Posted: April 24th, 2023

JOURNAL OF FINANCIAL AND QUANTITATIVE ANALYSIS VOL. 33, NO. 2, JUNE 1998
Country and Currency Risk Premia in an
Enrierging Market
Ian Domowitz, Jack Glen, and Ananth Madhavan*
Abstract
The magnitude and determinants of credit and currency risks are topics of considerable
importance. This paper uses data on peso- and dollar-denominated debt issued by the
Mexican government to identify currency and country risk premia. We show that shocks
in equity and debt market returns translate into long-term increases in the premium demanded by investors with respect to currency and country factors. Country and currency
premia help explain equity returns and closed-end fund discounts. Additional evidence is
provided showing that investors did not anticipate the magnitude or timing of the currency
dAssessment of December 1994 and the subsequent financial crisis.
I. Introduotion
This paper uses unique term-structure data obtained from the primary market for Mexican sovereign debt to analyze the magnitudes and determinants of
credit and currency risks. The Mexican government issues both local and dollardenominated debt instruments. These instruments allow us to isolate the two
major components of the risk premia demanded by investors without recourse
to indirect statistical procedures. The first component—the currency (peso) premium measured as the yield spread between peso and dollar-denominated Mexican sovereign debt—represents the compensation for risks associated with adverse movements in the exchange rate. The second component—the country
(credit) risk premium measured as the yield spread between dollar-denominated
Mexican government debt and U.S. Treasury bills—represents the risk that the
• Domowitz, Department of Economics and Institute for Policy Research, Northwestern University,
Evanston, IL 60208; Glen, Economics Division, International Finance Corporation, Washington, DC
20433; and Madhavan, Department of Finance, University of Southern California, Los Angeles, CA
90089. Funding from the World Bank is greatly appreciated. Domowitz also thanks the Institute for
Policy Research, Northwestern University, for support. Special thanks are due to Michael Pettis and
George Nishiotis for Helpance in obtaining the interest rate and closed end fund data used here, and
to Mark Coppejans for expert research Helpance. We thank Warren Bailey (the referee), Steve Brown
(the editor), Margaret Forster, Robert Hodrick, and Aris Protopapadakis for their helpful comments.
Seminar participants at the Atlanta Finance Forum (Georgia State, Georgia Tech, Emory, and the
Atlanta Federal Reserve Bank), New York University, and the UCLA/UCIAJSC Finance Conference
provided many helpful suggestions. Any errors are entirely the authors’ own.
189
190 Journal of Financial and Quantitative Analysis
government might “default” on its obligations by delaying or refusing to repay
the debt or to restrict the movement of capital outside of the country.’
An analysis of these components is important for both practical and academic reasons. Sovereign borrowing is a significant source of capital for development in emerging markets, and debt instruments often carry significant premia
over their counterpart equivalents in more mature markets such as the United
States because of concerns over credit and currency risk. Concerns over related
risk factors have played a major role in triggering recent financial crises in Southcast Asian nations. Consequently, there is considerable interest in isolating the
relative economic importance of investors’ perceptions of currency and country
risk. The observed premia help us to understand better the evolution of beliefs
regarding country and currency risk, and the role of exogenous events in determining the cost of capital for both the public and private sectors. In this regard,
the term structure of currency and country risks may contain important information about investors’ beliefs regarding future economic events. Indeed, recent
studies by Ferson and Harvey (1991), (1993), Bailey and Jagtiani (1994), Bailey and Chung (1995), and Bekaert and Harvey (1995) show that expected stock
returns reflect exposure to macroeconomic and financial risks.
The relation between currency and country risk and returns in financial markets is an important issue. Intuition suggests that investors will revise their beliefs
regarding future currency and country risks following price movements in the debt
and equity markets. Alternatively, changes in risk premia may anticipate future
volatility in these markets, or common factors may affect both risk premia and
market volatility. Finally, we examine the relation between our measures of currency and country risk premia and the premium/discount of price over net asset
value for Mexican closed-end funds traded in the United States. The closed-end
fund premium is of interest because it is a measure of international capital market
segmentation. We also examine separately the ability of risk premia to predict
closed-end fund returns and changes in fund net asset values.
Our analysis yields several interesting findings:
i) Both currency and country risk premia arc economically significant, implying that borrowing costs can be substantially lowered by reducing the perceived risks of a currency dAssessment and sovereign default. This is especially
important for emerging markets where outside capital is scarce and costly.
ii) Changes in currency and country risk are weakly correlated, suggesting
that these two risk components do indeed refiect exposure to economically distinct
factors.
iii) The term structure of interest rates and its priced components reflects
rational expectations of future movements in rates and risk premia.
iv) There is no evidence that investors anticipated the major dAssessment of
the peso in December 1994, which may help explain why the dAssessment led to a
loss of confidence in Mexico by foreign investors.
‘ The isolation of country and currency premia via interest rate compari.sons is not new to this
paper, but is relatively unexplored. See, for example. Bailey and Chung (1995) and Frankel and
Okongwu(l996).
Donnowitz, Glen, and Madhavan 191
v) Country and currency risk premia rise in response to volatility in debt
and equity markets. These increases are persistent, suggesting that a reduction in
volatility in financial markets may lower interest rates over long horizons.
vi) The discount for the Mexico closed-end fund, which captures off-shore
demand or sentiment towards Mexican investments, decreases with both currency
and country risk.
vii) Equity returns to the fund based on both U.S. market prices and net asset
values are systematically related to our risk premia, suggesting that both currency
and country risks are priced factors in the return-generating process.
The paper is closely related to several disparate literatures. Our analysis of
currency and country risk premia is complementary to studies that directly estimate these components and use them to analyze financial markets. In particular.
Bailey and Chung (1995) use local and dollar-denominated interest rates to create a factor for currency risk in a multi-factor model of equity returns. Similarly,
Frankel and Okongwu (1996) emphasize the importance of currency and country risk factors in the context of emerging market monetary policy and capital
controls. De Santis and Gerard (1997), by contrast, use statistical procedures to
isolate indirectly the currency component of the risk premium. The investigation
of the intertemporal behavior of risk premia within the context of the expectations
hypothesis is similar to that in Barr and Campbell (1995), who examine expected
inflation using a term structure model. Cumby and Evans (1995) analyze alternative models of the dynamics of default in a probabilistic setting, and demonstrate
that the market can distinguish between current and future credit quality. Campa
and Chang (1995) test the expectations hypothesis with respect to a term structure
of implied options volatilities, i.e., risk as opposed to risk premia, in the foreign
exchange market. Our analysis of the 1994 dAssessment adds to existing literature on that topic (Lustig (1995), Bailey, Chan, and Chung (1997), and references
therein). Our examination of capital market segmentation in the context of the
relation between the closed-end fund premium and currency and country risk factors parallels the work of Bailey, Chan, and Chung (1997); it is also consistent
with Domowitz, Glen, and Madhavan (1997), who provide direct evidence on
internal market segmentation in the domestic equity market. Finally, the paper
complements the recent literature (see, e.g., Claessens and Pennacchi (1996)) on
the pricing of Brady bonds.
The paper is organized as follows: Section II describes the institutional structure of the market and develops our measures of currency and country risk premia; Section III provides a framework to analyze term structure of interest rates
and risk premia under rational expectations; Section IV contains empirical results
concerning term structure; Section V analyzes the dynamic relation between the
risk premia and volatility in debt and equity markets; Section VI contains results
on the relation between risk premia and the closed-end fund premium and equity
returns; and Section VII concludes.
192 Journai of Financial and Quantitative Analysis
II. Institutions and Data
A. Fixed-Income Securities in Mexico
The federal government of the United Mexican States issues several different
fixed-income securities. In recent years, the most important of these are Certificados de la Tesoreria (Cetes) and Bonos de la Tesoreria (Tesobonos). Both Cetes
and Tesobonos are short-term pure diseount notes issued at weekly auctions for
a variety of maturities.^ Subsequent to the auctions, a secondary market for the
instruments exists. Our analysis focuses on the weekly primary auction prices
that determine a yield to maturity. Restricting our attention to the primary market
also circumvents possible problems with secondary market prices that may not be
entirely representative in periods of illiquidity.
