metadata: authors: 0: author: Claessens,Constantijn A.
1: author: Pennacchi, George
count: World
docna: 0: docna: Deriving developing country repayment
            capacity from the market prices of sovereign debt
docty: Policy Research Working Paper
subtopic: Public Sector Economics,Banks & Banking Reform,Reproductive Health,Educational Sciences,International Trade and Trade Rules,Family Planning Research,Public Finance Decentralization and
            Poverty Reduction
teratopic: Environment,Macroeconomics and Economic Growth,Finance and Financial Sector Development,Law and Development
abstracts: cdata!: The market prices of developing
            countries' debts are imperfect indicators of the
            countries' payment capacity for three reasons: the
            concave shape of the debt's payoff structure, the
            presence of third-party guarantees, and the differences in
            the terms of various debt claims. Claessens and Pennacchi
            derive an improved indicator of payment capacity by
            developing a pricing model - using option valuation
            techniques - that takes these three factors into account.
            Applying the model to bonds issued recently by Mexico and
            Venezuela, they find that the estimated indicator of payment
            capacity often behaves differently from the raw bond prices
            themselves, confirming the importance of cleaning the raw
            prices for these three factors. In order of importance, the
            benefits of cleaning raw prices come first from correcting
            for the effects of different terms (such as fixed versus
            floating interest rates), followed by the value of
            third-party enhancements and then by the concavity of the
            payoff structure. They find some evidence that the new
            indicator of repayment capacity conforms better than the raw
            prices themselves to generally held beliefs about which
            variables drive a country's repayment capacity. In
            particular, they find that variables that are often assumed
            to be related to payment capacity - such as oil prices and
            the countries' stock market prices - are more closely
            (and with the right sign) associated with the new estimated
            measure of payment capacity than are the secondary market
            prices of the bonds.
repnme: repnme: Deriving developing country repayment
            capacity from the market prices of sovereign debt
display_title: Deriving developing country
            repayment capacity from the market prices of sovereign debt
listing_relative_url: /research/1992/11/699538/deriving-developing-country-repayment-capacity-market-prices-sovereign-debt
topicv3: Commercial Banking m1326069 1236,Trade m1326924 698,Treasury m1327009 1045,Education m1327048 470,Family Planning m1327501 1452
publishtoextweb_dt: 2010-07-01T00:00:00Z
historic_topic: Environment,Macroeconomics and Economic Growth,Finance and Financial Sector Development,Law and Development
origu: International Economics Department
no_of_pages: 43
model_extractions: <!-- Start of picture text --> Policy Research<br>Debt and International Flnanoo<br>WPS 1044<br><!-- End of picture text --> This paper - a product of the Debt and Intemational Finance I ;vision, International Economics - Deparument is part of a larger effort in the department to study the determinants of<sup>secondary market</sup> prices of developing countries' debt. Copies of the paper are available free<sup>from the World Bank, 1818 H</sup> Street NW, Washington, DC 20433. Please contact Rose Vo, room<sup>S8-042, extension 33722 (November</sup> 1992, 37 pages).

The market prices of C ¶veloping countries' debts are imperfect indicators of the countries' payment capacity, for dthee reasoins: the concave shape of the debt's payoff structure, the presence of third-party guarantees, and the differences in the terms of various debt claims.

order of importance, the benefits of cleaning raw prices come first from correcting for the effects of different terms (such as fixed versus floating interest rates), followed by the value of thirdparty enhancements and then by the concavity of the payoff structure.

Claessens and Pennacchi derive an improved indicator of payment capacity by developing a - pricing model using option valuation techniques - that takes these three factors into account.

Applying the model to bonds issued recently by Mexico and Venezuela, they find that the estimated indicator of payment capacity often behaves differently from the raw bond prices themselves, confirming the importance of cleaning the raw prices for these three factors. In They find some evidence that the new indicator of repayment capacity conforms better than the raw prices themselves to generally held beliefs about which variables drive a country's repayment capacity. In particular, they find that variables that are often assumed to be related to - payment capacity such as oil prices and the countries' stock market prices - are more closely (and with the right sign) associated with the new estimteed measure of payment capacity than are the sc-ondary market prices of the bonds.

The Policy Research Working Paper Series disseminates the fmdings<sup>of work under way in the Bank. An objectiveof the series</sup> is to get these findings out quickly, even if presentations are less<sup>than fully polished. The fmdings, interpretations, and</sup> conclusions in these papers do not necessarily represent official Bank policy.

