International parity conditions and market risk

Abstract

This article presents a set of international parity conditions based on consistent and efficient market behavior. We hypothesize that deviations from parity conditions in international bond, stock, and commodity markets are attributable mainly to relative equity premiums and real interest rate differentials. Testing this hypothesis against four European markets for the recent floating currency period, we gain supportive evidence. Moreover, the deviations of uncovered interest parity, international stock return parity, and purchasing power parity are not independent; the evidence suggests that deviations from the three parities are driven by two common factors: equity premium differential and real interest rate differential.

Appendix

This Appendix provides additional empirical evidence on the popular parity conditions prevailing in international markets. The regression models are:

A. Efficient Interest Rate Parity:

B. Efficient International Stock Parity:

C. Efficient Purchasing Power Parity:

D. International Fama Parity:

E. Real Interest Rate Parity:

F. Equity Premium Parity:

G. Covered Interest Rate Parity:

H. Unbiased Forward-Rate Hypothesis I:

I. Unbiased Forward-Rate Hypothesis II:

Models A through C are efficient versions of the UIP, ISP, and PPP proposed by Roll (1979). An efficient market implies that β ₀ = 0 and β ₁ = 1.The evidence presented in Panels A, B, and C of Table 6.3 is quite consistent with the efficient nature of the spot exchange rate, suggesting that all

Table 6.3. Estimates of international parity conditions

information concerning future exchange rate adjusted return differentials is incorporated into the current spot exchange rate. The supportive evidence holds true for all three parity conditions. However, it should be pointed out that specifying the model in this form tends to lead to not rejecting the efficient-market hypothesis. In particular, Roll’s specification is more or less to test spot exchange rate efficiency rather than to test parity conditions. If we check the estimated equations, the series of return differentials is stationary and its magnitude is rather small as compared with the level of exchange rates. As a result, the dominance of the lagged exchange rate variable in the test equation gives rise to a high R-square.

Next let us consider the efficient-market hypothesis for U.S. Treasury bills. Fama (1975) argues that the one-month nominal interest rate can be viewed as a predictor of the inflation rate. Applying this notion in international markets implies that the nominal interest rate differential can be used to predict the inflation rate differential. The evidence in Panel D does provide some predictive evidence for the German and Swiss markets. However, the efficient-market hypothesis is rejected in the international context. This also casts doubt on the validity of real interest rate parity. The results from Panel E confirm this point; the correlations of real interest rates for three of the four markets are positive and statistically significant, but the parity condition still fails. The reasons advanced by Koraczyk (1985) are the existence of risk premiums and market imperfections.

In the text as well as in the finance literature, we are concerned with the relationship between stock equity premiums. The evidence derived from Panel F indicates that the correlation for each country is highly significant, although we are unable to find strong support for the parity condition. If we view the U.S. equity premium as a proxy for the world-portfolio premium, the slope coefficient for each estimated equation can be treated virtually as a beta coefficient in light of the CAPM framework.¹⁶

Panel G contains the results for testing covered interest rate parity. Since all the variables in this equation are directly observable and readily assessed by economic agents, the estimated equation is closest to the parity condition. It is generally recognized that arbitrage profit derived from this equation is very negligible, if there is any. Thus, any gap in this equation must reflect country risk (Frankel and MacArthur, 1988), transaction costs (Fratianni and Wakeman, 1982), or simply data errors.

The forward premium (or discount) has been commonly used to predict foreign-exchange risk premiums as well as currency depreciation as denoted by the equations in Panels H and I. The unbiasedness hypothesis in Panel H requires that β ₀ = β ₁ = 0; however, the unbiasedness hypothesis in Panel I implies that β′₀ = 0 and β′₁ = 1 (Hansen and Hodrick, 1980; Cornell, 1989; Bekaert and Hodrick, 1993). Fama (1984) notes the complementarity of the regressions in Panels H and I and suggests that β ₀ = -β′₀, that β ₁ = 1 - β′₁, and that ɛ _t+1 = -ɛ′_t+1 Consistent with the existing literature, the evidence presented in Panel H and Panel I apparently rejects the unbiasedness hypothesis.¹⁷ However, the complementary nature of the coefficients appears consistent with Fama’s argument. The puzzle entailed in this set of equations is that the estimated slope in the Panel I equation is typically negative. This interpretation has been attributable to risk premium (Fama, 1984; Giovannini and Jorion, 1987; Hodrick, 1987; Mark, 1988; and Jiang and Chiang, 2000), forecast errors (Froot and Thaler, 1990), and regime shifting (Chiang, 1988; Bekaert and Hodrick, 1993).