The difference between the two instruments lies in the manner in which the
return to the lender is calculated. A Cetes is a simple peso-denominated note
whose yield to maturity is determined by the discount demanded at the time of
issue. Payment is made in pesos at the time of maturity with no adjustment for
changes in the value ofthe peso relative to other currencies or Mexican inflation.
Tesobonos are more complicated. They are also peso-denominated instruments
issued at a discount, but the principal amount paid at maturity is indexed to the
peso-dollar exchange rate.-* Consequently, the Tesobono is essentially a dollardenominated security, subject to the added risk that the Mexican government will
suspend convertibility and renege on its promise regarding indexation.”*
B. Construction and Interpretation of Risk Premia
Define by rj the nominal risk-free yield on a dollar-denominated U.S. Treasury bill at time t with maturity in ; periods, C the yield on a Cetes bill at time t
with (• periods to maturity, and similarly define by V, the yield on a Tesobonos bill.
The Tesobonos rate V, can be thought of as the riskless treasury bill yield, r, plus
a risk premium, denoted by 7^,,, which represents the compensation required by
investors for the possibility that the issuer will “default” on its obligation. Default
^At year-end 1994, total Mexican internal public debt was NP171.3 billion, or slightly more than
$50 billion at the then-prevailing exchange rate. Of that amount, 55% consisted of Tesobonos, with
another 23% accounted for by Cetes. Tesobonos were not as important in previous years, having
grown from less than 1 % of the total at year-end 1992, with much of the growth taking place in early
1994. Subsequent to the December 1994 dAssessment ofthe peso, the market for Tesobonos collapsed
and they now account for only a fraction of the total public debt once again. See Umlauf (1993) for
details with respect to the structure of the auction market.
‘Tesobonos are a reincarnation of a previous instrument, Pagafes, with the switchover between the
two instruments taking place in 1991 when exchange controls were eliminated and the controlled and
market exchange rates were unified. For an examination of the links between the Cetes and Pagafes
markets, see Khor and Rojas-Suarez (1991). The Mexican government also issues bonds that are
indexed to Mexican inflation, known as Ajustabonos, but these were not as popular as Cetes during
our sample period.
“Capital controls were imposed in 1982 following the debt crisis and subsequent dAssessment. See
Melvin and Schlagenhauf (1985) for a description of the effect those controls had on eurodollar interest
rates paid by Mexican borrowers. During the period of our study, Mexican banks made insurance
against such controls available to investors for a nominal premium of 10-20 basis points. Following
the December 1994 dAssessment, the government offered investors a choice between payment in dollars
and payment in indexed pesos in an attempt to reduce investor concerns over repayment (see, e.g.,
Lustig(1995)).
Domowitz, Glen, and Madhavan 193
in this context is defined to be either a pure default (non-payment) or a refusal to
convert pesos into dollars (which imposes a significant cost on the lender). Then,
we can define the “country” or credit risk premium as
(1) iL = T-r.
Next, we can think of nominal, peso-denominated Cetes bond yield as the real
risk-free U.S. Treasury bill yield (i.e., the nominal yield less U.S. inflation), plus
terms that captures expected inflation in Mexico and compensation for real currency and credit (country) risks. Thus, we can write the Cetes yield as
(2) C = rj + ^^-^ ^ + T^^^ + Ti,,,
where TT^, is expected Mexican inflation over the remaining life of the bill, TT^,.,
is corresponding U.S. expected inflation, and 7^, is the real risk premium paid to
investors for the risk that changes in the exchange rate will affect the real value of
their investment. Using equation (1), the nominal currency (peso) risk premium
is
(3″) -y’ = -y’ + TT’ – TT’ — C’ – V
Thus, the nominal currency risk premium is the spread between Cetes and Tesobono yields, which consists of a compensation for foreign exchange variability
risk (see, e.g., Lewis (1995)) and expected peso depreciation. Note that the credit
risk premium, 7^,, is implicitly assumed to be the same for both instruments because they are issued by the same entity and are, hence, subject to the same pure
default (non-payment) and convertibility risks. One can argue that the credit risk
on Cetes is lower than for Tesobonos because they are peso-denominated and
the government can print an unlimited amount of pesos for repayment purposes.
This is misleading, however, because Tesobonos are also peso-denominated, albeit indexed to the exchange rate. The credit risk premium for Cetes bonds represents compensation for the risk that the government will unexpectedly devalue
the expected purchasing power of the bond by printing pesos. Such an event is
almost certainly likely to be associated with similar reduction in the real value of
Tesobonos through the imposition of capital controls.
C. Empirical Evidence on the Magnitude of Risk Premia
We obtained data on effective yields to maturity from weekly primary debt
auctions (both Cetes and Tesobono) for the period beginning July 1993 through
the end of November 1994 through Bloomberg Financial Markets. The instruments are issued with maturities ranging from seven to 360 days, but not all maturities are issued every week. For the sample used in this study, the most common
(and highest volume) maturities were 91 and 182 days. These two instruments are
the focus of our study. Additional data on weekly U.S. Treasury bill yields in the
primary market were obtained from Datastream. Finally, we obtained a monthly
series of the Consumer Price Index for Mexico from the International Monetary
Fund (IMF).
194 Journal of Financial and Quantitative Analysis
Sample statistics for the 91- and 182-day Cetes, Tesobonos, currency premia,
and country premia are presented in Table 1. We report separate sample statistics
for the two years to better isolate the effects of the major political and economic
events in Mexico in 1994. Both the country and currency premia are economically
significant. The median 91-day currency (or peso) premium, for example, was
8.4% in 1993. but actually declined to 6.9% in 1994. The corresponding figures
for the country premia are 2.0 and 2.4%, respectively, which are large considering
the short maturities of the instruments.
Series and Year
Cetes (91-day)
1993
1994
Cefes (182-day)
1993
1994
Tesobonos (91-day)
1993
1994
Tesobonos (182-day)
1993
1994
Currency premium (91-day)
1993
1994
Currency premium (182-day)
1993
1994
Country premium (91-day)
1993
1994
Country premium (182-day)
1993
1994
TABLE 1
Summary Statistics
Mean
0.136
0.142
0.134
0.140
0.051
0.066
0.053
0.071
0.085
0.076
0.080
0069
0.022
0.023
0.026
0.028
Median
0.139
0.145
0.137
0.143
0.051
0.068
0.052
0.074
0.089
0.075
0.084
0.065
0.020
0.024
0.024
0.027
Standard Deviation
0.012
0.027
0.013
0.022
0.002
0.010
0.003
0.011
0.012
0.020
0.013
0.015
0.007
0.008
0.007
0.008
This table contains summary statistics on traded instruments and derived risk premia in the
Mexican debt market for 91-day and 182-day maturities. The data for Cetes (government
securities denominated in pesos) and Tesobonos (government securities denominated in
dollars, payable in pesos at the official exchange rate) are annualized effective yields calculated from the Mexican government’s weekly primary auctions, from the beginning of July
1993 through the end of November 1994. The currency risk premium (peso premium) is
calculated as the arithmetic difference between Cetes and Tesobonos yields, where yield
is expressed as a decimal (i.e., 5% is 0.05). The country risk premium (country premium)
is calculated as the difference between the Tesobonos yield and the yield on U.S. Treasury
bills. Data reported are the mean and median yields and premia and the standard deviation
of the yields and premia, all in decimals.
