TESTING FOR THE PRESENCE OF TIME‐VARYING RISK PREMIUM USING A MEAN‐CONDITIONAL‐VARIANCE OPTIMIZATION MODEL†
| Published date | 01 May 1994 |
| Author | Yerima Lawan Ngama |
| DOI | http://doi.org/10.1111/j.1468-0084.1994.mp56002005.x |
| Date | 01 May 1994 |
OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 56,2(1994)
0305-9049
TESTING FOR THE PRESENCE OF
TIME-VARYING RISK PREMIUM USING A
MEAN-CONDITIONAL-VARIANCE
OPTIMIZATION MODELt
Yerima Lawan Ngama
I. INTRODUCTION
In his tests of the mean-variance optimization model using monthly data,
Frankel (1982) found that international investors are risk neutral and thus
domestic and foreign assets are perfect substitutes. However, Frankel
recognized that his failure to reject the null hypothesis of risk neutrality does
not imply that the null is true; the test may simply not be very powerful.
Several researchers such as Frankel (1983), Giovannini and Jorion (1987),
Attanasio and Edey (1987), Lewis (1988) and Lyons (1988), also tested the
implications of the mean-variance model without much success.
The two most prominent reasons offered for the empirical rejection of the
mean-variance optimization model are that, investors may be too sophis-
ticated to maximize a function that depends only on the mean and variance of
end-of-period wealth, (Frankel and Engel, 1984), or that the degree of vari-
ability over time of the conditional variance of exchange rates is large enough
to account for the empirical failure of the model (Giovannini and Jorion,
1987). To account for the second possibility, Engel and Rodrigues (1989)
estimated a six-currency international CAPM allowing for time-varying
variances following an ARCH specification. Nevertheless, they failed to find
empirical support for the model.
This paper develops a version of the mean-variance optimization model in
which agents are allowed to cover their position in the forward foreign
exchange market. To gain some estimation efficiency, daily as opposed to
monthly data is used. Furthermore, the more parsimonious GARCH(p, q)
model is used to generate the estimates of the conditional variance.
tThe author thanks Peter Burndge for making his Phillips-Hansen program available and
Robert Lippens for providing the data used in this paper. He is also grateful to Patrick
McMahon and an anonymous referee for their helpful comments. The financial support of the
University of Maiduguri, Nigeria, is acknowledged.
© Basil Blackwell Ltd. 1994. Published by Blackwell Publishers, 1(18 Cowley Road. Oxford 0X4 uF,
UK & 238 Main Street, Cambridge, MA 02142, USA.
_(1+r)+(1+r*)=0 or F1 - S1 r - r*
S, 1+r*
If, however, the arbitrageur's positions were not covered, the expected
wealth would be:
E,( W2) = - L,(1 + r) +L1( 1+ r*) E1[]
and the expected variance:
I211
E1[var(W2)]L(1 + r*)2EivarI -
t[SL]]
C Basil Blackwell Ltd. 1994.
(2)
190 BULLETIN
II. THE MODEL
The model assumes a two-country world with foreign exchange and money
markets. Agents in both countries are classified as either speculators or
arbitrageurs. The speculators engage in open forward speculation, i.e. buying
or selling currencies foward with a view to profiting from the perceived
deviation between the forward rate and the speculators' expected future spot
rate. Arbitrageurs, on the other hand, engage in covered interest arbitrage in
the two money markets, i.e. borrowing an amount, L, from the domestic
money market at an interest rate, r, converting the amount at the spot rate, S,
lending it in the foreign money market at an interest rate r'', and then selling
the proceed foward in the forward market at the forward rate, F.
It is assumed that the preferences of all agents can be represented by a
utility function in expected mean and variance of period two wealth. Thus the
problem of a representative arbitrageur in country one can be written as:
max U{E1( W2), E1[var( W2)]}, (1)
L1
subject to W1 = C1
where C1 is the agents consumption in period one (all subscripts denote the
relevant period), and
E1(W2)= L1(1 + r)+L1(1 + r*),s'
where - L,(1 + r) is the arbitrageur's total liability and L1(1 + r*)(F,/S,) is
the turnover from the foreign investment. Since there are no unknowns in
E1( W2),
E1[var( W2)] = 0.
Thus the first order condition with respect to L1 is:
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