FOCUSED AND QUICK (FAQ) Issue 14
IS THE INTEREST PARITY AN URBAN LEGEND?
SUPACHOKE THAWORNKAIWONG
Summary
In this short article, we discuss the validity of the UIP theory in explaining the movement of the rate of appreciation of the Thai baht against the US dollar. Employing standard time series analysis, we found evidence indicating that the UIP does not hold. Moreover, employing fractional cointegration analysis, we found that there is not even a long-run linear relationship between the interest rate differential and the rate of appreciation of the baht. Instead, we found a long-run linear relationship between the rate of appreciation of the baht and the return on Thai stock. This finding indicates a common trend affecting both the stock and FX markets.
Suppose you are a resident in the United States and are deciding whether or not to hold your wealth in a form of Thai deposits/bonds. Suppose Thai and US interest rates at time t are It TH and It US, respectively. Let et be the exchange rate (dollar/baht) at time t. At the beginning of period t+1 the dollar rate of return on Thai deposits is approximately It TH + (et+1 — et)/et, the Thai interest rate plus the gain from the appreciation of the baht. Since et+1 is unknown at time t, the (approximate) expected dollar rate of return on Thai deposits is It TH + t{(et+1 — et)/et} where t denotes the expectation conditional on all information known up to period t. If you are risk-neutral, you will hold Thai deposits if and only if It TH + t{(et+1 — et)/et} ? It US, i.e. the expected dollar rate of return on Thai deposits is at least as large as that on US deposits. Note that our approximation has a negligible effect. The Uncovered Interest Parity (UIP) theory asserts that in equilibrium, under the no-arbitrage condition, the expected dollar rate of return on Thai deposits must equal the expected rate of return on US deposits. The UIP then implies that the expected rates of appreciation of the Thai baht against the US dollar, t{(et+1 — et)/et}, must equal the interest rate differentials, It US- It TH.
From a probabilistic point of view, the UIP asserts that t{ zt+1 } = 0, where zt+1 = (et+1 — et)/et - (It US- It TH). That is, {zt} is a martingale difference sequence and it can be shown that {zt} is just a white noise process, i.e. zt are not correlated through time. However, Figure 1 shows that {zt} is far from being a white noise process since it exhibits a high degree of persistence, i.e. a high value of z at time t tends to be followed by high values of z in later periods. We hope the green curve, a filtered series that may be regarded as a local trend after the noisy components have been removed, can help the readers see this pattern. A statistical test for no correlation of {zt} can be performed to provide a proper justification that {zt} are correlated. Hence we can conclude that the UIP does not hold.
The rejection of the UIP may not be enough to convince believers in an urban legend that the interest rate differential is the main culprit for the appreciation of the baht to change their minds. Therefore the rest of this article will focus on a search for a comovement of the interest rate differential and the rate of appreciation of the baht. The motivation is simple. If the interest rate differential is the main force responsible for the appreciation of the baht, then we should at least see a co-movement of the two time series over time.
Before proceeding any further, we should first agree on how we should define a co-movement of two time series. Back in the 1980s econometricians and economists believed that economic time series are either I(0) or I(1) processes. Please do not be intimidated by this jargon. Figure 2(a) shows the simplest type of an I(0) process, a white noise process. It can be seen that the movement of this I(0) process is stable in the sense that it only fluctuates around a particular value and has no tendency to deviate from this stable pattern. It can be proven mathematically that any I(0) process has this behaviour. On the other hand, Figure 2(b) shows the simplest type of an I(1) process, a random walk. It can be seen that this time series has no tendency to remain at any particular value and has an explosive behaviour. Just compare the scales of Figures 2(a) and 2(b). Again it can be shown that any I(1) process has this behaviour.
If two time series are I(0) processes, a regression analysis is capable of detecting their co-movement. However if one is I(0) and the other is I(1), there can never be a comovement since one is stable but the other has an explosive behaviour. See Figures 2(a) and 2(b). If both series are I(1), following Phillips (1986), a regression analysis is no longer valid. At about the same time Engle and Granger (1987) refined and popularized a statistical tool, known as cointegration proposed earlier by Granger, which is capable of detecting a co-movement of two explosive, I(1), economic time series. Figure 3(a) shows two explosive time series that move together in the long run. It turns out that {Yt — 0.8Xt} is an I(0) process,
Figure 3(b). Suppose we think the condition Yt = 0.8Xt specifies an equilibrium relationship and Ut = Yt - ?Xt can be regarded as disequilibrium terms. Thanks to some friction in an economy, Ut may not take value zero all the time but if such equilibrium exists, we would expect {Ut} to fluctuate around zero over time, as in Figure 3(b). Therefore having the disequilibrium component follow an I(0) process is an indication of a long-run equilibrium relationship. From the graphical and intuitive motivations, we are now ready to give a proper definition for a co-movement. Suppose {Xt} and {Yt} are I(1) processes. Following Engle and Granger (1987), {Xt} and {Yt} are cointegrated if there exists ? ? 0 such that {Yt - ?Xt} is an I(0) process.
Back it the 1970s, it was found that the I(0)/I(1) classification of time series is too restrictive. Between I(0) and I(1) processes, there is a great deal of wilderness in such a way that I(0) and I(1) processes are simply two small needles in a vast ocean. To be precise, a proper foundation for linear time series analysis can be based on fractional processes, i.e. instead of considering I(0), I(1), I(2), … processes, we should consider an I(d) process where d can take any real value. The readers should not be worried about this new technical concept. In order to follow the rest of this article, it suffices to bear in mind that a memory parameter can be regarded as an index representing behaviour of a time series.
