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:

$$ {{s}_{{t + 1}}} - \left( {{{r}_t} - r_t^{*}} \right) = {{\beta }_0} + {{\beta }_1}{{s}_t} + {{\varepsilon }_{{t + 1}}} $$

• B. Efficient International Stock Parity:

$$ {{s}_{{t + 1}}} - \left( {{{R}_{{m,t + 1}}} - R_{{m,t + 1}}^{*}} \right) = {{\beta }_0} + {{\beta }_1}{{s}_t} + {{\varepsilon }_{{t + 1}}} $$

• C. Efficient Purchasing Power Parity:

$$ {{s}_{{t + 1}}} - \left( {\Delta {{p}_{{t + 1}}} - \Delta p_{{t + 1}}^{*}} \right) = {{\beta }_0} + {{\beta }_1}{{s}_t} + {{\varepsilon }_{{t + 1}}} $$

• D. International Fama Parity:

$$ \left( {\Delta {{p}_{{t + 1}}} - \Delta p_{{t + 1}}^{*}} \right) = {{\beta }_0} + {{\beta }_1}\left( {{{r}_t} - r_t^{*}} \right) + {{\varepsilon }_{{t + 1}}} $$

• E. Real Interest Rate Parity:

$$ {{\bar{r}}_{{t + 1}}} = {{\beta }_0} + {{\beta }_1}\bar{r}_{{t + 1}}^{*} + {{\varepsilon }_{{t + 1}}} $$

• F. Equity Premium Parity:

$$ {{R}_{{m,t + 1}}} - {{r}_t} = {{\beta }_0} + {{\beta }_1}\left( {R_{{m,t + 1}}^{*} - r_t^{*}} \right) + {{\varepsilon }_{{t + 1}}} $$

• G. Covered Interest Rate Parity:

$$ {{r}_t} - r_t^{*} = {{\beta }_0} + {{\beta }_1}({{f}_t} - {{s}_t}) + {{\varepsilon }_t} $$

• H. Unbiased Forward-Rate Hypothesis I:

$$ {{f}_t} - {{s}_{{t + 1}}} = {{\beta }_0} + {{\beta }_1}\left( {{{f}_t} - {{s}_t}} \right) + {{\varepsilon }_{{t + 1}}} $$

• I. Unbiased Forward-Rate Hypothesis II:

$$ {{s}_{{t + 1}}} - {{s}_t} = {{\beta \prime}_0} + {{\beta \prime}_{1}}\left( {{{f}_{t}} - {{s}_l}} \right) + {{\varepsilon \prime}_{{t + 1}}} $$

Table A.1 Estimates of international parity conditions

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 A.1 is quite consistent with the efficient nature of the spot exchange rate, suggesting that all 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 1-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 Korajczyk (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 ${{\beta \prime}_0} = 0$ and ${{\beta \prime}_1} = 1$ (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 ${{\beta }_0} = - {{\beta \prime}_0}$, that ${{\beta }_1} = 1 - {{\beta \prime}_1}$, and that ${{\varepsilon }_{{t + 1}}} = - {{\varepsilon \prime}_{{t + 1}}}$. 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).