The forward exchange rate premium

The forward exchange rate premium

Economics Letters Olh5-1765/94/$07.00 169 44 (1994) 169-174 0 1994 Elsevier Science B.V. All rights reserved The forward exchange rate premium T...

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Economics Letters Olh5-1765/94/$07.00

169

44 (1994) 169-174 0 1994 Elsevier

Science

B.V. All rights

reserved

The forward exchange rate premium The case of Hong Kong D.P. Tang Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

Division of Social Science, School of Humanities and Social Science,

S.R. Lee* Department of Economics,

Benjaporn

St. John’s

University, Jamaica, NY 11439, USA

Thangkasemvathana

Department of Economics, Ramkhamhaeng Received 22 February 1993 Final revision received 18 August Accepted 24 August 1993

University, Bangkok,

Thaiiand

1993

Abstract

Using weekly data of the Hong Kong foreign exchange market, we perform a test suggested in Fama (Journal of .V.fonetary Economics, 1984, 14, 319-338) to analyze the source of variation in the three-month forward exchange rate premium. Prior to the visit to China by the Governor of Hong Kong to discuss the ‘1997’ issue, we find that the source of variation in the forward premium is not clear. After the visit to China, however, we find that the source of variation in the forward premium is mostly due to the variation of the risk premium. .IEL classification: F31

1. Introduction There have been a lot of papers testing whether or not the forward exchange rate is an unbiased predictor of expected spot rates. Studies in general found that the forward exchange rate fails to predict future spot rates. This failure has two implications: first, the foreign exchange market is inefficient; second, there exists a risk premium associated with forward rates which causes the forward rates to differ from expected future spot rates. In his seminal article, Fama (1984) presents a test that decomposes the variation in a forward exchange rate premium into a variation of a risk premium component and a variation of expected changes in the spot rate. Fama’s decomposition is right if the agents have rational expectations and the functional form assumptions are correct. Otherwise, alternative interpretations of the residuals are possible. Nevertheless, the Fama test is important because he is able to explicitly explain the source of variation in the forward premium. By decomposing a forward premium, one * Corresponding SSDI

author.

0165-1765(93)00318-I

D.P. Tang et al. I Economics Letters 44 (1994) 169-174

170

can test whether or not the source of variation in a forward premium is due to variation in expected changes in exchange rates or due to variation in a risk premium. This paper applies Fama’s model to the Hong Kong foreign exchange market in two periods using 24 March 1979 as a turning point for the Hong Kong foreign exchange market. The Hong Kong foreign exchange market is an interesting case to study on the forward exchange rate premium because China is formally expected to take over Hong Kong in 1997. The significance of 24 March 1979 is that on that date Sir Murray McLehose, the then governor of Hong Kong, first visited China through official invitation to discuss the ‘1997’ issue.’ The visit by the governor was viewed in Hong Kong as evidence of China’s willingness to accommodate Great Britain’s policies in Hong Kong subject to a series of negotiations between China and Great Britain. This visit created a lot of political uncertainty about sovereignty and administration in Hong Kong because a series of negotiations had to follow to determine the final details of the territorial status of Hong Kong. Through a series of negotiations this visit in 1979 by the governor led to a historic accord on 26 September 1984 between China and Great Britain, which restores Hong Kong to Chinese rule, effective 1 July 1997. In Hong Kong, the flexible exchange rate system was in place from 26 November 1974 to 16 October 1983. Since 17 October 1983, the Hong Kong dollar has been linked to the U.S. dollar, and it is currently pegged at HK $7.80 = US $1.00. Low interest rates and high inflation rates between 1977 to 1982 caused capital outflow and put downward pressure on the Hong Kong dollar. But there was no significant increase in foreign financial and economic conditions exchange market volatility until March 1979. Moreover, improved starting mid-1982, including deceleration in money growth, an increase in exports, and a reduction in the rate differential between domestic and foreign interest rates. Nevertheless, the volatility of the Hong Kong foreign exchange market accelerated. Thus, one might intuitively suspect the source of variation in the forward premium for Hong Kong was due to variation in the risk premium because of the expected eventual takeover by China. Our finding supports this intuition.* Before 20 March 1979, the source of forward premium variation is not clear. However, after 27 March 1979, the source of forward premium variation is mostly due to a variation in the risk premium. In section 2 a theoretical background of Fama’s test is discussed; in sections 3 and 4, data and results are discussed; in section 5, a conclusion is offered.