The relative magnitude of the currency premia refiects the risks investors
attributed to peso inflation and exchange rate dAssessment.’ We also compute a
‘Mexicans are taxed on all income, both foreign and domestic, so that Mexican interest rates
will adjust to reflect any tax differences between the United States and Mexico. Further, tax rates
Domowitz, Glen, and Madhavan 195
real currency premium where we assumed a naive (random walk) model for expectations regarding inflation. Inflation in Mexico was relatively stable over this
period and more sophisticated models provide little additional gains. Specifically,
the real premium is computed as the nominal currency (peso) premium minus the
difference between the U.S, and Mexican expected inflation rates, based on (annualized) percentage changes in the respective Consumer Price Indices over the
month prior to the auction. The median real premium for the 91-day maturity (not
reported in Table 1) is 3.2 and 4,5% in 1993 and 1994, respectively. Similar values of 3,0 and 3,6% are obtained for the 182-day maturity. Although considerably
smaller than the nominal values, these figures are still economically significant,
D, Variation in Risk Premia over Time
While the summary statistics provide valuable information on the behavior
of the different variables, they also conceal much of what took place. Figure 1
graphs the Mexican country and currency risk premia. Except for March 1994 and
a brief period in early 1995, the currency premium greatly exceeded the country
premium. The currency premium declined substantially over the eight months
that preceded the assassination of presidential candidate Luis Colosio in March
1994; the country premium remained flat over most of this time, falling only
shortly before the assassination. Both premia increased in March, although the
increase in the country premium took place prior to the assassination and the
increase in the currency premium was much larger and followed the assassination.
Following the assassination, the country premium declined until, by the time of
the August 1994 presidential election, it had reverted to its pre-assassination level.
The increase in the currency premium was more persistent, and never quite fell
back to its previous level. Also notable in the graph is the effect of the December
1994 dAssessment that led to dramatic increases in both premia. Given the sudden
and dramatic swing that took place at that time, our analysis is constrained to the
pre-dAssessment period,
III. The Term Structure of Rates and Risk Premia
A. Definitions
The term structures for Cetes and Tesobonos, respectively, are defined as
(4) r^ = c-d,,
(5) r’l = T’,-T{.
Most research on the term structure has been restricted to interest rates. The
underlying risk premia, in this case, can be constructed from traded securifies
for Mexican investors on ordinary income are 38—40% for the highe.st income group. U.S. investors
would pay a similar rate on income earned in Mexico and then get a credit for the amount paid on
their U.S. tax return. There is no capital gains tax in Mexico. Given the .similarity in tax rates in the
two countries, and the symmetric treatment of income, it is unlikely that the differences in rates are
driven by tax factors. Of course, the variation in interest rate differentials over time is unrelated to tax
factors.
196 Journal of Financial and Quantitative Analysis
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Donnowitz, Glen, and Madhavan 197
and, as such, they too are subject to the same economic arguments that support
the expectations hypothesis.^ Assuming that TT^, = TT’^” for small values of n,
equations (1) and (2) yield the following term structure variables for the currency
and country risk premia, respectively,
(6) r;{ = %,-%, = d – d, – [ri – Ti,
Equation (6) indicates that the term structure of the currency premium can be
measured using only the observable rates of return from the Cetes and Tesobonos.
In equation (7), the term structure ofthe country risk premium contains a term for
the term premium in risk-free rates. In what follows, that premium is assumed to
be equal to zero.^
The summary statistics in Table 1 suggest that there were substantial term
structure differences between the two underlying debt instruments. On average,
there was only a rather small term premium in the Cetes rates in 1993, with a
slightly downward-sloping term structure in 1994. This is surprising given the
dAssessment that occurred at the end of the year, but consistent with respect to
movements in risk-adjusted returns. Volatility of the rates for the two maturities was roughly comparable. The Tesobono term structure is notably different,
with the long rate being slightly higher in 1993, but sharply higher in 1994. The
downward-sloping Cetes term structure reveals itself again in the currency premium term structure, which is downward sloping, on average, in both 1993 and
1994. Like the Tesobonos, however, the country risk premium term structure retains its positive slope in both periods.
B. Time Variation in Currency and Country Risk and Term Premia
Figure 2 illustrates the term premium for both the Cetes and Tesobonos.
Both premia display a remarkable level of short-term volatility over time, with
substantial shifts taking place from week to week. Perhaps most notable is the
tendency for the Cetes premium to be negative, especially in 1994, whereas the
Tesobonos premium is generally positive. In particular, there was a significant
spike in the Tesobonos premium at the time of the Colosio assassination in March
1994, whereas the Cetes premium actually became more negative at that time.
We also computed the correlation coefficients between the currency and
country term and risk premia for both levels and changes in these variables. Interestingly, although the levels of country and currency risk premia are positively
correlated, changes in the two premia are negatively correlated. For example, the
^This argument is articulated in Barr and Campbell (1995) in the context of expected inflation and
a comparison of nominal and indexed notes. Campa and Chang (1995) also examine the validity ofthe
expectations hypothesis with respect to the term structure of volatilities in foreign exchange options.
”One alternative would be to employ U.S. Treasury bills as proxies for risk-firee rates, but it is
difficult to believe that six-month Treasury bills are viewed as truly risk-free by the investing public
because of the inflation risk that they contain. As a result, the term structure of Treasury bill rates
would contribute to our country risk measure and could actually introduce more noise than it removes.
Moreover, as shown below, under the expectations hypothesis, the term premium should be constant
over time.
198 Journal of Financial and Quantitative Analysis
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Domowitz, Glen, and Madhavan 199
correlation between the currency (“peso”) premium and the country risk premium
is 0.66 for the 91-day notes, but is -0.34 for changes in these variables. Anticipating evidence presented in Section IV with respect to cointegration, we note
that the levels of the premia contain a unit root. Nevertheless, the level correlations are consistent estimates (Stock (1987)). The proper interpretation is that
the level correlations represent long-run association, while the estimates using
the differences are short-run correlations. The findings also are reflected in the
negative correlation in both levels and changes in the currency and country term
premia. For example, the correlation between the changes in the country and currency term premia is —0.65. These results suggest that the two risk components
identified do indeed reflect exposures to different economic factors. We turn now
to a more formal investigation of these issues.
C. The Expectations Hypothesis
Under rational expectations, the slope of the term structure (and its priced
components) reflects investors’ beliefs about future movements in interest rates
and risk premia. In particular, the expectations hypothesis states that current longterm rates reflect optimal forecasts of future short-term rates.^ For pure discount
notes with maturities / andj (where i is some integer multiple ofj), Campbell and
Shiller (1991)—henceforth CS—show that under the expectations hypothesis,
/-Q ij — J T^ij Z7 D’~J ni
(°) ^l = ‘. 1-* ( — ^»”(+7 “” “(I
where F’/ is a term premium as previously defined, and R is the /-period rate
of return (or premium) used in the definition of T,^. Equation (8) states that the
term premium is proportional to the expected difference between today’s longterm rate and the future short-term rate. Assuming that expectations are rational,
equation (8) provides our first test of the expectations hypothesis: a regression
of the realized value of the right-hand side of the equation on a constant and its
predicted value, s’j, provided that the underlying rates are integrated of order one.
In the case of the risk premia defined here, the latter requirement translates into a
cointegration restriction.
This first test leads to the following four regression equations,
(9a) ipilj-ipt = a + l3s%-i-c,,
(9b) I’ni.ij-lL = a + ds’L + t,,
(9c) C~j – c; = Q + /35’^, -I- e,,
(9d) C7-^ ‘ = a + psl, + e,,
where, in each case, the null hypothesis under the expectations hypothesis is that
a = 0 and /3 = 1. Essentially, these equations try to predict the change in yield on
a bill as its maturity declines.
*’The expectations hypothesis has a long history and has been the subject of considerable empirical
investigation (Campbell and Shiller (1991)). A theoretical discussion of the expectations hypothesis
is presented in Cox, Ingersoll, and Ross (1981). The model has many variants including both linear
and non-linear forms. We focus upon the linear approximation.
