تغییراتی در روش نوسانات نرخ ارز و برابری بهره غیرپوشیده شده

We use a regime-switching model to examine how exchange rate volatility is related to the failure of uncovered interest parity. Main findings are as follows. First, exchange rate returns are strongly influenced by regime switches in the relationship between the returns and interest rate differentials. Second, low-yielding currencies appreciate less frequently, but once it occurs, their movements are faster than when they depreciate. Third, depreciation of low-yielding currencies and low volatility are mutually dependent on each other. Finally, these three findings are more evident for shorter horizons. The second and third results are consistent with a market participants’ view: short-term carry trades in a low-volatility environment and their rapid unwinding substantially influence exchange rates. We consider the effects of funding liquidity to explain these results.

Low-interest-rate currencies tend to depreciate relative to high-interest-rate currencies. This observation is inconsistent with one of the most popular theories, uncovered interest parity (UIP), but has been confirmed for many currencies and periods in the extensive literature on the subject. Even though more than 25 years have passed since Fama (1984) called this inconsistency the “forward discount puzzle”, the failure of UIP is still one of the most prominent puzzles in economics. In fact, there is no consensus on how to explain the puzzle yet, and researchers still continue to tackle the problem.1 In contrast, many market participants including monetary authorities have reached a consensus that depreciation of low-interest-rate currencies has been influenced by carry trade activities in a low-volatility environment.2 This view is well described in the speech of de Rato (2007), then Managing Director of the IMF. He said that the carry trades at that time reflected the environment of low volatility and wide interest rate differentials, and exerted downward pressure on one of the lowest-interest-rate currencies, the Japanese yen. This pressure, in fact, resulted in the gradual depreciation of the yen until the middle of 2007. He also warned that unwinding of carry trades could lead to rapid reversal movements of exchange rates, mentioning the episode that a disruptive reduction in carry trade positions forced the yen into sharp appreciation in October 1998.3 His warning, in fact, materialized. After the middle of 2007, the yen sharply appreciated several times while volatility increased and carry trades were unwound. In particular, after the bankruptcy of Lehman Brothers in September 2008, the yen appreciated by more than 15 percent against the U.S. dollar in three months. As illustrated in the episode of the yen, low-interest-rate currencies have experienced gradual depreciation and sharp appreciation. This behavior of exchange rates is described among currency traders that “exchange rates go up by the stairs and down by the elevator”. Brunnermeier and Pedersen (2009) construct a theoretical model in which volatility and financial positions influence each other, although this model does not focus on the foreign exchange markets. In this model, speculators borrow from financiers, who accept speculators’ positions as collateral but require margins to control the risk of losses on the collateral. The margins must be financed with the speculators’ own capital. So, when financiers set higher margins, speculators are more likely to hit funding constrains and be forced to reduce their positions. Such forced reductions in speculator positions increase volatility and thus the risk of losses on the collateral, which forces financiers to set even higher margins. Brunnermeier and Pedersen (2009) call the mutually dependent relationship between volatility and speculators’ positions through margins “the margin spiral”. In their model, the market switches between two equilibriums: one is the low liquidity equilibrium with high volatility and reduced positions, while the other is the high liquidity equilibrium with low volatility and increased positions. Only recently, a few papers including Brunnermeier et al. (2009) empirically study the relationship between exchange rate returns and market volatility. They find that low-interest-rate currencies are more likely to sharply appreciate when VIX, a stock market volatility measure, is higher. Brunnermeier et al. (2009) also argue that sharp appreciation of low-interest-rate currencies may be the underlying cause of the failure of UIP. That is, speculators may require risk premiums for taking short positions in low-interest-rate currencies, with which speculators would face losses when the low-interest-rate currencies sharply appreciated. If so, the premiums move depending on the interest rate differentials. The time-varying premiums may be a source of the failure of UIP, in which the premiums are assumed to be time-invariant. We study what role exchange rate volatility, rather than stock market volatility, plays in the failure of UIP. To this end, we apply a regime-switching model to exchange rate data. The idea of using regime-switching models for examining exchange rates is not new. After Hamilton (1989) proposed the regime-switching model to examine the persistency of recessions and booms, many papers, including Engel and Hamilton, 1990, Bekaert and Hodrick, 1993, Engel, 1994 and Bollen et al., 2000, and Dewachter (2001), applied this model to exchange rate data. We extend their regime-switching models to investigate the relationship among exchange rate returns, volatility, and interest rate differentials. To estimate the model, we employ a Bayesian Gibbs sampling. Our method is an extension of those used in previous studies, such as Albert and Chib, 1993 and Kim et al., 1998, and Kim and Nelson (1999). There is a new aspect in our method, however. With this estimation method, we can examine high-frequency state transitions and, at the same time, avoid possible estimation biases arising from the use of high-frequency data. The empirical results basically support the market participants’ view: low volatility influences depreciation of low-interest-rate currencies. In fact, the reverse is also true. That is, depreciation of low-interest-rate currencies contributes to maintaining a low-volatility environment, which implies a tendency that volatility does not increase until carry trades start to be unwound. More specifically, our result suggests that when low-interest-rate currencies start to appreciate, exchange rate return volatility increases by more than expected by the fast appreciation. This finding may be attributable to funding liquidity of speculators. That is, when speculators are forced to unwind their positions, they lose their ability to take advantage of investment opportunities and to provide market liquidity. The absence of liquidity-providing speculators may lead to high volatility. All these results suggest that a low-volatility environment and depreciation of low-interest-rate currencies are mutually dependent on each other. In addition, the results are more evident for shorter horizons. This implies that short-term carry trade activities play important roles in the mutual dependence. The rest of this paper is organized as follows. Section 2 uses OLS regressions for finding basic empirical facts on the relationship among exchange rate returns, volatility, and interest rate differentials. Section 3 describes our regime-switching model. Section 4 discusses the estimated results. Section 5 concludes this paper.