Produced by the Policy Research Dissemination Center
# Deriving Developing Country Repayment Capacity from the Market Prices of Sovereign Debt

by Stijn Claessens World Bank

## and

George Pennacchi University of Illinois at Urbana-Champaign
# Table of Contents

|1.<br>Introd|uction|1|
|---|---|---|
|2.<br>The M|odel|4|
|2.1<br>22<br>2.3|Mexican and Venezuelan Bonds<br>The Analytical Model<br>Estimation Techniques|4<br>6<br>8|
|3.<br>The R|esults|11|
|3.1|Raw Prices|11|
|3.2<br>3.3|Estimates of the State Variable Process<br>The Relationship between State Variables and Economic Variables|12<br>14|
|4.<br>Concl|usions|16|
|Appendix A||17|
|Appendix B||22|
|References||25|
|Tables||28|
|Figures||33|
# 1. Introduction

In 1985, a secondary market in developing country debt was established. Initially, the market was composed largely of rescheduled commercial bank claims and served as the principal vehicle for transferring ownership between banks and, to a limited extent, other investors. Trading was concentrated in the claims on a few large debtors. In 1989, United States Treasury Secretary Brady proposed official support for debt reduction. Since then the IMP, World Bank, and other official creditors have provided financial support in the form of credit enhancements to five countries (Mexico, Philippines, Costa Rica, i enezuela, and Uruguay) in exchange for debt relief from the commercial creditors of these countries. With the introduction of the Brady plan in 1989, a large share of commercial bank claims have been (or will be) securitized by conversion into bonds, often containing third-party enhancements. This securitization has greatly improved the liquidity and efficiency of the developing country debt market in recent years. Trading volumes have increased from $1.5 billion in 1985 to about $200 billion in 1991 and the efficiency of the market has also increased (as measured for instance by bid/ask spreads which have fallen by half or more in the past two years). Mexican Brady-bonds are now one of the most actively traded and most liquid of international bonds.

The secondary market prices of developing country debt have been used as indicators of relative creditworthiness in cross-country and time series analysis. As the market has become more efficient, prices are also increasingly used as benchmarks in the formulation of debt and debt service reduction and/or restructuring packages negotiated by developing countries with their commercial creditors. In general, terms on debt and debt service reduction transactions reflect prices in the secondary market prevailing at the time of the agreement. Because of their use as relative creditworthiness indicators as well as their use in debt negotiations, prices-and the determinants of prices-are of importance to developing countries, the commercial banks and the official creditors (that are financing part of the third-party enhancement).
2 Many researchers have attempted to explain secondary market debt prices by regressing prices (cross-section, times series or panel data) on a set of explanatory variables such as debt-toexports ratio, reserves-to-imports ratio, inflation, etc. (e.g., Sachs and Huizinga (1987), Huizinga (1989), Claessens (1990), Cohen (1990), Cohen and Portes (1990), Boehmer and Megginson (1990) and Ozler and Huizinga (1991)). Although this research has provided some valuable insights, it suffers from a number of problems. First, the range of possible repayments on a debt contract implies that an upper limit on the debtor's liability exists (as when no default occurs). As a result, the (present value of) repayments will likely be a concave function of the underlying fundamental factors determining the ability or willingness to pay. Option-based pricing models can derive the secondary market valuation consistent with this (see further Genotte, Kharas and Sadeq (1987), Borensztein and Pennacchi (1990), Cohen (1991), Claessens and Wijnbergen (1990), Chesney and Morisset (1992) and Bartolini and Dixit (1991)). This option-type, nonlinear relationship between prices and fundamentals needs to be taken into account when secondary market prices are related to fundamentals.

Second, debt traded in the secondary market is not homogenous across countries or across time. Most research papers make the implicit assumption that the debts of different countries traded on the secondary market are direcly comparable and, hence, that available prices can be used in cross-country regressions. But, this assumption is unrealistic: often there will exist a large number of claims on a given country, each with different contractual terms.' An obvious difference in terms will be between bonds with fixed and floating interest payments, in which case the relative prices will vary, in part, due to movements in international interest rates.

'For instance, currently about 20 claims on Brazil and at least five claims on Venezuela are traded, all at different discounts. Across countries, commercial bank obligations will have different maturities, different coupon rates, different indentures, etc. Over time, terms on claims will vary due to reschedulings and restructurings. For instance, restructurings lead to different maturities, grace periods, and/or interest rates.
3 Accounting explicitly for the terms of the bonds can lead to more efficient estimates of the country's underlying payment capacity (as perceived by the market).