200 Journal of Financiai and Quantitative Analysis
D. The Perfect-Foresight Spread
A second method for testing the expectations hypothesis discussed by CS
(1991) uses the perfect-foresight spread, i.e., the spread that would obtain under
the expectations hypothesis, if there were perfect foresight about future interest rates. Our second test of the expectations hypothesis involves regressing the
perfect-foresight spreads onto their respective actual spreads, r’/-‘, yielding.
(10a)
(10b)
(10c) 1^1 (y^,+,-y«,j = a+p I
(lOd) (1](J J) = a + ph–i,,]+e,.
These regressions can be thought of as predicting the change in yield holding
maturity constant. Under the expectations hypothesis, the slope will be unity in
regressions (lOa)-(lOd).
E. The Theoretical Spread
Regression-based tests involve overlapping data that limit the number of independent observations, and do not tell us how similar are the movements in the
actual spread to those implied by the expectations hypothesis. CS (1987) propose an alternative vector-autoregressive (VAR) approach for evaluating present
value models. From the VAR coefficients, one can compute the optimal forecast
of 7-period interest rate changes. The long-run behavior of interest rates is then
inferred from their short-run behavior in the sample period, rather than being estimated directly. The theoretical term structure spread can then be calculated from
the model and compared with the actual spread.
Application of the VAR methodology involves projection of the perfectforesight spread, 5f, onto a subset of the information available to market participants. Assuming that A;, = [AR’,,S’i] is a stafionary vector-stochastic process,
past values of JC, can be used as the information set. Under the assumption that x,
is a pth-order VAR, the system can be rewritten as a first-order VAR Zi=Azi-i+ Ut
where z, consists of current and lagged values of the components^f A:, and A is a
matrix of coefficients, CS (1991) show that the theoretical spread, 5f, which is the
spread that would obtain if the expectations hypothesis were true (the dependent
variables of equations (lOa)-(lOd)), can be expressed as
(11) ~S’i = h’ .
where /i is a vector defined such that h’zt = A]^,, and / is an appropriately defined
identity matrix.
Domowitz, Glen, and Madhavan 201
The theoretical spread should equal the actual spread if the model accurately
describes the term structure of interest rates. It follows that the correlation between the two and the ratio of their standard deviations should both equal one if
the theory is correct. Our third and fourth tests of the expectations hypothesis involve estimating these theoretical correlations and variance ratios and testing for
unitary values.
IV. Empirical Tests of the Term Structure
A. Unit Root and Cointegration Tests
Our regression and VAR-based tests on interest rates and constructed preiTftk presGppuiftr cafdiiT amV rum’ ana’ c^oihtegratfon requirements. TRe unit root
requirement is that the rates and premia at both maturities be integrated of order
one; the cointegration requirement, if satisfied, justifies the stationarity of the relevant term spreads in all regressions, including the term spreads of the risk premia.
We cannot reject the hypothesis of a unit root in any of the series. Similarly, we
cannot reject stationarity of the spreads; i.e., cointegration appears to hold for the
same securities over different maturities, with a cointegration coefficient of unity.
Cointegration is rejected only for the pair of 91-day Tesobonos/182-day Cetes,
but this spread is not used in our subsequent analysis. These results are similar
to those obtained using secondary market data by Khor and Rojas-Suarez (1991)
for Cetes and Pagafes, the latter being a precursor of Tesobonos over the period
1987-1990.
B. Regression Tests
Results for both sets of expectations hypothesis regressions are reported in
Table 2. Panel A contains the regression of the long rate on its theoretical counterpart and Panel B contains the regression of the perfect-foresight spread on the
realized spread. Although we report results for the underlying instruments for
completeness, the focus of the discussion is on the term structure of the premia,
which is the essential contribution here.
1. Comparison of Theoretical and Actual Long Rates
The point estimates for the regression slopes in Panel A vary across instruments and the standard errors of individual coefficients are relatively large. The
expectations hypothesis, however, entails a joint test of a zero constant term and a
unitary slope. The joint test for the currency premium and the peso-denominated
Cetes yields significance levels of 0.56 and 0.14, respectively, indicating a failure
to reject the expectations hypothesis at reasonable levels of statistical significance.
The joint test for the country premium and the dollar-denominated Tesobonos rejects the null soundly in both cases, however.
Both the Cetes and the currency premium generate positive slope coefficients, unlike the corresponding results for U.S. data, and in this sense, the Mexican data are more supportive of the expectations hypothesis. Further, the joint
tests for the peso-denominated instrument and the associated currency premium
202 Journal of Financial and Quantitative Analysis
TABLE 2
Term Structure Regressions under the Expectations Hypothesis
Panel A. Repression of the Change in the Long Rate on its Theoretical Counterpart
Cetes
Constant (a) -0.009*
(0.005)
Slope (/3) 0.343
(0.775)
Currency
Tesobonos
0.002
(0.003)
-0.403
(0.439)
Country
Pretniutn
0.009
(0.009)
1.545*
(0.778)
Panel B. Repression of the Perfect-Foresight Spread on the Realized Spread
Constant (a) -0.005*
(0.002)
Slope (0) 0.672
(0.388)
0.001
(0.001)
0.299
(0.219)
0.005
(0.004)
1.273**
(0.389)
Premium
-0.002
(0.002)
-0.570
(0.411)
-0.001
(0.001)
0.215
(0.206)
This table contains regression results upon which tests of the expectations hypothesis of
the term structure are based, for traded instruments and derived risk premia in the Mexican
debt market. Panel A contains results from the regression.
where the superscripts denote maturity, n = 182 days, and m = 91 days. Panel B contains
results from the regression.
with the same notational conventions. Standard errors in parentheses are corrected for serial correlation and heteroskedasticity in the errors. The data for Cetes (government securities denominated in pesos) and Tesobonos (government securities denominated in dollars,
payable in pesos at the official exchange rate) are annualized effective yields calculated
from the Mexican government’s weekly primary auctions, from the beginning of July 1993,
through the end of November 1994. The currency risk premium (peso premium) is calculated as the arithmetic difference between Cetes and Tesobonos yields. The country risk
premium (country premium) is calculated as the difference between the Tesobonos yield
and the yield of a three-month U.S. Treasury security, in decimals. Asterisks * or ** indicate
significance at the 5% and 1% levels, respectively, in a two-tailed test.
fail to reject the hypothesis. In short, while currency risk appears to be priced
consistently with the expectations hypothesis, country risk is more unpredictable.
2. Comparison of Perfect-Foresight and Realized Spread
The data contained in Panel B of Table 2 for the regression of the perfectforesight spread on the realized spread yield a similar set of results. Once again,
both the Cetes and peso premia fail to reject the null hypothesis, whereas both
the Tesobonos and country premium reject quite soundly. The point estimates
for all slopes are now positive, and the estimates are substantially more precise
than those reported in Panel A, suggesting that the larger standard errors in Panel
A may reflect the nature of those regressions as much as the short time-series
involved. CS (1991) also report generally smaller standard errors for the perfectforesight regressions.
Domowitz, Glen, and Madhavan 203
3. Exogenous Events and Investors’ Expectations
The second year of our sample was an especially tumultuous period for Mexico, and it is intuitively plausible that exogenous events (e.g., political turmoil)
would affect estimates of the expectations regressions. We investigate the possibility by reestimating the regressions of both Panels A and B using both constant
and slope dummy variables for major political events. These include the Chiapas
uprising (January 1, 1994), the Colosio assassination (March 23,1994), the election of Zedillio (August 21, 1994), and the assassination of Massieu (September
28,1994). We also include the approval of NAFTA in 1993 (November 17).^ The
general conclusions reported above for all sets of regressions do not change with
the introduction of controls for political events.
On the other hand, for the periods surrounding such events, we obtain a pair
of interesting results. First, the expectations hypothesis for the currency risk premium is rejected over such periods. This appears intuitive since accurate forecasts
of exchange rates would be particularly difficult during such periods of relative
uncertainty. In contrast, the expectations hypothesis cannot be rejected for the
country risk premium during such periods. The significance level of the hypothesis test is approximately 0.4 for both the regression of the long premium on its
theoretical counterpart and for the regression of the perfect foresight spread on
the realized spread. It would appear that, once attention is closely focused on the
Mexican political situation, country risk is priced more accurately.