Low-interest-rate currencies tend to depreciate relative to high-interest-rate currencies. This observation is in opposition to what is predicted by UIP, and, according to a many market participants’ view, this is caused by carry trade activities in a low-volatility environment. We use OLS regressions and a regime-switching model to examine how exchange rate volatility and depreciation of low-interest-rate currencies are related to each other. The regime-switching model allows the slope regime, which governs the relationship between exchange rate returns and interest rate differentials, and the volatility regime to be neither necessarily perfectly dependent nor independent. This property of the model enables us to investigate the relationship among exchange rate returns, volatility, and interest rate differentials. We estimate this model using a Bayesian Gibbs sampling approach, in which the state and the transition matrix are generated conditional on the monthly data and/or state, while the parameters of intercept, slope coefficient, and volatility are generated conditional on the quarterly or semiannual data and state. With this method, we can examine the state transitions in a high frequency, while avoiding possible estimation biases arising from overlapping data. The main findings are as follows. First, a statistical test using the Bayes factor supports our model in comparison with the alternatives. The evidence suggests that regime switches in exchange rate returns should be interpreted as switches in the relationship between the returns and interest rate differentials without switches in the trends of exchange rates. The evidence also implies that the slope and volatility regimes are partially dependent; we should not assume that the regimes are perfectly dependent or independent. Second, low-interest-rate currencies appreciate less frequently, but once it occurs, their movements are faster than when they depreciate, as described among currency traders that “exchange rates go up by the stairs and down by the elevator”. This may be because low-interest-rate currencies appreciate when speculators are forced to unwind their carry trade positions rapidly to meet their margin requirements. Third, low-volatility tends to cause low-interest-rate currencies to depreciate. This may be because lower volatility results in lower margins and enables speculators to take more carry trade positions. In fact, the reverse causality is also true. That is, depreciation of low-interest-rate currencies contributes to maintaining a low-volatility environment, which implies a tendency that volatility does not increase until carry trades start to be unwound. Our result suggests that exchange rate return volatility increases not only because unwinding of carry trades is rapid. Since speculators are forced to unwind or liquidate their positions, they lose their ability to take advantage of investment opportunities and to provide market liquidity. This may increase exchange rate return volatility additionally. These results imply that a low-volatility environment and depreciation of low-interest-rate currencies are mutually dependent on each other, and the stability would be lost once one of these two underling conditions is failed to meet. Finally, the second and third findings are more evident for shorter horizons. This implies that the exchange rate behavior of slow depreciation and fast appreciation of low-interest-rate currencies, and the mutual dependence between depreciation of low-interest-rate currencies and a low-volatility environment are influenced by short-term carry trade activities.