Third, the Brady deals have involved the issuance of a number of new instruments with different forms of enhancements (from third parties and/or through the use of collateral). These enhancements can contribute as much as 20% of the total value of the bonds. Without accounting for these enhancements, cross-section regressions attempting to explain prices of partly collateralized bonds on the ground of country risk factors alone would lead to biased results. The value of the enhancements-such as principal collateralization-is partly a function of international, risk-free interest rates, not only of country risk factors. Preferably, one explicity values the two components: the value derived from the country's underlying ability and willingness to repay its debt; and the additional value of the third-party enhancements (where the additional value of the enhancements wIll obviously depend on the stochastic process determining the country's abiity and willingness to repay).

In principle, an analysis of a country's repayment capacity would start by modeling the factors that determine its likelihood of repayment. This is complex, however, because one must consider factors that determine both a country's ability as well as its willingness to make debt payments. In the absence of an international bankruptcy court (or the use of "gunboat diplomacy"), the debtor can choose to make payments in order to avoid the imposition of various possible penalties. These penalties can be intertemporal (exclusion of future access to capital markets, see Eaton and Gersovitz (1981)) or intratemporal (trade sanctions, withdrawal of trade credits, see Bulow and Rogoff (1989)). To avoid these penalties from being imposed-which may generate little direct benefits to the creditors-the debtor and the creditors will try to reach an agreement involving some (partial) payment by the debtor. Since the bargaining power of the creditors will depend on the severity of the penalties they can impose, the agreement reached will likely imply that the debtor will pay in relation to the severity of the penalties.
4 These considerations make it clear that repayments by the country will be driven by a large number of factors, affecting the country's as well as its creditors' position (for example, the general state of the banking system may affect the bargaining power of commercial banks visa-vis the debtor country, see Fernandez and Ozler (159*1) and Ozler and Huizinga (1991)). A priori it will be difficult to determine the relative importance of each of these factors and to develop an econometric model accordingly. Hence, empirical studies have typically tried to identify variables that best explain repayment capacity by conducting goodness of fit regression tests.

An alternative to this regression fitting approach is to first assume that a developing country's repayment capacity can be summarized by a given stochastic repayment process and then derive a valuation model for particular types of debt claims (e.g., enhanced with third-party guarantees) based on this stochastic process. Using actual secondary market prices of developing country debt, one can then infer the country's underlying stochastic repayment process that is consistent with the previously derived debt valuation model. The derived stochastic process can then be related to the underlying fundamental factors and some hypotheses regarding ability and willingness to pay factors can be tested. In this way one deals in a consistent fashion with: the option-type nature of sovereign debt; the different terms of the various claims (which determine, for instance, the impact of changes in international interest rates on their prices); and the extra value provided by third-party enhancements.

# 2. The Model

# 2.1 Mexican and Venezuelan Bonds

We develop such a pricing model for the Mexican and Venezuelan Brady bonds. The Mexican bonds were created in March 1990 by converting approximately $40 billion of commercial bank claims. They trade in a very liquid and efficient market (bid-ask spreads are around 25 cents, or about 0.4 percent of their price). Two different Mexican Brady bonds exist:
_5_ (i) a discount bond, a bond with a principal discounted to equal to 65 percent of its original (prerescheduled) face value and having a floating interest rate of LIBOR plus 13/16; and (ii) a par bond, a bond with a principal equal to its original face value but having a low, fixed interest rate of 6.25 percent.

Both bonds have an original maturity of 30 years. The principal of both bonds is guaranteed through the collateralization of a 30-year, US Treasury zero-coupon bond. The bonds are further credit enhanced by a rolling guarantee that covers a limited value of interest payments and is collateralized by an escrow account.<sup>2</sup> Specifically, this rolling interest guarantee covers 18 months worth of interest payments (three semi-annual interest payments). The interest earned on the funds in the escrow account accrues every six months to Mexico, provided of course that Mexico pays in full the then due interest repayment. In addition, both bonds include an oil price recapture clause that gives creditors a share in Mexico's oil export revenue if oil prices increase by a certain percentage in the years 1997 and beyond.

The Venezuelan Brady bonds were created in August of 1990 from the conversion of approximately $19 billion of commercial bank debt. Their terms are very similar to the Mexican bonds: a discount bond (face value equal to 70% of pre-existing bank debt); and a par bond (interest rate of 6.75%).3 Both Venezuelan bonds also have a 30 year maturity, have their principal collateralized, and have an interest guarantee on a rolling basis provided through an escrow account containing 14 months of interest payments. The two Venezuelan bonds have oil recapture rights that are similar to those of the Mexican bonds. The Venezuelan bonds have 2Te escrow account is established at the New York Federal Reserve and only securities with at least a AA-rating can be used as collateral.

3In addition, bonds with temporary low interest rates an4 new money bonds (with no enhancement) were created in the context of the debt conversion. To maintain comparability with Mexico, we did not analyze these bonds.
6 relatively a higher bid-ask spread than the Mexican bonds, possibly a result of the fact that their outstanding amount Is less.

