Risk premia and the foreign exchange market

Risk premia and the foreign exchange market

Economics Letters 23 (1987) 95-98 North-Holland 95 RISK PREMIA AND THE FOREIGN EXCHANGE MARKET The European Monetary System Versus the ‘Rest of the ...

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Economics Letters 23 (1987) 95-98 North-Holland


RISK PREMIA AND THE FOREIGN EXCHANGE MARKET The European Monetary System Versus the ‘Rest of the World’ * Anna Nuffield

MARGARITA College, Oxford OX1 INF, UK

Received 2 September 1986

This paper presents a new test of the hypothesis of uncovered interest rate parity. The possibility of investors’ risk aversion is taken explicitly into account. The empirical work investigates proxies for various forms of risk over the period 1974(l)-1982(4) between the EMS and the ‘rest of the world’. Our results show that investors are sensitive to interest rate risk.

1. Introduction In this paper the issue of perfect substitutability among assets between System (EMS) and the ‘rest of the world’ is empirically tested. The uncovered interest rate parity can be expressed as ,e,+i -e,=ln(l+r,‘)-ln(l+r,*), where e, is the unit of foreign conditional on mately equal to Defining the ,e,+l

the European



logarithm of the spot exchange rate (number of units of domestic currency for one exchange); ,e,+, is the mathematical expectation of next period’s exchange rate the available information set; ln(1 + r,‘) and ln(1 + r,*) are, respectively, approxithe domestic and foreign nominal rates of interest. interest rate differential as r,, (1) can be written as:

- e, = r,.


The hypothesis of (weak) foreign exchange market efficiency guarantees absence of persistence in forecast errors. In other words, the future spot exchange rate differs from its expected value only due to the occurrence of serially uncorrelated random shocks with zero mean: e,+, =rc,+l

+E fil7


E(E,~,) = 0,

= 0,


where i#j.


eq. (2) and eq. (3) one obtains

et+, - e, - r, = c,+~.


* I wish to thank John Muellbauer for his help and guidance. The results reported in this note are part of a more general macroeconometric study focusing on the EMS versus the ‘rest of the world’. 0165-1765/87/$3.50

0 1987, Elsevier Science Publishers B.V. (North-Holland)


A. Margarita

/ Risk premia and the foreign exchange market

Since all variables on the left-hand side of eq. (4) are observable ex post, one may test the perfect substitutability hypothesis by testing whether the process { cl+i } is white noise. The hypothesis of uncovered interest parity in the form of eq. (4) has been tested by Cumby and Obstfeld (1981). They find evidence of high serial correlation in the series of ex post nominal return differentials. This result can be interpreted as evidence of the existence of a risk premium. In what follows we attempt to investigate directly the possibility of investors’ risk aversion. Notice that if a risk premium exists, lagging eq. (4) one period, the condition t_lAe, - rLl

= 0

must be satisfied, where rt?i is the risk premium-corrected c





interest rate differential,

that is,


where ,_ 1H, is the risk premium. Substituting eq. (6) into eq. (5):

,-lAer -

(rtpl - b,-,H,) = 0,

which implies de, -





+ c,,

so that the coefficient on the risk-premium is expected to have a negative sign. We propose to capture investors’ risk aversion by explicitly considering what we regard as the three main possible sources of risk, namely exchange rate risk, purchasing power risk and interest rate risk. The possibility of the existence of an exchange rate risk is based on an ‘asymmetry’ assumption for the two countries (or two groups of countries) considered. If they were symmetrical, that is, if they had the same importance in the world’s economy, exchange rate risk would not be relevant in the aggregate as the net effect would be zero. In the particular case under consideration, exchange rate risk could be quite significant, given the importance of the U.S. dollar as an international store of value. If risk-averse investors balance their portfolios in order to diversify risk originating from uncertainty in currency values, the risk premium can be modelled as a function of the variability of returns. In this case the uncovered interest rate parity condition would be modified as follows: de, -


= a - b E,_,(Ae,

- r,_i)* + u,.


The variable (de, - rt_1)2 measures deviations from uncovered interest rate parity. A second potential source of risk is purchasing power risk. It may be that risk-averse asset holders get compensated for international differences in purchasing power risks that exist between national monies. Notice that purchasing power risk and the exchange risk are not independent if there is a tendency towards purchasing power parity. In the extreme case where purchasing power parity holds exactly, there is no independent exchange rate risk and only the purchasing power risk becomes relevant. Taking the difference between the logarithms of the standard deviations of inflation rates over the past four quarters ’ for the domestic and foreign countries as an indicator of purchasing

1 The choice of the lag length is dictated by the small size of the sample.

A. Margarita

power risk, (ul,(Ap)),

/ Risk premia and the foreign exchange market


one can write

de, - r,_, = a - b,u[,(Ap)

+ u,.


Finally, the possibility of interest rate risk is also taken into account. Interest rates on foreign and domestic assets are obviously of primary importance for asset holders, being so closely related to asset values, so interest rates variability is expected to play an important role in investors’ decisions. This is modelled as the difference between the logarithms of the standard deviations of short-term euro-currency interest rates over the past four quarters for the domestic and foreign countries ( ul, (r )). So we have de, - r,_ 1 =a+b,ul,(r)tu,.

