Abstract
1 INTRODUCTION
A large number of academic papers have investigated empirically whether the forward rate is an unbiased predictor of the future spot exchange rate or not. These tests are closely connected to Uncovered Interest Parity (UIP) theory, which states that the expected rate of depreciation of a currency against another currency is equal to the interest rate differential between the two countries’ assets. Consequently, investors assume that the expected change in the exchange rate must be offset by the opportunity costs of holding funds in this currency, i.e. the interest rate differential. Furthermore, in a situation where Uncovered Interest Parity does not hold, the profit opportunity exists by taking a short position in a low interest‐rate currency to finance the purchase of a high interest‐rate currency, while taking advantage of the fact that the low interest‐rate currency is inclined to depreciate relative to the high interest‐rate currency.
Surprisingly, past studies have shown that the forward rate is not an unbiased predictor of the future spot exchange rate for a large variety of currencies and time periods (Fama, 1984; Froot and Thaler, 1990; Macdonald and Taylor, 1992; Isaard, 1996). These studies have not only shown that the UIP condition does not hold, but also that the higher interest rate currency tends to appreciate rather than depreciate. This term is formally known as the “forward bias” or “forward premium puzzle”.
How the forward bias has changed over time and different economic periods has been investigated by many scholars before (Baillie & Bollerslev, 2000; Flood and Rose, 2002; de Koning & Straetmans, 1997).
As a considerable amount of time has passed since the last studies about the changes in the forward bias over time have been conducted, the following paper is going to shed light onto the question of how the forward bias has changed during the world financial crisis of 2007‐2009. With the burst of the real estate bubble on the US housing market in 2007 and the resulting collapse of Lehman Brothers in the beginning of 2008 the world has witnessed one of the worst financial crises since the great depression. The consequential worldwide drop in interest rates and the follow‐ on worldwide increase in inflationary pressure give reason to believe that the overall forward bias has changed. More specifically this paper is going to answer the following research question:
Has the unbiasedness of the forward rate (forward bias) as a predictor of future spot exchange rates improved during the financial crisis of 2007‐2009?
free assets in the home and the foreign market respectively. Simply stated the difference between the forward and spot rate (the forward premium) should be equal to the interest differential between two countries’ assets. Since every variable in the above equation is known beforehand, any deviation in the model would mean excessive profits and therefore cannot exist in equilibrium. CIP has been validated by several studies to lie within the bounds implied by existing transaction costs (Obstfeld and Taylor, 2004; Clinton, 1988; Frenkel and Levich, 1975).
In addition, assuming risk neutral rational agents, the expected change in the exchange rate would be equal to the interest rate differential between two currencies assets, also known as the Uncovered Interest Parity condition, depicted in equation (2):
Δst+1e = it – i*t (2)
Where Δst+1e is the log of the expected change in the exchange rate during the period t+1 and it and i*t are the nominal interest rates on risk free assets in the home and the foreign market respectively.
Since the presence of an expected variable makes it difficult to test for UIP directly, it has been tested empirically by assuming rational expectations, CIP and the non existence of a risk premium in the forward rate (risk neutral efficient market hypothesis). Rearranging equations (1) and (2) then allows us to discuss UIP in terms of the contextual relationship between spot and forward exchange rates by replacing the interest rate differential (it – i*t) with the forward premium/discount.
Δst+1e = ft ‐ st (3)
UIP has then been generally tested as the null hypothesis of α = 0 and β = 1 and the disturbance term ηt+1 uncorrelated to any information available at time = t in the equation (also known as the Fama‐regression, named after its inventor Eugene Fama):
Considering (4), one can assume that any realized change in the exchange rate must be equal to the prevailing forward premium, which is the market’s best prediction of the future exchange rate using all available information.
However, in a world with oligopolistic players in financial markets, underdeveloped money markets, exchange or capital controls or risk of such controls, differential taxation, limited supply of capital, sovereign immunities, transaction costs and other inconveniences, the forward rate may not be a perfect predictor of the future spot rate (Pasricha, 2006). At this point it is worth clarifying a few things about equation (4) and its underlying assumptions. Equation (4) is not a direct test of UIP but rather a test of whether the forward rate is a perfect predictor of the future spot exchange rate. The reason for this is, that under UIP the term on the left hand side should be the expected change in the exchange rate, in this equation, however, it is the actual change in the exchange rate. Therefore, equation (4) can only be seen as a test of UIP if one assumes rational expectations, which states that the expected exchange rate in the next period will on average equal the actual exchange rate although it might deviate by a random error (the average of the random error being zero). Or, put it differently: On average economic agents do not systematically over or under predict the exchange rate (Pilbeam, 2006). This can be defined as:
st+1e = st+1 + ut+1 (5)
Where st+1e is the expected exchange rate at t+1, st+1 is the actual exchange rate observed at t+1 and ut+1 is the random error (on average zero).