# 2.2 The Analytical Model

The pricing of the collateralized principal of a Brady bond Is straightforward: its value at each point in time will equal the current value of the U.S. Treasury zero-coupon bond expiring on the same maturity date. What Is then left to value are the interim interest payments. Valuing the bond's interim interest payments is complicated since they possess default risk but that they are also covered by a limited, rolling guarantee. We characterize the developing country's default risk by a stochastic state variable, z,, which can be thought of as an index of the country's capacity for repaying its debt. If z, falls below zero. we assume that the country will default on its interest payments for a limited time equal to r periods.

The state variable, z,, is assumed to follow the arithmetic Brownian motion process:

# (1) dz = Pdt + adq

# where dq is a standard Wiener process.

The rolling guarantee is assumed to cover 7 periods of interest payments. For analytical simplicity, we assume that if the rolling interest guarantee is called upon, then it is used in full, i.e., in the case of Mexico, it is disbursed over 18 months (three consecutive semi-annual interest payments) and in the case of Venezuela, it is disbursed over 14 months (two and one-third consecutive semi-annual interest payments).' The state variable, z2, determines when the guarantee is first employed and when the bond issuer subsequently defaults on its promised payments. It is assumed that the guarantee is disbursed over the period T to **_T+T_** if, falls below 4This is not as strong an assumption as it may seem: it is likely that once the country defaults on one interest payment, it will default completely on the interest guarantee.
7 zero fr flte flrst ti during any time within the interval T-r to 1'. If , later takes on a value less than or equal to zero at any time during any future interval T'-T to T', where T' 2 T + T, then it is assumed that complete default occurs on all promised bond payments over the interval T' to T'+T.

Our strategy for computing the value of payments for the bond described above is to first value the payments of a bond without the rolling interest guarantee. Second, we then calculate the value of the rolling guarantee alone. By combining these two values, we will obtain the value of payments of a bond thai includes the guarantee. A description of this valuation technique is given in Appendix A. There we make the simplifying assumption that bond investors view the country's default risk as diversifiable, a somewhat weaker assumption than risk neutrality.' We then find that if the initial time t=O value of the state variable is z4 = z, then the time 0 probability of the bondholder receiving an interest payment over the interval t2 to **t2** + T is equal to (2) <!-- Start of picture text --> 0) (-Z a z+X&ti<br>2 2"zesN2i -ZPtl e z-g02 _ V1UV.Z)<br><!-- End of picture text --> where t, * **t2-r.** This implies that the value of the bond's payments over the interval **t2 to** t2 + r is equal to their default-free value times the expression **0(t 2 ).** Hence, if we define 1, as a par bond's promised fixed interest payment that comes due at time t, where t2 s t < t2 +r, then the time 0 value of this interest payment is given by 5We allow for interest rate risk premia since our model embeds the Vasicek (1977) model of the term structure of (default-free) interest rates.
8 (3)

# vOMI) = **pO(t) I,o(t 2)**

where p0(t) is the time 0 price of a default-free zero coupon bond that pays $1 at time t. Similarly, one can value a discount bond's promised floating rate interest payment to be paid at time t. Let D denote the discount bond's level of principal and let s be the spread over the yield on a default-free six month bond issued six months prior to the interest payment date (e.g., the spread of 13/16% over LIBOR). Then the value of this discount bond interest payment equals<sup>6</sup>

# (4)

**VI (D,t)** = [e<sup>0</sup> 2po(t -.5) - po(t)] D 0(t2 )

These valuation formulas imply that the variability of the prices of the bonds will be less than that of the underlying state variable; for an enhanced bond, both its rolling guarantee as well as its limited liability will lead to the bond's price being a concave function of the state variable. This is illustrated in Figure 1 which plots the theoretical price of Mexico par and discount bonds as a function of the state variable, z.'

# 2.3 Estimation Techniques

Formulas (3) and (4) require default-free, zero-coupon bond prices, po(t), maturing at each coupon payment date. We constructed this term structure of bond prices using data on Treasury bill, Treasury strip, and LIBOR rates to estimate the parameters of the Vasicek (1977) bond pricing model. This model then allowed us to find values of po(t) for any time until

## 6See Borensztein and Pennacchi (1990) for details in valuing floating rate payments.

These bond prices represent interest rates and times until maturity that existed on March 24, 1990, the beginning of our sample period. A value of eu/u = -.222725 was assumed, which is the value we later obtain using our estimation procedure. The estimates for the state variables z (see below) varied between 1 and 3. Note that the discount bond can be valued above 100 for large values of z because of the spread, s, on the bond.
9 maturity, _t._<sup>_8_</sup> Given these default-free bond prices, note that formulas (2), (3), and (4) imply that Brady bond prices are a nonlinear function of the fractions z,/o and _A/a_ only. Hence, we can normalize a = 1, and denote these theoretical bond valuation formulas as ztZ,; ), where i = 1, ..., n indexes a particular type of bond issued by a given country, such as a discount bond or a par bond.