This generalization had not been useful until the late 1980s and early 1990s when there were a series of breakthroughs in the mathematical foundation of linear time series analysis. Following this generalization, there have been attempts to generalize the concept of cointegration based on fractional processes in the past ten years.
If {Xt} and {Yt} are I(d1) processes and there exists ? ? 0 such that {Yt - ?Xt} is an I(d2) process where d2 < d1, then we say that {Xt} and {Yt} are (fractionally) cointegrated. Further motivation and justification for this definition of fractional cointegration can be given but require a working knowledge of spectral analysis. Therefore it is omitted in this short article.
It can be proven that for {Xt} and {Yt} to be cointegrated, it is necessary that they must have the same memory parameter. Hence if they do not have the same memory parameter, we can immediately conclude that they cannot be cointegrated. In order to investigate an existence of a long-run linear relationship between the rate of appreciation of the baht and an interest rate differential, we employ a test in Robinson and Yajima (2002) to test for an equality of the memory parameters of the rate of appreciation of the baht and of various interest rate differentials calculated from the US Fed funds vs the Thai over-night rates, US/Thai 3-month T-Bill rates, 1-year bond rates, 2-year bond rates, 3-year bond rates and 5-year bond rates. (We employ daily data from January 2000 to September 2010.) From the tests we conducted, the null hypothesis of an equality of the memory parameters can be rejected at the 1% level, and thus we can conclude that there is no evidence of a long-run linear relationship between the rate of appreciation of the baht and various interest rate differentials mentioned above. This result is not surprising if we consider Figure 4.
It can be seen that no matter how much the interest rate differentials change, the rates of appreciation of the baht keep fluctuating around some value without any tendency to respond to the changes in the interest rate differentials. From this cointegration analysis we may infer that the interest rate differential may play a role in determining the rate of appreciation of the baht but this particular role is at best trivial in explaining the movement of the currency.
As the FX market and the stock market tend to move in the same direction (see Figure 5), we also investigated if there is a long-run linear relationship between the rate of appreciation of the baht and the rate of return on Thai stock calculated from the SET index. Employing the test in Robinson and Yajima (2002), we cannot reject the null hypothesis of an equality of the memory parameters of the rate of appreciation of the baht and of the returns on Thai stock. In addition, employing a test for fractional cointegration proposed by Robinson (2008), there is evidence to conclude that the rate of appreciation of the baht and the return on Thai stock are cointegrated, indicating a long-run linear relationship of the two series.
In this short article we investigated the validity of the UIP and of the hypothesis that there is a co-movement between the rate of appreciation of the baht and the interest rate differential. Employing fractional cointegration analysis, we can reject these claims. There are a few possible explanations for this.
First, if an agent is indeed risk-neutral, then his objective function is simply to maximize his expected returns. It should be clear to the readers that interest rates that are returns on relatively safe assets tend not to exceed those of risky assets such as stock. Therefore, under the assumption of riskneutrality, instead of looking at the interest rate differentials, we should perhaps look at the differential of stock returns.
Second, the assumption on risk neutrality may be too strong. Risk aversion may play an important role even in a financial market. If a nontrivial proportion of players in the FX market are risk-averse, then other factors containing information on risk should also play an important role in determining the exchange rate. These factors may include foreign investors’ attitude towards risk and their perception on relative risk of Thai assets.
Actually we have conducted many other tests to check for long-run linear relationships between the rate of appreciation of the baht and many other time series such as differentials of the US/Thai stock returns and some push and pull factors. It turned out that we cannot find any cointegration of the rate of appreciation with these series. This, as a consequence, puts the return on Thai stock in a special position since it is the only series fractionally cointegrated with the rate of appreciation.
One may argue that high returns on Thai stock may signal more information to investors than just the returns themselves. If players in the Thai stock market are risk averse, then high returns on the market (due to high demand for Thai stock) can reflect investors’ perception of low risk of Thai assets. On the other hand, high returns on Thai stock tend to be accompanied by demand for Thai stock from foreign investors indicating risk appetite of foreign investors. Hence it should not be surprising to learn that stock returns and currency returns move together in the long run since a great deal of information, likely to determine the movement of the exchange rates, is also embedded in the movement of the SET indices.
There are a few directions of future research. First, it is interesting to see how Granger-causality can be extended in this context to check if the SET returns lead the rates of appreciation or the other way round. Second, some microeconomic studies to investigate the link between the Thai stock and FX markets should be pursued to shed light on the long run relationship between the rate of appreciation of the baht and the Thai stock return.
The author is grateful to Roong Mallikamas and Nasha Ananchotikul for useful discussions. He thanks Nantaporn Pongpattanon and Thipsuda Sukdam for useful comments on the presentation of the article. He also thanks Roong Mallikamas and Mantana Lertchaitawee for helpful comments which have improved the presentation of this article substantially.
Engle, R.F., Granger, C.W.J., 1987. Cointegration and error correction: representation, estimation and testing. Econometrica 55, 251-276.
Phillips, P.C.B., 1986. Understanding spurious regressions in econometrics. Journal of Econometrics 33. 311-340.
Robinson, P.M., 2008. Diganostic testing for cointegration. Journal of Econometrics 143, 206-225.
Robinson, P.M., Yajima, Y., 2002. Determination of cointegration rank in fractionally integrated processes. Journal of Econometrics 106, 217-241.
Mr. Supachoke Thawornkaiwong
Researcher Economic Research Department
Monetary Policy Group
Source: Bank of Thailand