4. Was the DAssessment Anticipated?
The evidence so far suggests that the expectations hypothesis is a reasonable
description of the term structure of our constructed country and currency premia.
If so, an examination of the residual errors that represent deviations from the
hypothesis may shed light on whether events such as the dAssessment in December
1994 were in any way anticipated or reflected in the term structure. This question
is also highly topical given the recent financial crises in Thailand, Malaysia, and
other Southeast Asian nations.
We define the residual by
where additional subscripts for country and peso premia have been suppressed.
These residuals are equivalent to what would be generated from the expectations
hypothesis using the perfect-foresight spread as the model of expectations. Under
that hypothesis, these residuals should be random errors, although they will have a
moving average component due to the overlapping data used in the computations.
By examining the behavior of these residuals, one can learn something about
investor expectations regarding future movements in short-term risk premia. In
particular, when the residuals are positive, it indicates that the long rate was priced
‘For events that were clearly anticipated, the dummy variables took on a value of one for two
weeks prior to the event and two week.s after the event. For the uprising and assassinations, the
dummy variables were a.ssigned the value of unity only for the two weeks after the event. The precise
timing (i.e., two weeks, one week, etc.) does not affect the qualitative results reported here.
204 Journai of Financiai and Quantitative Analysis
below the rate that would have obtained if investors had had perfect foresight
about the future short rate. Similarly, when the residual is negative, it indicates
that investors overpriced the long rate relative to the rate that would have obtained
if investors had had perfect foresight.
Figure 3 presents time-series plots of the theoretical perfect-foresight residuals for both the country and currency risk premia. The residuals have been divided by their own standard deviations in order to facilitate comparison across
time-series. The sample period is constrained to the period ending October 26,
1994, because of the 13-week lead that is needed in order to calculate the residual. There is strong similarity in the behavior of the two time-series with respect
to the movements that take place just prior to the dAssessment. At that period in
time, September 21-October 26 (given the 13-week lead in the calculations), both
long-term risk premia were very underpriced relative to the values that would have
obtained with perfect foresight. This provides clear evidence that the expectations
that investors held prior to the dAssessment did not anticipate the large increase in
the short-term risk premia that followed the dAssessment.
This conclusion is consistent with an examination of the underlying interest
rates themselves. There was no obvious increase in yields since about April prior
to the dAssessment, with a large jump following that event. This suggests that the
Mexican government was successful in convincing the market that no dAssessment
was forthcoming. The strategy of the Bank of Mexico largely consisted of a policy of sterilized intervention during the March-April 1994 period, and again in
November and December, A decline in foreign exchange reserves was offset by
an increase in the Bank’s domestic assets, Relafively low interest rates were maintained early in the year and during a later period of selling pressure on the peso
prior to the dAssessment. Although there were some signals of potential internal
imbalances, positive moves by the government included a reduction in inflation
and maintenance of balanced government fiscal accounts (International Monetary
Fund (1995)),
Analysis of the perfect-foresight residuals further suggests that the dAssessment looks much like any other unanficipated shock over the sample period, except
for the sheer magnitude of the aftermath, the reasons for which are themselves
topics of debate (e.g., Lusfig (1995)). A couple of examples may help to illustrate
the reasoning behind this conclusion.
The long currency premium was underpriced in early 1994, indicating that
investors underestimated the future short rates that were subsequently realized.
The surprise was two-fold. The ruling party presidential candidate was assassinated in late March, and the upturn in rates and the currency risk premium led
to a substanfial error in the expected value of the future short-term premium as
measured by the model. The second surprise was due to external pressures. The
U.S, Federal Reserve raised the federal funds rate from 3,0 to 3,25% in February,
with other increases later in the year.
Similarly, the country risk premium was underpriced over the December
1993-February 1994 period, because the U,S, rate increase was unforeseen. The
increase in U,S, rates had the expected adverse effect on net capital flows into
Mexico, although the first sharp decrease in reserves occurred only around the
time of the assassination. Perhaps surprisingly, the Mexican government chose
Domowitz, Glen, and Madhavan 205
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206 Journai of Financiai and Quantitative Anaiysis
not to widen the exchange rate band, or otherwise change exchange rate policy.
Instead, domestic rates rose in March and April, accompanied by an increase in
the supply of dollar-denominated debt.
By late March, the country risk premium had become overpriced, as investors demanded higher term premia in the face of the increasing supply of
Tesobonos, although those premia were not justified by the short rates that were
realized ex post (but prior to the dAssessment). Interestingly, this observation mirrors the comments of Lustig (1995), who views the willingness of investors to
absorb the increase in Tesobonos, relative to Cetes, as a sign that investors did not
find the government’s exchange rate policy to be credible. On the other hand, the
degree to which the country premium was overpriced diminished sharply over the
two months just prior to the dAssessment. We are again left with the conclusion
that examination of the risk premia cannot support the thesis that the dAssessment
was anticipated by foreign investors.
C. Comparisons of the Actual and Theoretical Spread
An alternative approach to assessing the ability of the expectations hypothesis to describe the term structure of interest rates and risk premia is to compare
the actual spread and its theoretical counterpart under the expectations hypothesis. Table 3 contains correlations between those two variables and the ratio of
their variances, both of which should be one under the null hypothesis. The tirst
column in the table presents the correlations, which are uniformly positive and
close to the theoretical value. Only in the case of Cetes is the correlation statistically different from its theoretical value. However, the correlation, 0.939, is
economically very close to one. In contrast, the correlations reported in CS (1991)
are often much smaller in magnitude and are generally estimated with less precision. Notably, CS (1991) report a correlation for the six-month/three-month U.S.
instrument that is —0.355 and statistically not different from zero.
Ratios of the variances of the theoretical and actual spreads are presented in
the second column of Table 3. Of the values reported in Table 3, only the country premium has a value statistically different from the theoretical value of unity,
but the estimated values are small relative to the correlations reported in the first
column. These results are similar to those reported in CS (1991), where little relationship is found between the variance ratio and maturity. Comparing the results
in Tables 2 and 3, we conclude that currency risk appears to be priced consistently
with the expectations hypothesis, but that country risk is more unpredictable.
V. Risk Premia and Volatility in Financial Markets
The country and currency factors discussed above are risk premia because
they reflect return differentials demanded by the market for bearing certain risks.
In this section, we turn our attention to the dynamics by which investors alter
their perceptions of country and currency risk. Specifically, we analyze the relation between the volatility in Mexican financial markets and our measures of the
price of risk. The markets that we use for comparison include both ofthe Mexican short-term debt instruments—Cetes and Tesobonos—as well as the Mexican
Domowitz, Glen, and Madhavan 207
Correlation
(Theoretical, actual)
0.939
(0.021)
0.885
(0.106)
0.951
(0.030)
0.902
(0.131)
Variance Ratio
(Theoretical/actual)
0.548
(0.283)
0.563
(0.478)
0.680
(0.336)
0.215
(0.182)
TABLE 3
The Spread and its Theoretical Counterpart under the Expectations Hypothesis
Cetes
Tesobonos
Currency premium
Country premium
This table contains the correlations between the actual (182-day to 91-day) spread and
the theoretical spread, and the ratios of the variance of the theoretical spread to the actual spread, for traded instruments and derived risk premia in the Mexican debt market.