Equation (5) is a quite strong assumption, especially if one considers that various scholars have rejected the rational expectations hypothesis in the past (see Dominguez, 1986; Liu and Maddala, 1992; Cavaglia et al, 1994).
3 LITERATURE REVIEW
As mentioned earlier UIP has become famous as a theoretical model, which is often rejected by data. Froot and Thaler (1990), for example, report in a famous survey an average value of ‐0,88 for the β in equation (4). Similar results have been found in Sarno, Valente and Leon (2005), Hochradl and Wagner (2006), Flood and Rose (2002), Bansal and Dahlquist (2000) etc. Therefore I am going to take a closer look at some of the possible explanations of the forward bias, which have emerged in the literature.
3.1 Explanations for the bias
Generally, the explanations for the forward premium puzzle fall into one of the following three categories.
3.1.1 Risk premium
UIP sets known variables equal to unknown variables, which stands in contradiction to the theoretical intuition that investors are risk averse and demand a risk premium in case of uncertainty.
Backwardation and Contango can be explained by an excess of market participants, who use forward contracts as a hedge, compared to market participants, who use forwards as pure investments. For further explanation we can, for example, take a look at the market for crude oil. If oil producers want to hedge their oil production against falling oil prices, they sell their oil forward. In the situation where oil is not demanded in the same amount as it is supplied we have excess supply of oil in the forward market. This excess supply can be counterbalanced by investors who buy the oil in the forward market, demanding however a risk premium, which the risk averse oil producers are willing to pay. The risk aversion of the oil producers can be explained by the fear of falling oil prices, but mainly by the fear of not being able to sell the oil right after it has been pumped out of the ground. In that case inventory costs would occur. Oil producers than have an interest to sell their production early in the forward market for a price, which is below the expected price, by an amount equal to the inventory costs. In this case the forward rate will be lower than the expected oil price.
The other way around, in a situation where we have an excess demand for oil in the forward market by oil consumers who want to hedge themselves against price fluctuations, Contango will occur.
Contango situations can occur when the buyer is very dependent on the product. For example, a just‐in‐time producer of car tires is willing to pay a higher than expected price in the forward market for caoutchuc to ensure that the raw material is available at the right time to prevent a stop in production due to raw material shortage.
Connecting this to the FX market one can say that if investors are risk averse, then the forward premium can no longer be seen as a pure estimate of the expected change in future exchange rates, but must rather be seen as the sum of the expected change in the exchange rate and a risk premium. Thus, if the dollar is viewed as riskier than the foreign currency, dollar interest rates would have to be higher even if the exchange rate is not expected to change (Froot and Thaler, 1990).
Equation (6) illustrates this relationship. It is the same as equation (3) except a risk premium component is added. Fama (1984) showed that any explanation relaying on a risk premium for a negative beta must satisfy either the fact that there is a negative correlation between the risk premium and expected depreciation or that the risk premium is more volatile than the expected depreciation. Unfortunately, both risk premium models fail (Froot and Frankel, 1989; Lewis, 1995; Lucas, 1982). Also, the fact that the unbiasedness hypothesis seems to hold better in emerging markets might be a sign that a time‐ varying risk premium may not be the explanation for the forward bias as one would expect these markets to be riskier, but more on that later.
3.1.2 Forecast errors
Forecast errors can be due to irrational expectations and/or rational systematic errors. Froot and Frankel (1987) show that market participants’ forecasts of future exchange rates could have come closer to the actual change in the exchange rate, if they had relied on historical data. The reason for that could be due to rational systematic errors. Systematic errors can occur due to an insufficient sample size. If market participants expect an extreme exchange rate change for which the chances are small but still exist an insufficient small sample size might not capture this extreme event.
The so called “peso problem” is an example of that. Even though the Mexican government fixed the Mexican peso against the US dollar at a constant rate, the peso sold at a forward discount between 1955 and 1975. Of course, the large depreciation expected by investors eventually occurred, but one could not have guessed this from the 1955‐1975 sample alone. In this case the empirical test shows a systematic error even though the market participants expectations are rational (Froot and Thaler, 1990).
supply process can explain about half of the error implicit in forward rates. However, the errors do not seem to have died out over time, which is evidence against models of learning about once‐and‐for‐all shifts in the regime (Froot and Thaler, 1990).
