Predicting Default Probabilities and Implementing Trading Strategies for Emerging Markets Bond Portfolios 1

Transcription

1 Predicting Default Probabilities and Implementing Trading Strategies for Emerging Markets Bond Portfolios 1 Stefania Ciraolo Università di Verona Andrea Berardi Università di Verona Michele Trova Gruppo Monte Paschi Asset Management SGR, Milan First draft: September 2001 Current version: January Stefania Ciraolo and Andrea Berardi: Dipartimento Studi Finanziari, Università di Verona, via Giardino Giusti 2, Verona. Michele Trova: Gruppo Monte Paschi Asset Management SGR, via San Vittore 37, Milan. We are grateful to seminar participants at the 2001 X International Tor Vergata Conference on Banking and Finance for useful comments and suggestions.

2 Abstract In this paper we address two main issues: the computation of default probability implicit in emerging markets bond prices and the impact on portfolio risks and returns of di erent default probability expectations. Using a reduced-form model of the Du e-singleton (1999) type, weekly estimates of default probabilities for US Dollar denominated Global bonds of twelve emerging markets are extrapolated for the sample period The estimation of a logit type econometric model shows that weekly changes of the default probabilities can be explained by means of some capital markets factors. Recursively estimating the logit model using rolling windows of data, out-of-sample forecasts for the dynamics of default probabilities are generated and used to form portfolios of bonds. The practical application of the impact on portfolio returns of di erent default probability expectations provides interesting results, both in terms of testing the ability of a naive trading strategy based on model forecasts to outperform a customized benchmark, and in terms of the model ability to actively manage the portfolio risk (evaluated in terms of VaR) with respect to a constant proportion allocation. JEL Classi cation: G33, G15, G11 Keywords: Emerging markets, default probabilities, portfolio allocation

3 1 Introduction In the last decade, emerging markets have experienced numerous nancial crises. Recent cases include the Asian turmoil of 1997, the 1998 Russian default and, more recently, the downgrade of Turkish bonds and the crisis of Argentina, culminated in the January 2002 default. All these events have given rise to signi cant contagion e ects among emerging markets. Estimating the default probability implicit in emerging market bond prices has become extremely important for institutional investors (banks and mutual funds, in particular), given the relatively high weight reached by these securities in their portfolios. In fact, the high yields o ered by emerging markets bonds with respect to those obtainable investing in government securities make them particularly attractive. Those high returns are mainly explained by credit risk considerations due either to default events (issuer does not pay interest or principal or both) or market losses caused by more or less frequent downgrading and subsequent bonds price volatility. Knowing the degree of con dence nancial markets are currently using to discount a bond issuer s default is, therefore, at a practical level, extremely important under at least two di erent aspects. The rst one consists in the computation of the risk the investor is undertaking over a given horizon. The second one regards the impact on portfolio risks and returns of di erent default probability expectations. In this paper we address both these issues. First, we extrapolate weekly estimates of default probabilities from a reduced-form model of the Du e-singleton (1999) type. The empirical work is based on US Dollar denominated Global bonds of twelve emerging markets from February 1997 to July Then, we show that default probabilities can be predicted by some capital markets factors (essentially interest rates, exchange rates and credit spreads) and use them as explanatory variables in logit type econometric models for the prediction of the probability of a market increase/decrease in bond prices. In the nal part of the paper, we recursively estimate a logit model to produce out-of-sample forecasts for the probability of observing future appreciation/depreciation of the bonds. The practical application of the impact on portfolio returns of di erent default probability expectations provides interesting results, both in terms of testing the ability of a naive trading strategy based on model forecasts to outperform a customized benchmark, and in terms of the model s capability to actively manage the portfolio risk (evaluated in terms of VaR) with respect to a constant proportion allocation. The paper is organised as follows. Section 2 introduces the main features of emerging markets bonds. Section 3 illustrates the reduced-form valuation model used for the pricing of Global bonds. Section 4 describes the data used 1