The theoretical spread is derived empirically from a two-variable, fourth order, vector autoregression of changes in the short (91-day) rate and the spread between long (182-day)
and the short rate, embodying the expectations hypothesis, following Campbell and Shiller
(1991). The variance of the theoretical spread is calculated from the same vector autoregression. Standard errors are contained in parentheses. The data for Cetes (government
securities denominated in pesos) and Tesobonos (government securities denominated in
dollars, payable in pesos at the official exchange rate) are annualized effective yields calculated from the Mexican government’s weekly primary auctions, from the beginning of July
1993, through the end of November 1994. The currency risk premium (peso premium) is
calculated as the arithmetic difference between Cetes and Tesobonos yields. The country risk premium (country premium) is calculated as the difference between the Tesobonos
yield and the yield of a three-month U.S. Treasury security.
equity market. An empirical analysis of this issue may help readers better understand the pricing of risk.
Previous work also has explored a correlation between risk measured in one
market and returns in another market. Korajczyk and Viallet (1992), for example,
examine the ability of equity risk factors to explain foreign exchange risk premia
in a group of developed countries. They find that risk factors derived from equity
returns explain a significant part of foreign exchange risk, but that a substantial portion remains unexplained. Bailey and Chung (1995) examine the relation
between political/country risk (defined as the spread between free and official exchange rates) and equity returns in the Mexican context. They find a link between
both of those risk factors and the level of equity returns, but the relationship is statistically weak for the country risk factor. Harvey (1995) examines a measure of
foreign exchange risk and equity returns in both developed and emerging markets.
He finds that there is a meaningful relationship in many, but not all countries.
The cited work relating risk and return between markets has concentrated
on specific models of return behavior and the ability of certain risk factors to
explain returns, either equity or currency, within that model. Our approach is
different in two respects. We focus on volatility, as opposed to returns and, as a
consequence, we posit no specific model of return behavior. Instead, we estimate
the correlation between the dynamics of volatility in one market with changes in
risk premia that should, in theory, affect all related markets. This simplification
208 Journal of Financial and Quantitative Analysis
allows us to observe the dynamics between volatility and the risk premium over
time, as described in detail below.
A. Estimating Conditional Volatility
Let (7? be the conditional volatility at time t for market). We are interested
in the correlation between this measure of conditional volatility and our risk premium, generically denoted by Xn+k, defined as pf-, = {/T)ElXi,+kaf,/cTxtcrat,
where the correlation is calculated for k leads/lags between the two markets.
These correlations provide information on the extent to which increased volatility
in one market induces investors to raise the risk premium demanded in the other
market at a subsequent date. They also provide information on the time duration
between increases in volatility and subsequent changes in the risk premium, and
the degree of persistence of any increase in risk premia that follows a volatility
innovation.
Correlations are calculated for leads and lags of up to 10 weeks using conditional volatilities estimated from three markets: Cetes, Tesobonos, and the Mexican equity market. The rationale for using a 10-week window is to measure
the relation, if any, between risk premia and equity and debt market volatility
over relatively long horizons so as to detect low-frequency effects arising from
macroeconomic policies or business cycles. Let Y denote the relevant stationary
series in the market to be investigated; e.g., first differences in Tesobonos and
Cetes rates, stock market returns, and term spreads in the debt markets. Volatility
is measured by estimating the following MA(3)-ARCH process,
(13) Y, = ii + 9ie,^i-^-92ei^2 + 0}.f,-}, + ei,
(14) a^ = u! + a£,-__ I.
We estimate (13)-(14) using quasi-maximum likelihood under the assumption
that e, I !^;-1, where ^,- j denotes information available at time r — 1, is distributed
as A'(0, af). The MA(3) formulation for the conditional mean is designed to capture any serial correlation in the measures of underlying market activity that bias
estimates of the volatility dynamics. Although the normality assumption may not
hold exactly in the data, quasi-maximum likelihood estimates of the parameters
are generally consistent and asymptotically normally distributed, provided that
the conditional mean and variance are correctly specified.’°
B. Estimated Correlations
For the Cetes and Tesobonos markets, two different measures of volatility
are estimated: one using first differences in Cetes and Tesobonos rates for a given
maturity; and another for the term spread between the Cetes (or Tesobonos) for 91
maturity. For the equity market, volatility is based on weekly returns for the Mexican Stock Market Index (MSMI), calculated from treasury auction to treasury
‘”See, for example, Bollerslev and Wooldridge (1992). The MA(3) process delivers white noise
innovations for all series examined here. A more general GARCH process was investigated, but failed
to converge, in most cases, owing to very low levels of persistence in volatility in these markets.
Domowitz, Glen, and Madhavan 209
auction, so that stock returns and volatility are computed over exactly the same
period as those for debt instruments and associated risk premia. Correlations are
then calculated between these conditional volatilities and the 91-day currency and
country risk premia for different leads, lags, and maturities. In total, seven different sets of correlations were calculated: three for the Cetes volatilities—one each
for the two different maturities and one for the 91-182-day spread—three for the
Tesobonos volatilifies, and one for Mexican equity market volatilifies. Each set
contains correlations with the country and currency risk premia for 91-day and
182-day maturities.
All seven sets of correlations display similar behavior. The correlations for
volatilifies for 91-day Tesobonos, the 91-182 Cetes spread, and the Mexican equity market are presented as representafive, including one debt instrument, one
term spread, and the relationship with the stock market. Correlafions with 182-
day premia exhibit similar patterns and are not reported here. Table 4 contains
estimates of the correlations between 91-day country and currency risk premia
and the volatility measures for various lags and leads. For example, the first column in the table contains the correlations between the 91-day country premium
and volatility in the Tesobonos rate. In that column, Tesobonos market volatility
at time t — 6 was associated with a correlation of 0,4067 with time t country risk
premia,
1. Volatility in Fixed-Income Returns
Tesobonos volatility shocks lead to subsequent increases in country and currency risk premia. Increases in risk in the debt market lead to increases in the
premium demanded for risk components in future bond auctions. This effect is
much more pronounced for the country premium at long horizons, while at horizons shorter than one month, the magnitude of the relationship between lagged
volatility and current premia is roughly the same across country and currency
premia. This is consistent with our discussion of the variability of premia in Section II. The dynamics of country premia are far smoother than those of currency
premia, on average.”
The relationship between current period premia and subsequent volatility
shocks is negafive across both premia and maturifies. Further, this effect is much
more evident for currency premia, as measured by the absolute values of the correlations. These results are explainable by considering the relative persistence of
volatility and premia, as well as the variability of the premia themselves. Esfimates of the model of market volatility dynamics indicate very low persistence
of volatility in the Mexican markets. In contrast, both the country premium and
currency premium are highly persistent. The former implies a swift regression to
the mean of conditional volatility after a volatility shock. The country premium is
persistent, and relatively constant compared to the currency premium. It follows
” A central issue in Khor and Rojas-Suarez (1991) is the extent to which the domestic debt and U.S.
dollar-denominated debt issued by Mexican authorities behave in the same fashion. Using primary
market data, as opposed to their use of secondary market prices, we confirm that the two types of
debt move together over the long run, although there are significant difference.s in behavior over short
horizons. In particular, peso-denominated rates tend to follow the expectations hypothesis, while
dollar denominated instruments clearly adhere less strongly to that model.