3.1.3 News Model
The basic rational behind the news model is that if foreign exchange markets are efficient, meaning that current market prices reflect all available information, then any difference between the forward rate and the corresponding rate that later transpires must, in an efficient market, be due to the arrival of new information (see Pilbeam, 2006). Consequently, since the information that results in changes in expectations about exchange rates must be new, fluctuations in the spot exchange rate cannot be predicted by the lagged forward rate. Moosa (2002) tests the News Model as an explanation for the forward bias based on a sample of quarterly observations covering six exchange rates during the period of 1975‐2000. He rejects the hypothesis that the News Model can explain the fluctuations in the exchange rate and therefore the forward bias. Instead he finds more support for the Risk Premium as an explanatory variable for the forward bias. Overall, however, empirical evidence for the News Model is mixed (Frankel, 1981; Edwards, 1983; Hoffman & Schlagenhauf, 1985; Hardouvelis, 1988; Hogan & Roberts, 1991), but in general it seems that no combination of news variables in the model has yet been able to explain the entire volatility of exchange rates.
3.1.4 Non-linearities
Lyons (2001) was the first to come up with the theory of limits to speculation. Financial institutions usually only take up a currency trading strategy, if this strategy is expected to yield a Sharpe ratio (excess return per unit of risk) that is higher or equal to the one implied by alternative trading strategies, such as a simple buy and hold equity strategy. Over the last 50 years a buy and hold strategy in US equities has yielded a Sharpe‐ratio of about 0,4 on an annual basis (Lyons, 2001). Lyons (2001) than argues, that it is only when beta equals about ‐1 or 3 that the Sharpe ratio for currency strategies is about the same as that of equities. As long as the beta stays within this band of inaction, no speculative capital will be allocated to exploit the forward bias and it will persist. His explanation for the persistence of the forward bias has then basically four parts. Part one, as just mentioned, if speculative capital is not allocated to exploit the forward bias, then the forward bias will persist. Part two, institutions with a competitive advantage in exploiting the forward bias allocate their speculative capital based, in large part, on Sharpe ratios. Part three, Sharpe ratios of reliable currency strategies that exploit the forward bias are roughly 0,4 on an annual basis, similar to that of a simple buy and hold equity strategy. Part four, because a Sharpe ratio of 0,4 is well below most institutions’ minimum threshold for inducing capital allocation, the anomaly persists.
Non‐linearities have empirically been proven by Sarno, Valente and Leon (2006). They show that for relatively small deviations from the band of inaction, only some investors are willing or able to invest in currencies. But as the deviations get larger, more and more traders will start to invest. As a consequence, the forces of supply and demand begin to work and push beta back toward the band of inaction: a reversion back to where UIP holds.
The larger the deviations from the band of inaction, the faster the market forces actively drive beta towards unity and we find that UIP holds.
In other words, once Sharpe ratios are substantial enough to attract speculative capital, violations of UIP become mean reverting at a magnitude that is dependent on the size of the Sharp ratio.
By taking these results into account, one can see that beta is a function of time‐ varying Sharpe ratios and is likely to vary over time.
3.2 Trading the Forward Bias
In practice, however, we find investors (especially banks), who typically allocate capital based on Sharpe ratios speculating in the foreign exchange markets all the time, betting against UIP and receiving profitable returns, even after adjusting for transaction costs (see ZEW Bericht, 2006). According to Sarno, Velente and Leon (2006) this should not happen in an efficient market because once the deviations become large enough, market forces would work to peter out any excessively profitable opportunities until equilibrium is reached where UIP holds.
Therefore, it must be true that strategies exist which allow investors to profit from the forward bias.
3.2.1 Carry-trade strategies
Carry‐trade strategies seek to exploit the fact that the forward rate is not an unbiased predictor of the future exchange rate. Investors can profit from selling short a low interest‐rate currency to fund the purchase of a high interest rate currency, while at the same time exploiting the fact that low interest‐rate currencies are inclined to depreciate relative to the high interest‐rate currency. A recent study by Burnside et all (2006) tested these carry‐trade strategies only to find that a simple two‐currency strategy does not yield Sharpe ratios that are high enough to attract speculative capital, since greater returns per unit of risk can be achieved with other investment opportunities.
3.2.2 Multi-currency strategies
Multi‐currency strategies are strategies where a portfolio is constructed consisting of multiple currencies. Using diversification one can get rid of the unsystematic risk associated with currency trading and receives a deposit portfolio that yields a higher return than single currency strategies. Furthermore, multi‐currency strategies are not solely based on Sharpe ratios, contrary to the LSH approach, but also take downside and covariance risk into consideration. This strategy was compared to other investment strategies by Wagner and Hochradl (2007).The Deutsche Bank Forward Rate Bias Trading System is also adopting a diversified strategy. The strategy consists of going long the three highest yielding currencies and going short the three lowest yielding currencies. This strategy has yielded estimated Sharpe ratios averaging 0,77 for the past 16 years (see. Fig. 1). As one can see from Fig. 2 this strategy has been quite successful.