4 in the empirical work and section 5 shows the underlying default probabilities extrapolated by the estimation of the model. Section 6 provides empirical evidence on predicting the dynamics of default probabilities and on the performances, in terms of returns and VaR measures, of emerging markets bond portfolios built on such forecasts. Finally, section 7 contains some concluding remarks. 2 Emerging markets bonds The genesis of the Emerging Markets debt dates back to the early 1970s when, as a consequence of the 1973 oil shock, a great number of commercial banks in almost all developed countries suddenly found themselves facing the problem of investing sizeable amounts of funds deposited by oil producers. At the same time, on the other hand, increasing commodity prices led to a worldwide increase in in ation rates and, therefore, to a generalised increase in the average level of interest rates. That was the reason that induced the aforementioned commercial banks to search for highly pro table investments. The solution was somehow a fait accompli : investing in those less developed countries whose fundamentals were improving thanks to the increase in commodity prices, and which were much more worried about the lack of foreign investments than about paying high interest rates. The economic agencies of those less developed countries, believing that commodity prices would rise forever (remember the predictions that the world would have run out of oil in the 21st century), therefore, begun to borrow sizeable amounts of foreign debt. As commodity prices continued to rise through the early eighties, the loan demand and supply also continued to rise, inducing a very dangerous cycle: the increase in commodity prices increased the Gross Domestic Product of a country and therefore its capacity to service additional debt. When banks looked at this newfound additional capacity they were willing to give loans to Emerging Markets on their demand. Unfortunately, at the beginning of the 1980s, commodity prices began to fall destroying a sizeable portion of the Emerging Markets richness and led developing countries to face the problem of a growing external debt, in the presence of a reduced repayment capacity. Since the end of 1986 the average secondary market value of developing country loans plummeted going from seventy percent (end of 1986) to thirty percent (end of 1989) and showing a loss of credibility of the issuers in that period. This was due to a growing default rate and a growing appreciation of the default probability among money managers invited to invest in the so 2

5 called high yield bond markets. The cited loss of credibility had disruptive e ects on the Emerging Markets; American banks reduced the share of developing country loans in their portfolios and increased the ratio of bank capital to such loans. The resulting sharp drop in nancial resources dedicated to developing country loans caused serious problems to countries (such as developing countries) used to repaying debt by contracting further debt. By the early 1990s the secondary developing countries bond market had reached (on average) the above-mentioned lows. The persistence of the debt problem forced the U.S. Government to propose a new debt initiative, the Brady Plan, in March Essentially, what the Plan did was to recognize that a full repayment of the debt for developing countries was no longer a reasonable goal. In particular, it put pressures on commercial and investment banks to concede and to manage some form of debt and debt-service relief and also called for an increase in secondary market activity, in order to grant liquidity to these issues. The implementation of the Plan led to the birth of a new kind of Emerging Market (high yields) bonds: the Brady Bonds. So far, several countries have bene ted from the program issuing di erent types of Brady Bonds.The majority of debt is from Latin America, with Argentina, Brazil, Mexico and Venezuela covering about 70% - 80% of the outstanding market. Nowadays the emerging markets bonds market is capturing the interest of both individual and institutional investors because of its uniqueness in at least two respects: rst, yields are extremely high, and, second, some issues are very large and liquid (which was one of Brady s main aims). Moreover, these features support an active over-the-counter derivatives market, so that investors can take views on country risk, bond spreads or volatility, as well as hedging their own portfolios through the use of customized options and/or futures. As widely known, developing (as well as developed) countries are used to issue several types of bonds in di erent markets, aimed at covering the outstanding principal amount of their bank loans and government debt and one or more bonds covering previous interest payments due, as well. Usually, we distinguish between Locally traded bonds (Government, Agencies, and Corporate securities quite illiquid, except for some issues, traded exclusively in the local bond markets and rarely present in institutional investors portfolios), Brady bonds and Eurobonds (otherwise known as Sovereign Bonds). The two main types of Brady bonds are par and discount bonds, year registered bullet bonds representing the largest, most common and most liquid issues in the Brady bond market. Par bonds are issued at par in exchange for the original face value 3

6 of the rescheduled loans but carry a xed, below-market interest rate. As an alternative to the plain vanilla most common case, in some other cases they also have some additional features complicating the computation of the present value of their cash ows (for example the Mexican par bonds have 17 series of Value Recovery Rights (VRR) which entitle the holder to additional payments linked to the price of oil). Discount bonds, instead, are bonds whose principal is a reduced fraction of the original obligation (typically a 35% reduction is allowed by the creditors) and that carry a oating interest rate. Both par and discount bonds have generally a principal collateralised by a U.S. Treasury zero coupon bond (rolling collateral) and the interest is collateralised by cash deposits maintained at the Federal Reserve Bank of New York to cover a speci c number of coupon payments (usually 12 to 18 months). Among Eurobonds, the most liquid (and therefore reliable for our analysis) type of bonds issued by developing countries are the so called Global Bonds, usually long-term, plain vanilla, uncollateralised bonds, whose cash ows are easily computed and discounted at each point in time, the only need being the term structure of risk-free interest rates and coupon payment dates. Market prices of Brady discount bonds have been used in the empirical investigation of Izvorski (1998), whereas Eurobonds have been used by Du e, Pedersen and Singleton (2000) and Merrick (2001). In this paper, we prefer to use Global bonds to extrapolate default probabilities because of the following reasons: (i) the simplicity of the calculations involved; (ii) the long-term view their pricing is based on; (iii) no assumptions on future term structures, future commodity prices or macroeconomic fundamentals (implied forward exchange rates, future oil prices, GDP growth, in ation rates, etc.) are required; and (last but not least) (iv) the implied default probability measure is somehow pure, as Global bonds are (usually) uncollateralised. 3 The pricing model Several models for the pricing of defaultable bonds have been proposed in the literature. Usually, three main approaches are distinguished 1. i) Merton s (1974) option pricing based model, which computes the payo at maturity as the face value of the defaultable bond minus the value of a 1 For a recent comprehensive review, see, among the others, Crouhy, Galai and Mark (2000), Gordy (2000), Jarrow and Turnbull (2000), Du e and Singleton (2001). 4

