due to their heavy load on downside risk.

Global imbalances affect currency returns as countries with external foreign-currency net debt have to compensate investors with higher average returns as their currencies depreciate in bad times.

FX momentum refers to the tendency of past winners to outperform in the near future.