3.2.3 Option strategies
A second strategy proposed by Wagner and Hochradl (2006) aimed at exploiting the forward bias is an option strategy. Given that the prices for options are based on the Black & Scholes Formula, it is possible for an investor to speculate against the forward rate by placing a call option if he or she thinks the forward rate is overpriced, or a put option if he or she feels that the forward rate is under priced. A strategy including options is very risky and should therefore be used only for a small percentage of the portfolio depending on the risk aversion of the fund manager applying this strategy.However, option strategies also record significantly higher returns than the tested benchmarks and with these strategies even very small deviations of UIP can result in profitable returns.
3.2.4 Long Horizon Strategy
3.3 Unbiasedness at very short and long horizons
3.3.1 Long horizons
Most literature on UIP typically focuses on short maturities, usually forward, spot and interest rates of maturity less than a year. This is most likely due to the fact that it is more difficult to obtain data of longer‐term rates in offshore markets (Chinn, 2006). Nevertheless, several researchers in the past have tested the unbiasedness hypothesis and found that UIP seemed to hold better in the long run. Chinn and Meredith (2004), for example, show that panel beta coefficients are positive and closer to unity for 5‐ and 10‐year government bond yields than for government bonds maturing 1 year or less (see Fig.3). Similar results were found by Alexius (2001), Flood and Tylor (1997) and Lothian and Simaan (1998). As already mentioned in the previous section, a different approach to test long‐run UIP was recently taken by Chin and Liang (2009). They developed a trading strategy assuming that if long‐ run UIP holds ex post, then, if a foreign long‐run bond produces a lower holding period return than a home bond of the same maturity, for their remaining lives the foreign bond should produce a return higher than the home bond. Their strategy was tested for investment horizons of 1‐, 2‐ and 3‐years and they show that the return increases with the investment horizon, being interpreted as giving further support for long‐run UIP.
Explanations for the validity of UIP over longer horizons include: Weaker exogeneity of long‐term rates as monetary authorities can only directly affect the short rate, and indirectly the long rate (Chinn & Meredith, 2004); “Preferred Habit Model” meaning that short‐ and long‐term bond markets are segmented from each other (Lim and Ogaki, 2003); Differences in expectations at short and long horizons (Frankel and Froot, 1987).
3.3.2 Very short horizons
not actually devalued, they appreciate intraday because investors need to be compensated for the risk they take. Overnight they can be compensated by the interest differential, but this is not possible during the day. Chaboud and Write (2003) basically investigated in the opposite direction. Instead of taking a look at intraday data, when no interest was paid, they considered the over night period when interest did occur. The rationale behind this is that if trading is liquid around this time, one should expect to see a jump in the exchange rate at exactly this point to offset the interest differential, similar to the situation when a stock goes ex dividend. Their findings show that in all cases, but the yen‐dollar trade, the slope coefficient is positive and not significantly different from unity.
3.4 Unbiasedness in Emerging Markets
it = rt + π (7)
where it is the nominal interest rate, rt is the real interest rate and π is the expected rate of inflation. The nominal interest rate is the actual exchange rate observed in the market and the real interest rate is the nominal interest rate adjusted for inflation. Thus, an increase in expected inflation π will lead to an increase in the nominal interest rate it. If real interest rates are the same internationally rt = r*t then the nominal interest rates differ solely by expected inflation. it – i*t = π ‐ π* (8)
Equations (1) and (2) indicate that the interest differential is also equal to the expected change in the exchange rate and the forward premium/discount. We can then summarize the link between interest rates, inflation and exchange rates in the following equation: it – i*t = π ‐ π* = Δst+1e = ft ‐ st (9)
Interesting to note at this point is that according to Pilbeam (2006) a greater variance of the expected domestic inflation rate raises the relative riskiness of domestic bonds as compared to foreign bonds and vice‐versa. That means we would expect that in cases of high inflation volatility the risk premium in equation (6) should increase. However, Bansal and Dahlquist (2000) and Flood and Rose (2002) both affirm the opposite, saying that in countries with high inflation volatility UIP holds better, in which case one would expect the risk premium in equation (6) to decrease (zero if UIP holds). This can be used as another argument against a risk premium.
whose coefficients are usually negative. They interpret their results indeed as proof of the non‐existence of the time‐varying risk premium as one would expect that emerging markets should be seen as riskier than developed markets.