Now consider the following strategy for estimating the values of A and the time series of the state variable z,. Let V equal the average of the secondary market bid and ask prices of a particular country's type i bond at time t. This average of secondary market quotes corresponds to the theoretical valuation, v defined above. Given that we can observe a time series of these secondary market prices for n differen **t** ypes of debt issued by a particular country, we assume that these bid-ask averages measure the country's "true" debt prices with error: where V, is the n dimensional vector o, observed secondary market prices of debt of types i, i = 1, ..., n, observed at time t and v, is the corresponding n-vector of "true" debt prices; and _e,_ is an n-vector of measurement errors. For simplicity, we assume that this vector of In the Vasicek (1977) model, equilibrium bond prices take the form p0(t) = exp[(l-e at)(r.-r)-tr,. -a,I(l-e)<sup>2</sup> /(4ci)J where r and r. are the time 0 yields on instantaneous maturity and infinite maturity zero coupon bonds, respectively. a is a measure of the mean reversion of r and a,2 is the instantaneous variance in the change in r over time. ca and a, were estimated by maximum likelihood following a simplified version of the procedure given in Pennacchi (1991). This involved using a univariate Kalman filter to compute the likelihood function. The data consisted of end of month observations on 30, 90, 180, and 345 day Treasury bills over the period 1968 through 1988 and produced estimates of a=.095k3l and o,=-.025339. Given these parameter values and the above bond price formula, we then solved for the date 0 values of r and r, that were implied by contemporaneous observations on 6 month maturity LIBOR and the price of a Treasury strip that matured nearest to the maturity date of the Brady bond we were evaluating.
10 measurement noise, e,, is serially uncorrelated and distributed as N(O,R), where R is an nxn covariance matrix.

Next, note that equation (1) can be rewritten in discrete time form as

# _(6)_

where , - N(O,At). (Recall we normalized o = 1.) Hence (5) and (6) are in the form of a generalized state space system. z, is an unobserved 'state" variable and (6) is referred to as the "state-transition equation." V, is a vector of observed variables and (5) is referred to as the "measurement equation." Now if v,t(z;) were lin=ar functions of z", then maximum likelihood estimates of u and the z's could be obtained using a standard, recursive Kalman filter. (For example, see Harvey 1981, Chapter 4.) However, **Pj(z#,)** is a vector of non-linear functions of z,. Therefore a modification of the Kalman filter that considers functional nonlinearities, called the extended Kalman filtr, is needed to obtain (approximate) maximum likelihood estimates of i and z's (Harvey (1989, p. 160) and Anderson and Moore (1979, p. 195)). The extended Kalman filter uses the same simple recursive computational technique as the standard Kalman filter. However, it does so by linearizing (5) around the conditional mean of z, using a Taylor series expansion. Further discussion of this technique can be found in Appendix B.

The attraction of this estimation procedure is that it combines a time series of crosssectional observations in a theoretically consistent and computationally efficient manner. The technique is in the same spirit as Chesney and Morisset (1992) in that it uses information regarding the assumed time series properties of the state variable, z,, to impose restrictions on the time series of observations. However, the present technique, given the extended Kalman filter's linear approximation, has known statistical properties that allow for hypothesis testing or the computation of confidence intervals. In addition, this technique does not require estimates
11 of the bonds' instantaneous variances as was needed in previous work such as Borensztein and Pennacchi (1990).

The most important results of our estimation are a point estimate and an asymptotic standard error for _y/I_ and a times series of estimates of the z,'s. These "smoothed" estimates of z,, t= 1,..,T, make use of the full sample of bond price observations to infer each estimate. This times series of the estimated state variable can then be analyzed in terms of its relationship to other factors affecting the country's debt repayment capacity.