2. Estimation



In order to test for the existence of a risk premium, a regression including proxies for the types of risk considered above was run over the period 1974(l)-1982(4) for the EMS-‘rest of the world’ group of countries. 2 The equation considered has the form de, - r,_, =a-bE


- r,_J2

- b,ul,(Ap)

- b&,(r)

+ cr,_, + u,.


The interest rate differential r, _ 1 has been included among the regressors so that the coefficient rl_, on the left-hand side of the equation is not constrained to be equal to one. Under the null hypothesis side is equal to zero, so this specification gives a simple the coefficient on r,-, on the right-hand t-test. Estimating eq. (11) gives the following results: 3 de, - r,_, = 0.0105 - 2.72(Ae,_, (0.53) SE = 0.04166,

0.009 uZf(r) - 0.004 uZ,(Ap) - 0.48 r,_,,


( - 0.85) R2 = 0.1757,

(-1.95) DW=





obs. = 36.

The variable chosen as a proxy for exchange rate risk, that is, (de,_, - r,_2)2, is not significant; 4 also the variable reflecting purchasing power risk, that is, ul,(Ap), does not play any major role. 5 Both these variables are then dropped from the equation, obtaining de, - r,- 1 = 0.0009 - 0.0081 uZ,(r) - 0.3 rl_i, (0.056)( - 1.90) SE = 0.04098,

R2 = 0.1506,


(-0.22) DW=


obs. = 36.

Though the EMS began operating in May 1979, some sort of exchange rate agreement was already in existence prior to this date among the countries considered (snake). 3 The means of the variables in the regression are (de, - r,_t) = -0.00711, (de,+, - r,_2)2 = 0.00195, u/,(r) = 0.548, ul,(Ap) = 0.409, r,_t = 0.12. 4 To proxy E,-t (de, - rr_1)2. the term (de, - rr_1)2 has been regressed on a constant and on its own lagged values (up to the third lag); the constant was the only significant term. However, we did include (de,+, - r,_*)* in the estimation of eq. (ll), as it was the lag with the highest t-ratio. 5 Collinearity between exchange rate risk and purchasing power risk could be a reason for them to appear not significant when they are both introduced in the same regression. However, they were also entered separately and the result did not change.


A. Margarita

Dropping left-hand

the constant side appears



and the foreign

and also rtPi from the right-hand to be valid, gives 6



side, as the unity restriction

de, - r,_, = 0.0089 uZ,(r),

on r,_, on the


( - 2.67) SE = 0.03989, When

R2 = 0.1464,

the variable

Ae, - r,_, = -0.81


AR2 = 0.1464, interest


rate risk, ul,(r)



obs. = 36.

is excluded,

one has (15)

(1.54) SE = 0.04237,

R2 = 0.037,



obs. = 36.

When interest rate risk is not taken into account the coefficient on r,_, is rather large and almost significantly different from zero. Eq. (14) both fits better and is more plausible than eq. (15). This finding implies that interest rate risk is not diversifiable as the tendency for interest rates to move with the market indeed suggests.

3. Conclusions In this paper the hypothesis of uncovered interest parity has been tested. Given covered interest parity (i.e., the interest rate differential is equal to the forward premium or discount), this is equivalent to the hypothesis that the forward exchange rate is an unbiased predictor of the future spot rate. A number of empirical studies ’ in recent years has rejected the joint hypothesis of rational expectations and risk neutrality. We have retained the assumption of rational expectations and investigated the possibility of risk averse investors. A regression including proxies for various forms of risk was run over the period 1974(l)-1982(4) for the EMS-‘rest of the world’ group of countries. Our results show that investors are sensitive to interest rate risk. Application of the proposed methodology to bilateral exchanges is an interesting area for further research.

References Baillie, R.T. et al., 1983, Testing rational expectations and efficiency in the foreign exchange market, Econometrica 51, no. 3, May, 553-563. Bean, C.R., 1985, Exchange rate, risk premia and new information: A note, Discussion paper no. 53, Feb. (Centre for Economic Policy Research, London). Cumby, R. and M. Obstfeld, 1981, A note on exchange rate expectations and nominal interest differential: A test of the Fisher hypothesis, Journal of Finance 36, 697-704. Hansen, L.P. and R. Hodrick, 1980, Forward exchange rates as optimal predictors of future spot rates: An econometric analysis, Journal of Political Economy 88, 829-853. Hansen, L.P. and R. Hodrick, 1983, Risk averse speculation in the forward foreign exchange market: An econometric analysis of linear models, in: J.A. Frenkel, ed., Exchange rates and international macroeconomics (University of Chicago Press, Chicago, IL). 6 The Lagrange multiplier test for the presence of autocorrelation in the residuals (up to the fourth lag) was not significant. ’ See for example Hansen and Hodrick (1980, 1983), Cumby and Obstfeld (1981), Baillie et al. (1983), Bean (1985).