Taking the above results into account one would consequently suggest that any trading strategy that tries to exploit the forward bias in emerging markets should fail. However, the opposite seems to be the case. As one can see from Fig. 4 the Deutsche Bank G10 Currency Harvest Index (which includes only G10 currencies) performed significantly worse than its counterpart, the Global Currency Harvest Index (which includes next to G10 currencies also emerging market currencies), which is obviously contradicting to the findings above. Also interesting to note is that the Balanced Currency Harvest Index, which has always a two to three mix of G10 currencies and non‐G10 currencies in its portfolio performs best.
3.5 Impact on Firms Cost of Debt
According to the European Central Bank (2008), residents of the countries that have joined the EU since 2004, but are not yet part of the Euro area, issue almost 80% of their foreign currency denominated debt securities in euro. Also, euro‐denominated debt securities account for about 60% of international issuance in the UK, Sweden and Denmark and more than 50% in North America.
In practice, firms are motivated to issue foreign currency debt for three reasons. First, firms may structure their financial obligations to match the currency composition of expected cash inflows. In this way, they achieve a “natural hedge” and minimize their currency risk exposure. Second, they may wish to tap broader and more liquid markets in the major international currencies. Especially borrowers in emerging markets may decide to target international investors because their domestic currency markets are too thin or virtually absent, in particular for long maturities. And third, firms may reduce their cost of capital by issuing debt in those countries that offer the lowest effective borrowing costs.
Alternative 1: Un‐hedged domestic currency borrowing at cost (1+r) Alternative 2: Un‐hedged foreign currency borrowing at costs E(s1 ÷ s0)(1+r*) Alternative 3: Hedged foreign currency borrowing at costs (f0 ÷ s0)(1+r*) Here r is the domestic interest rate, r* is the foreign interest rate, St is the time t exchange rate, expressed in units of domestic currency per unit of foreign currency. F0 is the t = 0 forward rate for purchasing foreign currency at t = 1. If markets were efficient than the costs of each alternative should be the same: 1+r = E(s1 ÷ s0)(1+r*) = (f0 ÷ s0)(1+r) (10)
By taking logs and rearranging the first equality of equation (6) we arrive at the standard expression of UIP: r = r* + E0(s1‐s2) (11) Equation (7) states that the domestic interest rate is the foreign interest rate plus any expected foreign currency appreciation.
McBrady et al. (2004) examine the correlation between aggregate bond denomination choice and estimates of uncovered and covered borrowing costs across a broad set of currencies from 1991 to 2003 to explore firm behavior. Their findings show strong evidence that managers respond to measures of covered but not uncovered borrowing costs. In other words, managers do take the fact of the forward premium puzzle into account when making decisions about issuance of foreign or domestic debt, however they only exploit the fact that CIP fails in the long run, not that UIP does not hold. According to McBrady et al. (2004), there are substantial deviations from CIP over the long‐run when currency swap rates are being used and these deviations are large enough to trigger one‐way arbitrage opportunities, which are exploited by bond issuers.
3.6 Test of UIP with survey data
3.7 Unbiasedness over time
As mentioned earlier the main purpose of this study is to investigate how the slope coefficient in the Fama‐regression has changed over time, especially during the financial crises 2007‐2009. Past literature gives reason to believe that not only the slope coefficient changes over time but also that tests of the unbiasedness hypothesis may hold better during times of crisis. Flood and Rose (2002) test for UIP using daily data of 23 developed and developing countries and find that UIP holds better during the 1990 and during times of financial crisis in the sense that the slope coefficient from a regression of exchange rate changes on interest differentials is positive and sometimes even insignificantly different from unity. Baillie and Bollerslev (2000) use 208 5‐year rolling regressions starting in March 1978 until November 1995 and also find that the slope‐coefficient turned positive during the 1990´s after a long period of negative values during the 1980´s. Both Flood and Rose (2002) and Bansal and Dahlquist (2000) find that UIP held better during times of high inflation and inflation volatility, which was especially the case in Iceland and some Eastern European countries during 2007‐2009. Variations in the slope coefficient of the Fama‐regression were also tested by de Koning and Straetmans (1997). They used a so‐called “return to normality” model and show that in a sample of six bilateral USD exchange rates most currencies follow a v‐shape pattern, meaning the beta coefficient first drops until the middle of the sample before eventually raising again.
exact reason why carry trades perform so poorly during times of crises is not 100% clear. What we know is that when speculators risk appetite declines, as measured in CBOE VIX option implied volatility index and the Ted spread (the difference between 3‐month LIBOR Eurodollar and the 3‐month T‐Bill rates), speculators unwind their carry trade positions resulting in negative returns for such strategies (see Brunnermeier, Nagel & Pedersen, 2009). So basically we can say that during times of crises, when the VIX index and the TED spread increase, investors loose their risk appetite and start unwinding their carry trades and we witness a “flight to liquidity” or “ flight to quality” resulting in a crash of the investment currency.