# 3. The Results

# 3.1 Raw Prices

We use secondary market prices of the Brady bonds since their introduction (March 24, 1990 for the Mexican bonds and August 4, 1990 for the Venezuelan bonds) until July 1991. Table 1 presents some summary statistics for the raw bond prices for Mexico and Venezuela. As can also be observed from Figure 2, prices of the Mexico par and floating interest discount bonds tend to move together. The two series toward the bottom of Figure 2 give the respective bond prices as a percent of their face values, while the series at the top of Figure 2 give their prices as a percent of their price on the first observation in our sample. The correlation between the rates of return Oog differences) on these Mexican Brady bonds is 0.726. While this is certainly high, and up to the end of 1990 bond prices moved together quite closely, it is less than perfect. As can be seen in Figure 3, which plots the time series of Venezuelan Brady bond prices, these bonds move together even less perfectly. The correlation of their rates of return is 0.445. Since a developing country's capacity for repaying its discount and par bonds is driven by the same set of underlying variables, this less than perfect correlation indicates that these prices should not be used as direct measures of this repayment ability. Rather, prices might indeed be viewed as noisy (non-linear) functions of repayment capacity as well as other variables. Figures 2 and 3 indicate that part of their relative price behavior may be explained by interest
12 rate movements: at the beginning of 1991, the decrease in U.S. dollar interest rates (e.g., LIBOR) contributed to the relatively more rapid rise of the par bond for both Mexico and Venezuela. This points to the value of appropriately modeling the effects of riskfree interest rates.

# 3.2 Estimates of the State Variable Process

Based on the analytical model of section 2.2, we employed the extended Kalman filter estimation technique outlined in section 2.3. The data consisted of weekly Brady bond prices that were adjusted to account for the additional value of their oil recapture clauses. Using the model of Claessens and van Wijnbergen (1992), oil recapture clause values of 2.11 cents per dollar of old face value for Mexico and 3.14 cents for Venezuela were obtained.<sup>9</sup> On the basis of the above model, we estimated the parameters of the state variable processes for both Mexico and Venezuela based on a bivariate measurement equation consisting of each country's par and discount bonds. The results are given in Table 2.

The state variable process's drift, _,Iar,_ is negative both for Mexico and Venezuela (somewhat smaller in magnitude for Venezuela) and measured quite precisely in the case of Mexico. This suggests that in spite of the ex-post rise in the value of the state variable over our sample period, investors were pessimistic about each country's future repayment capacity; they expected the countries' repayment capacities to decline over time.

A measure of how well our theoretical model describes the actual Brady bond prices is given by the coefficients of the measurement error matrix, R. The standard deviations of the measurement "noise" for the par bonds, _Vr,,,_ are very similar but estimated with more precision for Mexico. This might be due, in part, to the longer sample period for Mexico. For both Moxico and Venezuela, the standard deviations of the measurement errors for the discount bonds, 'The values of the recapture clause were calculated every week. Since there was very little variation in the value of the recapture clause (standard deviation of .032 cents for Mexico and .023 cents for Venezuela) the average value was used throughout.
13 the coefficients Vr22, are smaller than the corresponding par bond measurement errors and are not significantly different from zero. We also see that the point estimates of the correlation coefficients between the par and discount bond measurement _errors,p12 ,_ are negative, but due to their huge standard errors, little can be said regarding this interaction. However, looking at the matrix, R, as a whole, the result that each of the estimated standard deviations are less than $1.80 (on bonds whose prices ranged between $40 and $80) indicates that our model fits the data fairly well.

Table 3 presents statistics on the (smoothed) sample estimates of the fractions z/a. (To maintain comparability with Table 1, the standard deviations of the log differences of the state variables are calculated here). The volatility of the underlying state variable is much higher, almost by a factor of three, relative to that of the prices (Table 1). This is consistent with the fact that the pAces themselves are a concave function of the underlying state variable. Figures 4 (for Mexico) and _5_ (for Venezuela) also show that the underlying state variable behaves at times quite different from the prices of the par and discount bond. For Mexico, this is especially evident in early May, 1990, when the state variable experienced a much sharper drop than that of bond prices, and also during the first half of 1991, when the state variable increases more sharply. As for Venezuela, a much sharper improvement of the state variable started during December 1990. Since the effect of the drop in U.S. interest rates on the bond prices is already incorporated, in both cases it represents a genuine improvement in repayment capacity.

Table 4 presents the correlations between the (rates of return on the) bond prices and the (first differences of the) state variable. The results confir n what is apparent from Figures 4 and 5. The correlations between the bond prices and the underlying state variable are significantly different from 1; in case of Venezuela, the par bond price and the state variable have only a correlation of 0.529, confirming the importance of extracting the state variable before modelling ability or willingness to pay.
14