2. Theoretical

background

Let s(r) be the log of the spot exchange rate at time t, f(t) be the log of the forward exchange rate for delivery at time t and Z(t) be the information set upon which the market participants 1With rational expectations,

Wilson (1979) discusses how exchange rates can jump when the government simply announces a change in policy before the policy is actually implemented. Although nothing was settled at the March 1979 meeting regarding the status of Hong Kong, the impact on the Hong Kong foreign exchange market was immediate in anticipation of future negotiations. ’ Beside Hong Kong there are only two countries in Asia, Japan and Singapore, that have competitive foreign exchange markets without heavy government controls. Since the role of the Japanese economy is important in Asia, we compare the behavior of the Japanese foreign exchange market with that of the Hong Kong market to see if its behavior changed after 1979. Koedijk and Ott (1987, p. 11, Table 1) find that there is no evidence of rising risk premium in the Japanese foreign exchange market, before and after October 1979 when the Federal Reserve changed its operating procedure. In addition, they show that there is no evidence of rising risk premium in the foreign exchange markets in France, Canada, Italy and Switzerland. Thus, rising risk premium in the Hong Kong foreign exchange market was unique to Hong Kong and not a world-wide phenomenon.

D.P. Tang et al. I Economics

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condition their expectations. If the joint hypothesis holds, then the forward rate for maturity in n periods of the spot rate n periods ahead: f”(t)

171

of rational expectations and risk neutrality should be equal to the market’s expectations

(1)

= E[s(t + n)lZ(t)] .

then the forward rate If agents are, however, risk averse but still have rational expectations, may differ from the market’s expectations of the future spot rate by a risk premium, p(t). Thus, E
= EM

+ n)iZ(t)l + P(CI .

(2)

Agents still have an unbiased expectation of the n-period ahead spot rate but will not drive the current n-period forward rate into full equality with the n-period ahead spot rate. This is due to the existence of time-varying premiums in the forward rates. By subtracting s(t) from Eq. (2), we get (f”(t)

- s(t)) = (EM

+

4iWl - 44 + At>

(3)

As shown in Eq. (3), Fama (1984) decomposes the forward premium (f”(t) - s(t)) into its two components: the risk premium (p(t)) and the expected change in the spot exchange rate (E[s(t + n)]Z(t)] -s(t)). Using the forward premium as the explanatory variable and the forward rate error (f”(t) - s(t + n)), as well as the actual change in the spot rate (~(t + n) - s(t)), as dependent variables, Fama runs two regressions shown below: f”(t)

- s(t + n) = a, + b,(f”(t)

s(t + n) - s(t) = The regression

1

=

2

b2(fn(t)

slope coefficients

b = cov(fV)

b

a2 +

cow +n>- 497 f”(t)

Relying on the assumptions and (7) as follows:

-s(t))

- s(t)) of rational

(4)

+ u(t + n) .

are defined

- s(t + n), f”(t) var(f”(t) -s(t))

var( f”(t)

+ ~(t + n) >

-s(t))

(5)

as

-s(t))

(6)



- s(t))

(7)

. expectations

implicit

in Eq. (2), we can rewrite

varMQ>+ COV(P(~, Eb@+ 4lWl - 44 b1 = var(p(t))

b2 = var(p(t))

+ var(E[s(t

+ n)] - s(t)) + 2 cov(Z’(t), E[s(t + n)] - s(t)) ’

Eqs. (6)

(8)

var( E[s(t + n)] - s(t)) + cov( p(t), E[s(t + n) ] - s(t)) + var(E[s(t + n)] - s(t)) + 2 cov(p(t), E[s(t + n)] - s(t)) ’

b, represents the risk premium component of the forward premium; b, represents the accuracy of the forward premium in predicting the actual change in the spot exchange rate. As shown in Eqs. (8) and (9), the coefficients in (4) and (5) cannot be used directly to measure the proportion of variation due to risk and forecast errors. This is because the risk premium and the expected change in the spot rate may have non-zero covariance. The difference between b, and b,,

172

D.P. Tang et al. I Economics Letters 44 (1994) 169-174

however, provides some information about the source of variation in the forward premium, which is decomposed into variation in the risk premium and variation in the expected spot rate. Notice that since (f”(t) - s(t + n)) and (s(t + n) - s(t)) must sum to (f”(t) - s(t)), the sum of the intercepts in Eqs. (4) and (5), a, +a*, must be zero, and the sum of the slope coefficients, (b, + b,), must be unity. In principle, therefore, regressions (4) and (5) contain identical information. The importance of analyzing both equations is that the difference between the slope coefficients indicates the relative size of variances of the risk premium and the expected change of the spot exchange rate: b

_

1

b

=

2

var(&>>- var(Eb@+ n)lZ@)l - 44) Wf “(4 - 44)

(10)

From Eq. (lo), a significantly positive (b, - b2) implies that the variation in the forward premium is mostly due to the variation of the risk premium; a significantly negative (b, - b2) implies that the variation in the forward premium is mostly due to the variation in the expected change of the exchange rate; it is not possible to draw any conclusions about the source of the variation if b, - b, is not significant.