Since carry trades exploit the fact that the forward rate is not an unbiased predictor of the future spot exchange rate, I assume a negative correlation between carry trade excess returns and the unbiasedness hypothesis and therefore expect the slope coefficient in the Fama‐regression to be significantly positive during the financial crisis 2007‐2009.
4 DATA AND ANALYSIS
month forward rates observed on a monthly basis), the core of the empirical work is based on st and f1t at the monthly frequency level, whereas I use monthly and weekly observations of f3t and f6t in my robustness analysis. The entire analysis will be based on equation (4). First, I am going to run the regression over the entire sample period for all currencies against the USD in order to reject the null hypothesis of beta = 1. H1: The beta coefficient in equation (4) is equal to unity (β = 1) over the entire sample period. H1 is tested in the following way. H0: β ‐ 1 = 0 against the alternative Ha: β ‐ 1 ≠ 0
The t‐value to test if the beta coefficient is significantly different from one is determined as follows: tn‐2,α/2 = (β ‐ 1) ÷ (Std. error of β) H0 is rejected if: tn‐2,α/2 > 1,282 or ‐ tn‐2,α/2 < ‐1,282 where n = ∝ and α = 0,1.
final estimate is based on data from July 2004 to August 2009 (the dates will differ of course for each currency depending on the sample size). Based on previous literature I expect the beta coefficient to fluctuate over the sample period and to turn positive and maybe even equal to one during the financial crisis 2007‐2009.
H3: The beta coefficient in equation (4) will significantly change during the sample period and eventually turn positive during 2007‐2009.
The results are expected to help answer the research question of whether the unbiasedness of the forward rate as a predictor of the future exchange rate (forward bias) has improved during the financial crisis of 2007‐2009.
5 RESULTS
Table 1 shows the outcome of equation (4) for all individual currencies against the USD over the entire sample period (max. 31.01.1089 – 31.08.1989 / min. 30.09.2004 ‐ 31.08.2009). One can see that in 16 out of 24 cases the beta coefficient is significantly different from one, meaning the null hypothesis of β = 1 can be rejected for most of the cases, which is in line with previous literature. Surprisingly, however, I find that on average the beta coefficient is slightly positive, which is contradicting to previous research, which usually reports a negative average beta (see previous sections). Argentina, China, Thailand and Taiwan are the only countries, which have a significant beta coefficient at the 5% level, all being positive (all emerging market countries). One possible explanation could be that these currencies are fixed against the USD and therefore fluctuate only very little.
positive even though slightly smaller as under the 1‐month forward rates. However, the number of countries where H1 can be rejected increases. Table 4 shows the results obtained when equation (4) was tested during the financial crisis 2007‐2009. Indeed, we can see that the average beta turns positive and now in only 8 out of 24 cases H1 can be rejected. China, Japan, South Korea, New Zealand and Taiwan all have significant positive betas at the 10% level (for all β > 1). Worth mentioning is the extreme high and significant beta of New Zealand which is 24,339. A beta above unity means that the higher yielding currency depreciated more than expected against the lower yielding currency. Thus, the results support H2 in the sense that in most cases the sign of the slope coefficient is positive and H1 cannot be rejected for the majority of the cases. The robustness checks in Table 5 and 6 also show a positive average beta. Interesting to note is the average beta 0,924 when equation (4) was tested with 6‐month forward rates, which is very close to one. In order to increase the sample size I tested equation (4) during the financial crisis 2007‐2009 also with weekly observations (see Table 7). However, weekly data was only available for 18 out of the 24 countries. Again, we see a positive average beta and only in seven out of the 18 cases H1 can be rejected supporting H2 that the beta coefficient is positive and insignificantly different from one. Charts 1 to 6 show the five‐year rolling regressions and the corresponding p‐values for Australia, Japan, Switzerland, Singapore, Thailand and Turkey. Clearly in all cases the beta coefficient varies significantly over time and in all cases, except Turkey, it eventually turns positive and above one during 2007‐2009 after a long period of negative betas.
the beta coefficient during the period of August 1993 and August 1998. After that the beta stayed negative and in some periods even significantly negative until the period of 2003‐2009. A similar picture is the one for the Japanese Yen. Here the graph shows that there are three periods of positive betas. The first one again during the 1990s, the second one between 1997 and 2002 and the last one again during 2003‐2009. Once more all of these periods are times of a financial crisis. The first period is the one during the burst of the Japanese Asset Price Bubble, which was the outcome of the aftermath of the Plaza accord in 1985. The second period of positive betas is during the time of the burst of the dot.com bubble, which was roughly from 1998 to 2001. And the last period again is the time of the current financial crisis. Things look almost the same in Switzerland except that the beta coefficient during the early and mid 1990s stayed between 0 and 1. But once more we see positive betas during the burst of the dot.com bubble of 1998‐2001 and the financial crisis of 2007‐2009.