# 3.3 The Relationship between State Variables and Economic Variables

To Investigate the economic determinants of our estimated state variables for Mexico and Venezuela, we regressed them on a number of economic variables. Given the weeldy frequency of the bond price data which produced our state variable estimates, we choose economic variables that could also obtained at a weekly frequency: oil prices, the performance of the domestic stock market (the value of the Mexico country fund as traded in New York and an index of the Venezuela stock market in dollars) and two series of Mexican domestic interest rates (one denominated in dollars, the other in pesos). Oil prices can be expected to influence Mexico's and Venezuela's ability to repay. Domestic stock prices will reflect domestic market expectations of future corporate profit growth and in that respect be an indicator of ability to repay. The value of the Mexico country fund in New York will not only reflect expectations about Mexico's future corporate growth but also be an indication of investors' perceptions about their ability to repatriate their earnings and capital (as reflected in the discount of the fund's price from its net asset value). Domestic interest rates will indicate the restrictiveness of Mexican monetary policy, which will reflect Mexico's general access to fresh foreign funds and its ability to repay.'° Table _5_ presents the results of (typical) regressions of the bond prices and the underlying state variables on the various economic variables. The first colunmn gives the dependent variable that is used in a particular regression. The Table documents that both bond prices and state variables are only wealdy related to the economic variables. Except for some regression intercepts, no one parameter estimate is significantly different from zero. What is encouraging, however, is that for both Mexico and Venezuela, the regressions of the state variable on economic variables result in an improvement in overall fit (R<sup>2</sup> as well as the p-values for the F- statistics) compared to the bond price regressions. In addition, the signs of the parameter

> **1 IOks** (1990) finds that the Mexican domestic interest rate reflects, in addition to international interest rates and expectations of exchange rate movements, the fiscal situation of the government. In particular, he finds that the difference between domestic bonds that fall due and Mexico's foreign exchange reserves is an important explanatory variable.
15 estimates using the state variable as dependent variable are more in line with predictions from theoretical models on the ability and willingness of sovereign countries to pay. For example, in the case of Mexico the parameter estimate for the Mexico country fund using the state variable is positive while it is negative for the raw bond prices. This result is robust to the inclusion of other independent variables as can be seen from the comparing the first and the last sections of Table 5. Similar results obtain when examining the regression coefficients on the oil price change for both Mexico and Venezuela. For the state variable regressions, this coefficient is positive and large, while the corresponding coefficient for the raw bond price regressions is either small or negative. Nevertheless, the fit of the regressions remains in general poor. Other variables, such as gross reserves, monetary base, and the amount of domestic debt that matured in a given month, were also used as independent variables. However, these had even less explanatory power, largely because these variables are only available at a monthly frequency. A more formal test was undertaken to check whether the parameter estimates in the regressions are significantly different from each other. Table 6 provides the F-statistics and p- values for pair-wise comparisons of equality of parameter estimates. For Venezuela there is some evidence that the parameter estimates reported in Table S are significantly different between using the state variable and the bond prices as dependent variables. Table 6 also reports the result for the regression for Mexico with only two independent variables (country fund and Pagafes); in this case parameter estimates are also more likely to be different (p-values of 9 and 12 percent). Our results taken together, there appears to be evidence that deriving a state variable process from secondary market bond prices leads to a better indicator of a country's underlying payment capacity.
16

# 4. Conclusions

This paper has shown that accounting for the effects of concavity in a developing country bond's payoff structure, as well as various bond contract features (including third-party guarantees), leads to an improved indicator of the country's repayment capacity. Applying the model to bonds recently issued by Mexico and Venezuela, we find that the estimated repayment capacity behaves, at times, quite differently from the secondary market bond prices themselves. We can attribute some of the variation in payment capacity to exogenous economic factors. Thus, the differences we find between secondary market bond prices and our derived measure of repayment capacity provides suggestive evidence that investigations into the determinants of repayment capacity that employ only secondary market bond prices may be biased.
17

# Appendix A

This appendix computes the probability of default for a bond which contains a rolling, partial guarantee of interest payments. The guarantee is assumed to cover r periods of interest payments and is assumed to be used, in full, once the bond issuer first fails to make an interest payment. The state variable, z(t), determines when the guarantee is first employed and when the bond issuer subsequently defaults on its promised payments. It is assumed that the guarantee is used over the period T to **T+T** if z(t) falls below zero for the first time during any time within the interval T-T to T. If z(t) later takes on a value less than or equal to zero at any time during any future interval **t'-7** to **t',** where t' > T + T, then it is assumed that complete default occurs on all promised bond payments over the interval t' to **_t'+r._** To derive the risk-neutral value of payments for the bond described above, we first value the payments of a bond without a guarantee. Second, we calculate the value of the guarantee, alone. By combining these two values, we will then obtain the value of payments of a bond that includes the guarantee.