3. Data The weekly data used (Tuesday) for the empirical study begins on 5 July 1977 and ends on 20 September 1983 and is dictated by availability. If the data were not available on Tuesday, Wednesday data were used. Three-month forward rates were collected from the Far Eastern Economic Review; the spot rates were collected from the Hong Kong Monthly Digest of Statistics. As mentioned earlier, we separate the period into two subperiods using the trip to China by the Governor of Hong Kong on 24 March 1979, as a turning point in the Hong Kong foreign exchange market. Thus, the first period is from 5 July 1977 to 20 March 1979; the second period is from 27 March 1979 to 20 September 1983.

4. Results In Fig. 1, the ex post forward risk premium is shown. A casual observation of the chart shows a significant risk premium after 20 March 1979. To further the analysis we ran regressions (4) and (5) for the two periods using the forward premium as an explanatory variable and the forward rate error as a dependent variable in Eq. (4); moreover, we also ran the actual change in the spot rate as a dependent variable in Eq. (5). The results of the regression analysis are shown in Table 1. Table 1 shows that (b, - b2) is positive and the t-statistic is not significant for the first period; it is not possible to conclude the source of variation in the forward premium. For the second period, however, (b, - b2) is significantly positive at the 5% level. Results are strikingly different between the two periods. Since (b, - b2) is significantly positive at the 5% level for the second period, it seems that the variation in the forward premium is mostly due to the variation in the risk premium, as was suggested in Fama (1984).

5. Conclusions Using exchange

a model suggested by Fama (1984), we analyze the source rate premium for the Hong Kong foreign exchange market.

of variation in the forward Using the visit to China by

D. P. Tang et al. I Economics

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44 (1994) 169-174

percent 40 30 20 10 0 -10 -20

-30 -40 -50 -60 -70 -80 -90

I

I

I

I

I

,

1

I

JUNl971

JUN1978

JUNl979

JUNl980

JUNl981

JUN1982

JUN1983

JUNl984

7

JlJN1916

DATE

Fig. 1. The ex post risk premium: Table 1 Estimates variable

of forward

rate

error

Hong

Kong

and actual

f”(t) - s(f + 13) = a, + b,(f13(t) s(t + 13) -s(f)

= a, + b,(f”(t)

dollar

changes

-s(f)) -s(t))

per U.S.

dollar.

in the spot rate using

+ u(t

+

the forward

rate premium

as an

explanatory

13)

+ u(t + 13)

Period

a,

b,

az

b,

s(a)

s(b)

@, - bz)

DW

5.7.77-20.3.79 27.3.79-20.9.83

-0.014 -0.035

0.668 0.661

0.014 0.035

0.332 0.339

0.009 0.019

0.112 0.081

1.53 2.01”

1.70 1.76

* Significant at the 5% level. errors of a, and a, are equal because Notes: s(u) indicates the common standard error of a, and aZ, The standard a, +a?=O. s(b) indicates the common standard error of b, and b,. The standard errors of b, and bZ are equal as well because b,+b,=l. t(b, - b,) represents the t-statistic of (b, -b,), and it is equal to (b, - bz)/2s(b) [see Koedijk and Ott (1987, p. lo)].

the Governor of Hong Kong on 24 March 1979 as a turning point for the Hong Kong foreign exchange market, this study shows that while the source of variation in the forward premium is not clear prior to the governor’s visit, after the visit, the variation in the forward premium is mostly due to the variation in the risk premium.

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Tang et al. I Economics

Letters 44 (1994) 169-174

References Fama, Eugene F., 1984, Forward and spot exchange rates, Journal of Monetary Economics 14, 319-338. Koedijk, Kees G. and Mack Ott, 1987, Risk aversion, efficient markets and the forward exchange rate, St. Louis Economic Review 69, no. 10, 5-13. Wilson, Charles A., 1979, Anticipated shocks and exchange rate dynamics, Journal of Political Economy 87, no. 3, 639-647.