In Singapore we have a long period between 1989 and 2002 in which the beta coefficient was mostly positive but almost never above one. Indeed the Asian Crisis did not affect Singapore’s economy as much as other Asian countries, which is mainly due to actions taken by the government. That is why we see only slightly positive betas in the graph during that time. After that we have a longer period of negative betas (sometimes even significantly) before they turn positive again during the world financial crisis 2007‐2009.
It is basically the same in Taiwan except that the data set does not go back as far in time as it did in the previous countries. But again we have slightly negative betas during the period of 2001‐2007 until the slope coefficient again (significantly) turns positive as soon as the period of the financial crisis is covered.
Only Turkey shows a different picture. Up until January 2006 the slope coefficient was almost constant at a rate of ‐0,2 before it turned slightly positive for a short period and then turned negative again until the end of the observation period.
different from one, which happens predominantly during times of financial crises. This has several important implications. First of all, it explains why carry‐trades perform so poorly during such periods. Carry‐trades are dependent on the phenomena that the higher yielding currency appreciates against the lower yielding currency, and therefore negative beta coefficients. If the beta coefficient now becomes positive and exceeds one, the exact opposite happens. The higher yielding currency will depreciate (more than expected) and the lower yielding currency will appreciate and hence, the carry trade will have negative returns.
depreciating less than expected in this area, meaning investors gain on the interest differential even though they lose on the exchange rate change.
Moreover, as argued by de Koning and Straetmans (1997), fixed coefficient methods such as rolling regressions often have the disadvantage of choosing the right rolling window size. They argue that this method is suboptimal in detecting stochastic or systematic coefficient variation, when it is indeed present in the data. A better model in that case would be the so‐called “return to normality” model (see de Koning & Straetmans, 1997).
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9 APPENDIX
Figure 1 Source: Deutsche Bank Global Markets Research Figure 2 Source: Deutsche Bank Global Markets ResearchDeutsche Bank @
5-Year Annualized Sharpes
18 August 2004 FX R es G lo b al M ar ke ts R es ea rc h Mira Farka ermira.farka@db.com FX Research New York (1) (212) 250-3628 David Folkerts-Landau Managing Director, Head of Global Markets Research
The figure shows annualized Sharpe Ratio measured as a fraction of annual average excess returns over annualized standard deviation for a rolling 5-year period. As shown in the graph, rolling Sharpes for the Forward Rate Bias Strategy are positive and for the most part w ell above 0.3 threshhold maintained as the average S&P500 annuzlaised Sharpe ratio.
The vie ws expressed in this report accurately reflect the personal vie ws of the undersigned lead analyst about the subject issuers and the securities of those issuers. In addition, the undersigned lead analyst(s) has not and will not receive any compensation for provid-ing specific recommendation or vie w in this report. [Mira Farka]
5-Year Annualized Sharpes for the Forward Rate Bias Stretegy
Source: DB GM Research IMPORTANT: Please see conflict disclosures
and analyst certification immediately at the end of the text of this report. Deutsche Bank does and seeks to do business with issuers covered in its reports. As a result investors should be aware that Deutsche Bank may have a conflict of interest that could adversely affect the ob-jectivity of its reports. Investors should con-sider this report only as a single factor in mak-ing their investment decision.
0.00 0.50 1.00 1.50 2.00 2.50
Feb-91 Apr-92 Jun-93 Aug-94 O ct-95 Dec-96 Feb-98 Apr-99 Jun-00 Aug-01 Oct-02 Dec-03
Deutsche Bank @
Cumulative Excess Returns
18 August 2004 FX R es ea rc h G lo b al M ar ke ts R es ea rc h Mira Farka ermira.farka@db.com FX Research New York (1) (212) 250-3628
The graph shows the Cumulative Excess Return Index resulting from investing in Forward Rate Bias Strategy. Our results show that de-spite volatility in returns, the Forward Bias Strategy offers attractive excess returns over time. As of August 1, 2004 the Cumulative Ex-cess Return Index stands at 320.