7 put option on the issuer s value with an exercise price equal to the face value of the bond. ii) Structural models, which relax one of the unrealistic assumptions of Merton s model, that is that default occurs only at maturity of the debt, when the issuer s assets are no longer su cient to face its obligations towards bondholders. On the contrary, they assume that default may occur at any time between issuance and maturity of the debt and that default is triggered when the issuer s assets reach a lower threshold level (Black and Cox (1976), Longsta and Schwartz (1995), Saa-Requejo and Santa-Clara (1997)). These models generally assume that debtholders, in case of default, get a fraction of debt s face value back named recovery rate, and that the latter is known apriori. iii) Reduced-form models, which do not condition default explicitly on issuer s value, and therefore are, in general, easier to implement 2. They also di er from typical structural models in the degree of predictability of default. In fact, they are considered more general than structural models as they can easily accommodate defaults coming as sudden surprises (see, for example, Jarrow, Lando and Turnbull (1997), Du e and Singleton (1997, 1999), Lando (1998), Schonbucher (1998)). Reduced-form models for pricing sovereign debt have been adopted by Du e, Pedersen and Singleton (2000) and Merrick (2001). Our pricing model is a discrete-time version of the Du e, Pedersen and Singleton (2000) model and works as follows. Assuming no arbitrage conditions, the market price of a defaultable asset should be a function of the default probability term structure, as well as of the future cash ows discounted using the current risk-free term structure. Interpreting the coupon bond as a portfolio of zero-coupon bonds, we get the following expression for the market price of a defaultable bond: V t = NX c ti exp( r ti t i )[(1 p ti )+± p ti ] (1) i=1 where t i =1; :::; N, indicates the time to i-th maturity, c ti the i-th cash ow, r ti the risk-free interest rate for the i-th maturity, p ti =1; :::; N, the probability that default occurs between times t i 1 and t i and ± the recovery ratio. Following Izvorski (1998) and Du e, Pedersen and Singleton (2000), we assume that p ti is constant over all time maturities and changes only for the e ect of changes in the term structure of risk-free interest rates, or for 2 This is particularly true when referred to sovereign debt. 5

8 the e ect of macroeconomic and/or political events that investors discount through prices. We also assume that, once a country defaults on some issues, just a fraction (the recovery ratio) of both coupon and principal will be paid for by the issuer in all the subsequent payments. This is a restrictive hypothesis, which does not allow us to account for the possibility that economic conditions could improve in the future and, therefore, the country repayment capacity be re-established. However, in our opinion, this drawback is a very marginal one; in fact, under the hypothesis that a default occurs prior to maturity, after the moratorium period, a new bond could be issued for an amount equivalent to the recovery ratio and for a maturity corresponding to the old one. In this case, the old bondholder will freeze its nancial situation along the lines outlined above. A third assumption concerns the recovery ratio, which we assume to be known and constant. Some more sophisticated models infer it from the historical recovery rates (those observed during past defaults) for identically rated issuers, some others describe the recovery ratio by means of a random variable. We believe that this is not a drastic drawback, since one can also extrapolate default probabilities conditionally on di erent measures of recovery ratio. Given these assumptions, the following equilibrium relationship between the market price of a defaultable bond and its expected cash ows can be derived: V t = NX c ti exp( r ti t i ) h (1 p) i + ± ³ 1 (1 p) i i (2) i=1 where p = p ti, i =1; :::; N. Given the term structure of risk-free interest rates, the bond price and the recovery rate, the equation above can be solved with respect to the probability of default p. In our application, all computations are carried out conditionally on the recovery rate parameter ±. In evaluating the bonds, we adopt a conservative hypothesis and x it equal to 20%, based on bond managers experience 3. From equation (2) we can recover, for each emerging market, the defaultable term structure: y ti = r ti + 1 t i ln h (1 p) i + ± ³ 1 (1 p) i i (3) where y ti is the credit-risky interest rate for the i-th maturity. 3 See, for example, Xu and Nencioni (2000) on J.P.Morgan practice. 6