210 Journal of Financial and Quantitative Analysis
TABLE 4
Correlations of Financial Market Volatilities with
Lead/Lag
in Volatility
-10
—9
– 8
– 7
– 6
– 5
—4
– 3
– 2
– 1
0
1
2
3
4
5
6
7
8
9
10
Tesobono Volatility
Country
Premium
0,3999
0,3913
0,2776
0,2684
0,4067
0,2923
0,3488
0.3984
0.2378
0.2347
0,3168
-0,0719
-0,0411
0,0082
-0.0421
-0.0105
-0,1933
-0,2447
-0.2918
-0.1921
-0,2219
Currency
Premium
0,0942
0,0485
0.1052
0.2584
0.1642
0,2600
0,3154
0,3071
0,3471
0,3506
0,3407
-0,2510
-0.2710
-0.3624
-0,3674
-0,3994
-0,3825
-0.3550
-0.3116
-0,3746
-0,3298
Country and Currency Risk
Spread Volatility
Country
Premium
0,1665
0.1403
0,2978
0,1709
0,2348
0.1855
0.1495
0.0983
0.0590
0,1067
0,1131
-0,0316
-0,1680
-0.2223
-0.2176
-0,1273
-0,1907
-0.0433
-0.1079
-0,0778
-0.1505
Currency
Premium
-0.0013
0,1726
0,0263
0,1118
0.0529
0.0885
0.0759
0,0800
0,1221
0,1162
0.0923
-0,1981
-0,1818
-0.1238
-0.1429
-0,1362
-0,1126
-0.1766
-0.1076
-0,1391
-0,0847
Premia
Equity
Market Volatility
Country
Premium
0,1903
0,3000
0.2620
0.1520
0.1891
0.1960
0.2035
0,1742
0,0729
0,0836
0,1175
0.1942
-0.2607
0.0644
-0.0619
-0,1902
-0.3364
-0.3289
-0.1532
-0.0650
-0,0539
Currency
Premium
0,1264
0,1079
0,0986
0.1319
0.1348
0.1725
0.2456
0.1674
0.1841
0.1888
0,2449
-0.1423
-0.2209
-0.2539
-0.3126
-0.2192
-0,2400
-0,2310
-0,2855
-0,2417
-0.1855
This table contains the correlations of the volatility of: 91 -day Tesobonos returns; the volatility
spread between 182-day and 91-day Cetes yields; and volatility of returns from the Mexican
Stock Market index at weeks ( +/, y = -10,. . .0,.. . 10, with 91-day country and currency
risk premia at week t. In all cases, volatility is the predicted value from a first-order autoregressive conditional heteroskedasticity (ARCH) model, using weekly changes in the rate as
the dependent variable. The data cover the period July 1993 to November 1994. The currency risk premium is defined as the arithmetic difference between Cetes and Tesobonos
yields and the country risk premium is the difference between the Tesobonos yield and the
yield of a three-month U.S. Treasury security
that both sets of correlations should be negative, but that the correlation of current
country premia with future volatility should be closer to zero, relative to that of
the currency premium.
Table 4 also reports correlations between the risk premia and the volatility
of the Cetes term spread. The Cetes bond appears to follow the expectations
hypothesis reasonably well, and so this spread is interpretable as the predictor of
the 91-day change in yield on the 182-day instrument. The same general pattern
as for the underlying debt instrument at a single maturity emerges. Volatility
shocks in the rate predictor have a positive effect on premia demanded in the
market for debt. Differences in relative persistence between the volatility of the
spread and the level of premia result in a negative correlation of current period
premia with future volatility. For small values of leads and lags in volatility, i.e.,
one to two weeks, the results for country and currency premia are similar. More
generally, however, country premium effects are significantly larger. The data
lead to the conclusion that only volatility shocks to the spread very close in time
Domowitz, Glen, and Madhavan 211
to the treasury auction yielding information on premia have any real effect on the
currency premium.
2. Volatility in Equity Market Returns
Higher volatility in stock returns results in increases in country and currency
risk premia, illustrated in the last two columns of Table 4. The data suggest an
interesting difference in the effects on the two premia with respect to timing,
however Increases in stock market volatility clearly take some time to translate
into a higher country premium. The correlations between market volatility at
weeks t — 1 and t — 2 with the country premium at time t are very small relative
to those involving volatility at longer lags. On the other hand, the correlations
between market volatility and currency premia are relatively large only for lags in
volatiHty of up to around six weeks, at most.
In summary, our results show that greater risk in financial markets (evidenced
by volatility shocks in equity and debt returns) induces increases in the currency
and country risk premia demanded in subsequent periods. These findings complement Bailey and Chung (1995), who document a relation between expected
equity market premiums and premia from Mexican currency and sovereign debt
markets. Together, they suggest that currency and country risks are important
factors in determining asset prices. Interestingly, we find that risk premia remain
high for several weeks subsequent to any volatility shock. Rapid mean reversion
in volatility combined with persistence in risk premia results in a negative correlation at leads. This dynamic behavior between country and currency risk premia
and volatility is of special interest since it provides insights into the process by
which risk premia are determined without having to posit a specific asset pricing
model.
VI. International Capital Market Segmentation and Risk
Premia
A. The Closed-End Fund Premium
In the previous seetion, we examined the relation between the currency and
country risk premia and volatility in the local debt and equity markets. In this
section, we extend our analysis to examine the relation between our measures
of currency and country risk and the premium or discount on Mexican closedend funds in the United States.’^ The existence of a long-run deviation between
the price of a closed-end country fund in the United States and its net asset value
(NAV) based on domestic market prices is a topic of considerable interest for both
academics and practitioners, because it reflects international capital market segmentation. In turn, such segmentation may reflect off-shore demand or investor
sentiment for Mexican securities.
We obtained data on the price and NAV ofthe Mexico Fund, which is traded
on the New York Stock Exchange (NYSE). We matched these data to our weekly
‘^We thank Warren Bailey for suggesting this to us and George Nishiotis for providing us with
data.
212 Journal of Financial and Quantitative Analysis
data by selecting the price and NAV two days after the yields of the Cetes and
Tesobono bonds are determined in the primary auction in Mexico. We compute
the closed-end fund premium as
(15) ^, =
where p, is the fund’s price in week t, and n, is its net asset value. Over the period
from July 21, 1993, to February 15, 1995, the mean premium was -2.62%, i.e.,
the fund traded at a slight discount relative to NAV, and the standard deviation
of the premium was 6.28%. The corresponding r-value is -3.74, confirming that
the premium is negative at the 5% significance level. These summary statistics
conceal considerable variation in the closed-end fund premium.
B. Analysis of Closed-End Fund Premiums and Returns
To examine the relation between closed-end fund prices and risk premia in a
more systematic way, we performed regressions of the form,
(16) y, = l3o + 0iA^pj + l32A-yn,^, + e,,
where, for week t, y, is the dependent variable, A is the first difference operator, and 7p_, and 7m,, represent the 91-day currency and country risk premia for
that week, respectively. As noted in Section IV, differencing is required to induce
stationarity in the premia, and we limit ourselves to this form of “short-run” regression, believing that the time period is too short to effectively capture long-run
relationships. We present regression results for three dependent variables: i) the
closed-end fund premium, !?„ a measure of market segmentation, ii) the closedend fund return based on the NYSE closing price, i.e., {p,/p,-i – 1), and iii) the
closed-end fund return based on the net asset value of the fund, i.e., {n,/n,^ l – 1) •
We distinguish between fund returns based on prices and NAVs because there
may be differences in the way in which U.S. and Mexican investors react to information regarding currency and country risks. Note that because the closed-end
fund price and NAV for week t is actually observed two days after the corresponding observation of the country and currency premium for week /, the independent
variables in equation (16) are completely predetermined. Consequently, there is
no overlap in the time periods over which the dependent variable is computed and
the corresponding times over which the independent variables are measured.
Table 5 contains several interesting results. From Panel A, it is clear that
there is a positive and significant relation between the closed-end fund premium
(or equivalently, a negative relation between the closed-end fund discount) and
changes in the country and currency risk premia.’-‘ Increases in perceived risk
widen the gap between the fund’s U.S. price and its NAV, possibly because investors in the United States react less aggressively than investors in Mexico to
“Additional lags in the differenced variables do nothing to enhance statistical significance or the
results obtained with the simpler specification. We also obtain similar results using the standardized
perfect-foresight residuals discussed above as independent measures of the innovations to currency
and country risk.
Domowitz, Glen, and Madhavan 213
perceived changes in risk factors. Closed-end funds are typically held by smaller,
retail investors who do not have the sophistication to directly purchase equity instruments abroad (or even ADRs at home; see Bailey, Chan, and Chung (1997)).
If this is the case, equity prices in Mexico may react faster in response to changes
in country and currency risk than prices for closed-end funds in the United States.