Valuing the payments for a bond that carries no third-party guarantee requires that we first compute the probability that z(t) is less than zero at any time during the interval t, to t2where ti = t2 - T. This measurement represents the probability of default on interest payments over the interval **t1** to t2+r for this bond. To simplify the following notation, denote z7 as tFe value of the state variable, z(t), at time t. Let the current time be to = 0, and assume z, = z > 0. Recall that the state variable, z(t), is assumed to be an arithmetic Brownian motion process with drift and standard deviation v. Denote 0(t1,t,) as the event that z(t) takes the value of zero (or passes through zero) at least once during the interval **t,** to t2. One can also think of this event as z(t) being 'absorbed' at the origin, where zero is an absorbing barrier. Then
is

## (Pmnin(z(t)) **C** 0, te(t 1 2)) = P(z 1 COl + P(z 1 >O)P(0(t 1 -tV1z1 > O))

# (A.1)

where N(.) denotes the standard normal distribution function and f is the conditional density function of z(t), given by (A.2) <!-- Start of picture text --> f(zj1 z(0)=z)= ((Zi u Pti)<br><!-- End of picture text --> where n(v) is the standard normal density function.

P(O(t 1 ,t2)Izj is the probability of z(t) being "absorbed" at the zero boundary over the interval (t1,t,), given it equals z, > 0 at time t1. This distribution is given by Ingersoll (1987) p. 353 equation (34b).

(A.3) Substituting (A.2) and (A.3) into (A. 1), we have (A.4) 'Me above integral can be simplified (e.g., see Geske (1979) p. 80) to obtain
19 P(Min(z(t)) **<** 0, **te(t1 2))** = <!-- Start of picture text --> (A.5)<br><!-- End of picture text --> <!-- Start of picture text --> N(-z-tt ) + N2 (z+Pt, -Z-It 2<br>art, ~ at i "<br>yA2<br>;N2 N(Z-p1 ; s - )<br><!-- End of picture text --> where N2(x,y,p) is the standard normal bivariate distribution function for random variables x and y having correlation coefficient, p. Hence, (A.5) gives the probability that a bond without a guarantee will default, making no payment, during the time interval t2 to t22 + _r._ One minus this probability times the value of the (default-free) promised payment on the bond over the interval **t2** to t2 + **_T_** then gives us the value of the payments on a bond that carries no third-party guarantee.

Our second step is to compute the value of the third-party, rolling guarantee. The riskneutral of the guarantee applied to bond payments over the interval from **t2** to **t2 +** **_T_** is equal to the promised bond payments over this interval times the probability of the guarantee being exercised. This probability of exercise is the probability that z(t) first equals zero during the interval t, = t2 - T to t2, i.e., the probability that z(t) is 'absorbed" at the zero boundary between **t-** and t2. This probability can also be thought of as being equal to the difference in the first passage (below the zero boundary) probabilities of z(t) at t2 and **t1.** The probability of z(t) being "absorbed" at the zero boundary from time 0 to time t2 is <!-- Start of picture text --> (A.6) P(0(0,t2)Izi = N ( t ) 2 ( Zi )<br><!-- End of picture text --> while the lower probability of z(t) being absorbed at the zero boundary from 0 to time t, is
20 <!-- Start of picture text --> (A.7) P(O(0,tj)IzI = N(.....Ut1) a 2l; N)<br><!-- End of picture text --> The difference between (A.6) and (A.7) is the probability of the guarantee being exercised beginning at date t2. Hence, this probability times the value of the promised payments on the bond over the interval t2 to t2 + **_T_** Is the value of the guarantee for this time period.

Using (A.5). (A.6), and (A.7), we see that the risk-neutral value of the bond's payments over the interval t2 to t2 + s iS equal to their default-free value times the expression <!-- Start of picture text --> _I_tI Z+At 'Z"tW2<br>-N(zl - ____<br>-2PWG2N2 (Z 5it 1 -Z+It 2 , +-<br>N( _zPt2 N (- -Z + 0e21W4 -Pt -z+gAt'<br>(A.8) ) N[N + eN(<br>)<br>N (Z+Pt + N (Z )2 - N(22 -A) - N 2 (Z Ptl, -Z /i /<br>+ [- N2( Z-ph , -Z+____ - t2 - ,/E:/)+ + N -z+It ( ) 2 ~ , N -Z'~(<br><!-- End of picture text --> Based on properties of the univariate and bivariate normal distributions (see Zelen and Severo (1972) p. 936), the above expression simplifies to
21 <!-- Start of picture text --> (A.9)<br><!-- End of picture text --> <!-- Start of picture text --> (+A -ZgAt1 Z+jAt2<br>- e-2R4 (-z+t 2 1 Z -<br><!-- End of picture text --> Hence, (A.9) is the probability of the bondholde **r** eceiving the bond's promised payments during the interval t2 to t2 + r.