The forward premium anomaly, discovered by Fama (1984), is one of the most prevalent puzzles in international finance. The uncovered interest parity (UIP) implies that high interest currencies should depreciate. However, a large body of empirical literature finds exactly the opposite high interest currencies tend to appreciate. Investors in high yield currencies benefit twice, once from the interest rate spread and once from the expected appreciation.
Given the complexity and resilience of the puzzle, economists have been searching for a potential explanation ever since its discovery. Approaches towards solving the puzzle may be organized into three categories: irrational expectations, market frictions and risk premia. This paper develops a two-country model under rational expectations without market frictions, and thus attributes the anomaly to large and time-varying risk premia.
This is achieved through two major model ingredients. First, markets are assumed to be incomplete. There is no asset that directly allows individuals to insure their income risk, preventing them from completely aggregating their individual risk. The extent to which insurance is possible depends on the correlation of income with existing financial assets. Second, we assume that consumers form habits according to their consumption history. The predominant effect of habit formation is that it changes the price of risk over time. When consumption drops close to the habit level, marginal utility increases and the implied risk aversion rises. Contrarily, a large wedge between consumption and habit implies small risk aversion.
We attribute the anomaly to time-varying international diversification decisions that arise endogenously due to the varying risk aversion. In the absence of habit expected exchange rates directly affect interest rates and thus the correlation between the two would be always plus one. Now, time varying risk aversion introduces time-varying international investment decisions, which are negatively correlated with the expected exchange rate. This allows, for sufficiently large habit levels, to overcome the primary effect and reproduce the negative correlation.
With habit levels common in the literature, we are able to reproduce the forward premium anomaly for six different country pairs, which are formed by combining Germany, Japan, United Kingdom and United States. We distinguish between two different calibrations. In a first attempt, we assume the same habit level for each country. Although this implies an almost complete lack of flexibility in the model calibration the UIP slope is still almost within the 95% confidence interval of the empirical estimation for each country pair. In a second attempt, we allow for different habit levels for each country pair. Then the slope of each country pair lies within one standard deviation of the empirical observation.
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Time-Varying International Diversification and the Forward Premium