We discuss this further below, in the context of the 1994 dAssessment. We view
the results of Panel A as evidence of market segmentation that, in turn, reflects
international clientele effects or investor sentiment. The evidence in this regard
is consistent with that of Domowitz, Glen, and Madhavan (1997), based on individual equity prices. If markets were efficient and fully internationally integrated,
the price of the fund should be equal to the NAV. As in Frankel and Schmukler (1996), one also might argue that the price of the fund, traded on the NYSE,
better reflects information and expectations held by international investors, while
the NAV, determined in the Mexican market, better represents information and
expectations held by local investors. The hypothesis of market segmentation then
translates into cross-market differences in information.
TABLE 5
Regression Models of Closed-End Fund Returns and Prennia
Change in Change in
Country Currency Adjusted
Intercept Premium Premium R^
Panei A. Regression of the Ciosed-End Premium
-0.029-* 1.390** 0.920** 0.128
(0.007) (0.423) (0.346)
Panel 5. Regression of Fund Returns
0.000 -0.734 -1.059** 0.102
(0.006) (0.403) (0.330)
Panel C. Regression of NAV Returns
-0.002 -1.464** -1.022** 0.176
(0.006) (0.385) (0.316)
This table contains regression estimates (with standard errors in parentheses) for models
where the dependent variable is: the weekly closed-end fund premium, where the premium
is defined as the ratio of price to net asset value, less one; the weekly return to the Mexican closed-end fund based on NYSE closing prices; and the weekly return to fund net asset
value, in week t. The sample consists of 80 observations in the period July 1993 to February
1995. The independent variables are the weekly changes in 91-day country and currency
(peso) risk premia, as defined below. The data for Cetes (government securities denominated in pesos) and Tesobonos (government securities denominated in dollars, payable in
pesos at the official exchange rate) are annualized effective yields calculated from the Mexican government’s weekly primary auctions. The currency risk premium (peso premium) is
calculated as the arithmetic difference between Cetes and Tesobonos yields. The country risk premium (country premium) is calculated as the difference between the Tesobonos
yield and the yield of a three-month U.S. Treasury security, in decimals. Asterisks * or **
indicate significance at the 5% and 1% levels, respectively, in a two-tailed test.
An examination of Panels B and C helps explain the finding of a significant
effect of risk premia on segmentation reflected by the fund premium. There is
reasonable evidence that the equity returns to the closed-end fund, as well as the
NAV returns, are predictable. The significance of the pre-determined variables
214 Journai of Financial and Quantitative Analysis
may reflect time-vary ing risk premia as discussed by Ferson and Harvey (1991),
(1993), Bailey and Jagfiani (1994), Bailey and Chung (1995), Bekaert and Harvey (1995), and De Santis and Gerard (1997). In both Panels B and C, closed-end
equity returns measured with respect to the fund’s price in the United States or
its NAV are negatively related to changes in currency and country risk premia;
although the country coefficient in Panel B is not significantly different from zero
at the 5% level, it is at a reasonable significance level of 7%. The results on
fund returns, in particular, are consistent with those of Bailey, Chan, and Chung
(1997) using post-dAssessment information, in the sense that these authors document intraday selling pressure on bad news with respect to currency and local
stock market information.
Returning now to Panel A, the positive relation between the closed-end fund
premium and risk premia may arise because Mexican investors react faster or
more aggressively to perceived increases in risk, especially risk embodied in the
country premium. Specifically, the country risk coefficient in the NAV regression
in Panel C is larger in absolute value than its counterpart in the fund return regression in Panel B. The supporfing evidence is weaker for currency risk premia. The
coefficient estimates in Panels B and C are actually quite similar in value, and are
not statistically different from each other.
The evidence complements that of Frankel and Schmukler (1996), pertaining
to the 1994 crisis. Their results support the claim of the International Monetary
Fund (1995), that the Mexican investors were the front-runners in the crisis. Interestingly, the decline in NAV, relative to NYSE prices, commenced only shortly
before the crisis began, as measured by the date of the dAssessment. Our data also
show the country risk premium beginning to rise a scant week before the crisis.
This fact, combined with our regression results, also then may be interpreted as
supporting the IMF hypothesis. Although our results, the findings of Frankel and
Schmukler (1996), and the conjectures of the IMF are broadly consistent, we sfiU
cannot support the hypothesis that the crisis was anticipated to any real degree.
The decline in the discount noted above was sfill well within the upper and lower
bounds of observed discounts following the elecfion of Zedillo in August 1994
to the dAssessment. Mexico Fund premia were appreciably negative until after the
dAssessment occurred, and the discount one week before the dAssessment was large
relative to the historical period following the approval of NAFTA. Full anticipation on the part of Mexican investors would have resulted in a posifive premium
prior to the dAssessment, or at least a sizeable drop relative to recent history, a
possibility refuted by the raw data.
VII, Conclusions
The unique nature of the short-term debt instruments issued by the Mexican
government allows us to estimate and analyze the intertemporal prices of country
and currency risk without recourse to assumptions about investors’ preferences.
We use these measures to test hypotheses about investors’ expectations regarding
these risks and their relation to return volatility in emerging markets. Our results
have important academic and practical implications.
Domowitz, Glen, and Madhavan 215
The magnitudes of the estimated country and currency risk premia indicate
that governments in emerging markets can significantly reduce domestic interest
rates if they can improve international perceptions of the risk of possible currency
dAssessments and sovereign default. Currency risk is the more important factor,
in both nominal and real terms. This point is especially noteworthy given the
recent financial crises in Thailand and Malaysia. To the extent that the prices of
corporate bonds are derived from the term structure for government bonds, these
conclusions may apply more broadly.
Our analysis also provides insights into the determinants of risk premia. The
premium demanded by investors with respect to currency and country factors
shows persistent increases in response to volatility shocks in financial markets.
We also document the importance of exogenous political shocks on interest rates
and risk premia. These results are consistent with Ferson and Harvey (1991),
(1993), Bailey and Jagtiani (1994), and Bailey and Chung (1995), who find that
exposure to financial and macroeconomic risks can forecast stock returns. Our
results support the view that these results can be attributed to the presence of
time-varying risk premiums that are imperfectly reflected in realized returns.
From a policy viewpoint, our results on the persistence of volatility shocks
also suggest that efforts to promote greater stability in security markets can substantially lower borrowing costs over longer horizons. Debates continue over
whether or not the 1994 dAssessment was anticipated and the reasons for which
the consequences were so severe. There has been extensive factual investigation of circumstances leading up to and beyond the dAssessment in terms of event
chronologies and macroeconomic statistics. However, there is little evidence
about investors’ expectations of the associated risks and the extent to which they
were priced. Our analysis of the structure of interest rates, country, and currency
risk premia, expectational errors with respect to the pricing of such premia, and
the behavior of country fund discounts all lead us to the conclusion that the dAssessment was unanticipated. One can only speculate as to the reasons for the violent
reaction by portfolio investors, but it is worth noting that the response experienced
is a new phenomenon. Typically, flows of such capital out of the country occur
before, not after, dAssessments. Presumably such dAssessments were anticipated to
some extent, and our evidence suggests that this was not the case in Mexico.
Our results shed light on the process by which investors’ expectations of risk
are formed. We find support for the expectations hypothesis as a simple description of the term structure of nominal interest rates and its priced components. The
currency and country risk premia are only weakly correlated, and the dynamic behavior of the two-term structure components is different. Whether this reflects differences in the types of investors holding peso- and dollar-denominated sovereign
debt, market segmentation, or other factors is as yet unclear. Finally, we document a significant relation between changes in country and currency risk premia
and the future closed-end fund premium. These patterns are consistent with international capital market segmentation arising from differences in the way country
and currency risks are priced in foreign and domestic markets. The exact nature
of this segmentation is, however, unclear. Some evidence is provided supporting
the hypothesis of stronger reactions of Mexican investors to country risk but, as
generally is the case, we are left with a continuing puzzle for future research.
216 Journal of Financiai and Quantitative Analysis
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