The vie ws expressed in this report accurately reflect the personal vie ws of the undersigned lead analyst about the subject issuers and the securities of those issuers. In addition, the undersigned lead
Cumulative Excess Returns: Forward Rate Bias Stretegy
Source: DB GM Research IMPORTANT: Please see conflict disclosures
and analyst certification immediately at the end of the text of this report. Deutsche Bank does and seeks to do business with issuers covered in its reports. As a result investors should be aware that Deutsche Bank may have a conflict of interest that could adversely affect the ob-jectivity of its reports. Investors should con-sider this report only as a single factor in mak-ing their investment decision.
60 110 160 210 260 310 360
37 Figure 3 Notes: Panel beta coefficients at different horizons. Source: M. Chinn (2006) Figure 4 Notes: The effective annual return over the period from the Balanced Currency Harvest was 15.22%. The Global Currency Harvest returned 12.07% and the G10 Currency Harvest returned 8.02%. Source: Deutsche Bank
shorter. This interpretation seems to be borne out by
Cheung et al.’s (2005)
finding that interest
parity predicts exchange rates better at long horizons than at short.
Chinn and Meredith (2004)
explain the divergence in short- and long-horizon results by
ap-pealing to a monetary reaction function that responds to exchange rate changes. The approach
broadly follows the mechanism first suggested by
McCallum (1994)
, and re-interpreted
econo-metrically by
Anker (1999)
and
Kugler (2000)
. However, Chinn and Meredith explain the
pat-tern of estimates by appealing to a term structure that links short- to long-maturity bonds; since
the monetary authority can only directly affect the short rate, and indirectly the long rate, there
is less endogeneity of the long-term interest differential.
This interpretation can be re-interpreted in an econometric framework following
Moore
(1994)
and
Villanueva (2005)
.
Chinn and Meredith (2005)
show that long-term rates are
more weakly exogenous than short-term rates, and that this can explain the divergence in results
in a statistical sense.
-0.8 -0.4 0.0 0.4 0.8 1.2 -0.76 -0.76 -0.54 0.09 0.67 0.683 mos. 6 mos. 1 year 3 years 5 years 10 years
/
Unbiasedness coefficient value
Fig. 3. Panel beta coefficients at different horizons. Notes: up to 12 months, panel estimates for 6 currencies against US$, euro deposit rates, 1980Q1e2000Q4; 3-year results are zero-coupon yields, 1976Q1e1999Q2; 5 and 10 years, constant yields to maturity, 1980Q1e2000Q4 and 1983Q1e2000Q4. Sources: 3, 6, 12 months, 5 and 10 years from
Chinn and Meredith (2004); 3 years, author’s calculations using data supplied by Geert Bekaert.
Table 3
Ex post depreciation and 10-year government bond yields ^ a b^ Reject H0: b ¼ 1 R2 N Deutschemark 0.001 (0.005) 1.025 (0.225) 0.51 88 Japanese yen 0.027 (0.011) 0.469 (0.202) *** 0.10 88 U.K. pound 0.006 (0.003) 0.767 (0.098) *** 0.45 88 Canadian dollar "0.004 (0.003) 0.672 (0.138) *** 0.09 88 Constrained panela e 0.758 (0.168) 0.56 352
Notes: point estimates from the regression in Eq.(6) (serial correlation robust standard errors in parentheses, calculated assuming approximately 2 # (k " 1) moving average serial correlation).
Sample period: 1983Q1e2004Q4. * (**)[***] Different from null of unity at 10%(5%)[1%] marginal significance level.
a
Fixed effects regression. Standard errors adjusted for serial correlation (assumes k " 1 moving average serial cor-relation, cross averaging across currency pairs).
Forward Bias in the World’s
Currency Markets
Currency forwards are derived from non-arbitrage arguments based on
nominal interest rates. Research shows that currency forwards may be a biased predictor of future spot. In other words statistical analysis
demonstrates that high yielding currencies tend to over-compensate investors for depreciation risk.
Eg:
! Currency 1 has a nominal
yield of 10%
! Currency 2 has a nominal
yield of 5%,
! The 1 year currency
forward has to be priced such that it is expected Currency 1 will
depreciate by 5% in 1 year’s time otherwise an arbitrage would be possible.
Historically there has been a bias that Currency 1 tends not to depreciate
Historic Performance of the Indices
The historic performance of the Deutsche Bank Currency Harvest indices is shown on an excess return basis net of costs. 50 100 150 200 250 300
Sep-00 Sep-01 Sep-02 Sep-03 Sep-04 Sep-05 Sep-06 Sep-07
Balanced Currency Harvest Global Currency Harvest G10 Currency Harvest
Performance of the Currency Harvest Indices:
Excess Return September 2000 – October 2007
Source: Deutsche Bank