• 1. Other parity conditions, including an unbiased forward-rate hypothesis, covered interest rate parity, and real interest rate parity will be discussed at a later point. A formal derivation of these parity conditions can be achieved by employing a consumption-based approach in the Lucas framework (Lucas, 1982; Roll and Solnik, 1979; Chiang and Trinidad, 1997; Cochrane, 2001).

• 2. In order to simplify the analysis, we ignore the coupon payment (c _t+1) to the bond and the dividend payment (d _t+1) to the stock by assuming c _t+1 = d _t+1 = 0. Different tax effects are also abstracted from the calculations. We can link the current model to a Lucas —Cochrane framework by setting pv _jt = p _t . Thus, p _t = E(m _t+1 x _t+1), where p _t is the current asset price; m _t+1 is the stochastic discount factor; and x _t+1 is the payoff at time t + 1. By setting x _t+1 = p _t+1, we have:

  

• 3. An equilibrium relationship between asset returns based on a continuous-time model can be found in Stulz (1981).

• 4. Frankel and MacArthur (1988) further decompose UIP into two parts: the covered interest differential and the currency risk premium. Thus, Equation (6.11) becomes:

  

  The first term on the right-hand side of this expression is a deviation of the covered interest rate, which is considered a country premium; the second term is the currency risk premium; and the third term is the change in the real exchange rate. Branson (1988) interprets these three components as the measure of a lack of integration of the bond, currency, and goods markets, respectively.

• 5. A systematic relationship between stock returns and inflation can be found in Stulz’s study (1986).

• 6. The Basle Accord was a landmark regulatory agreement affecting international banking. The agreement was reached on July 12, 1988. Its goals were to reduce the risk of the international banking system, and to minimize competitive inequality due to differences among national banking and capital regulations (Wagster, 1996).

• 7. Using realizations to proxy expectations could generate an error-in-the-variables problem. In fact, the formation of expectations has long been a challenging issue in empirical estimations. Expectations range from rational expectations, distributed lag expectations, adaptive expectations, regressive expectations, and random walk to expert expectations based on survey data (Frankel and Froot, 1987).

• 8. In the finance literature, expected returns are related to risk, which can be modeled by ARCH or GARCH in mean (Baillie and Bollerslev, 1990). Also, many recent studies incorporate conditional variance and covariance into various models to examine the relationship between excess returns and risk (Domowitz and Hakkio, 1985; Hodrick, 1987; Bekaert and Hodrick, 1993; Hu, 1997; De Santis and Gerard, 1998; Jiang and Chiang, 2000; Cochrane, 2001). In this chapter, we do not intend to explore these types of models.

• 9. Our test here follows the traditional approach by focusing on examining whether the slope coefficient differs significantly from unity. Rogoff (1996) provides a good review. Recent research pays particular attention to the stochastic properties of dynamics of adjustments toward PPP, and employs more powerful statistical techniques. Cheung and Lai (1993) Cheung and Lai (1998), Jorion and Sweeney (1996), Lothian and Taylor (1997b), and Baum et al. (2001) present evidence in favor of PPP.

• 10. Roll’s efficient estimations and other parity conditions are provided in the Appendix.

• 11. Expected inflation rate differentials can also affect the capital account through their effects on real interest rate differentials (Frankel, 1979).

• 12. As mentioned earlier, Frankel and MacArthur (1988) decomposed UIP into two parts: the covered-interest differential and the currency risk premium, while Gokey (1994) decomposed UIP into a real interest rate differential and an ex ante deviation from relative PPP as:

  

  Basically, Frankel and MacArthur’s decomposition (1988) is achieved by subtracting and adding the forward premium, (f _t - s _t ), into the UIP as we showed in Note 4, while Gokey’s decomposition (1994) is obtained by subtracting and adding the expected inflation rate differential, (Δp ^e _t+1 - Δp ^*e _t+1 ), into the equation.

• 13. The long-term interest rate differential can also be added to the right side of Equation (6.17) as an independent argument. As a result, difference in long — short rate spreads will be shown on the right side of Equation (6.18) to capture the information of relative liquidity risk, as implied by the expectations hypothesis of the term-structure of interest rates.

• 14. Using Equations (6.19) through (6.21), we obtain the following two equations as:

  

  .

• 15. A precise process and speed of adjustment to restore a new equilibrium can be very complicated, and so cannot be answered without having a complete specification of the model, which is beyond the scope of the current study.

• 16. Cumby (1990) tests whether real stock returns from four countries are consistent with consumption-based models of international asset pricing. The hypothesis is rejected by including a sample that began in 1974. However, the null cannot be rejected when only the 1980s are considered.

• 17. Estimates of the unbiasedness hypothesis are based on the sample period from 1989.1 to 1998.12 due to unavailability of FR, GM, and SW forward markets and the switch to the euro starting in January 1999.