9 4 The data In the empirical work, we consider long-run (usually 10 to 30 years to maturity at the time of issuance) US Dollar denominated Global bonds of twelve emerging markets, namely Argentina, Brazil, Colombia, Mexico, Russia, Venezuela, Panama, South Africa, Turkey, China, Philippines and South Korea. The main features of these issues are reported in table 1. The sample contains weekly market values of Global bond prices (mean of bid and ask quotes), ranging from 14 February 1997 to 27 July As we consider only US Dollar denominated emerging markets Global bonds, USD Libor and swap rates are used to t the risk-free term structure in correspondence of the payments dates. As for the Libor rates, we use all maturities between 1 month and 12 months, whereas for the swap rates we include all maturities between 2 and 10 years and the 15, 20 and 30 years maturities. The risk-free term structure of interest rates is obtained estimating a two-factor version of the Cox, Ingersoll and Ross (1985) model using a maximum likelihood - Kalman lter technique. 5 Extracting default probabilities Figure 1 shows the implied risk-neutral default probabilities estimated for the countries considered in the sample. Table 2 contains some summary statistics 5. As expected, the dynamics of the estimated risk-neutral probabilities re- ect the evolution of both the political and macroeconomic situations of the di erent countries during a four years period ( ) including deep nancial and economic crisis, such as the Asian nancial turmoil (1997), Russia s default (1998), the Turkish crisis (2001), Argentina s recession (2001), as well as subsequent exceptional recoveries. The sample initially exhibits rather stable dynamics, with low levels of implied default probability, which encouraged a low risk aversion attitude. Over this period investors commit the same error made almost twenty years before: they believe that emerging economies would not experience di culties in repaying their external debt, and that they would bene t from decreasing world interest rates, therefore continuing to improve their economic fundamentals. 4 The source of the data is Thompson Financial (formerly Datastream Ltd.). 5 Solving equation (2), which is non-linear with respect to p, requires the compilation of a dedicated GAUSS program, involving the use of an ad-hoc version of the Newton- Raphson algorithm. See Trova (2000). 7

10 Unfortunately, this view was undermined by disruptions in the balance of payments, disequilibria in the gross domestic product growth (e.g. a real estate bubble in most of Asian countries), stock exchange bubbles and extraordinary overvalued real e ective exchange rates in several less developed countries, all of which culminated in the outbreak of the Asian nancial crisis from mid 1997 onward (the mentioned outbreak dates back to July 1997 when Thailand s Monetary Authorities abandoned the pegged exchange rate system, leaving the Thai Baht to oat against major exchange rates). As a result, investors all over the world re-evaluated the risk implied in keeping Emerging Markets securities in their portfolios. This led to a di used panic reaction in late 1997, when World s nancial markets witnessed to a panic selling of Emerging Markets bonds and stocks in favour of safer assets in developed countries ( ight-to-quality e ect). During this period default probabilities for all the countries in our sample increased (even if not too dramatically according to our estimates). Argentina s implied risk-neutral probability of default almost doubled passing from a semi-annual 2% to almost 4%; Brazil s more than doubled, increasing from 2% to 5%; Mexico s and Venezuela s increased by 1% and 2.4%, while a less dramatic impact of the mentioned crisis is seen in Ecuador 6 and Colombia. After this critical period, another period of relative calm preceded the outbreak of a more dramatic and widespread Emerging Markets crisis in Beginning in June 1998 with Ecuador (whose currency - the Nuevo Sucre - was devalued in order to increase exports and thereby mitigate its severe balance of payments imbalances), a new nancial turmoil (the most severe since the Great Depression in the 1930s in peace periods), together with fears of a worldwide credit crunch following the failure of Long Term Capital Management (LTCM) in the United States and Long Term Credit Bank (LTCB) in Japan, infected the Emerging Markets, including Latin America. In July 1998 Venezuela, forced by a decrease in exports (due to decreasing oil prices, one of the most privileged safe harbours in bad times like those), devalued its currency, the Bolivar, (again) in order to increase exports. As a result, a general sell-o occurred rst in Latin America and then spread to other Emerging Markets, especially to Russia, whose banking system s fragility allowed for successful speculative attacks against the Ruble, by that way forcing the subsequent default (declared in august 1998), even if limited to the domestic debt. 6 Although we do not include Ecuador among the twelve countries in our sample, we estimate default probabilities for this country (using the 11.25% Global bond expiring in April 2002) for the period preceding default. 8

11 In this period, semi-annual risk-neutral default probabilities reached their peaks: 8.3% for Argentina, 14% for Brazil, 8.8% for Colombia, 16% for Ecuador, 6.1% for Mexico and 26.2% for Venezuela (the most dramatically hit country). For this period it is virtually impossible to obtain a convergence for our algorithm for the Russian bond if we consider recovery rates greater than 2%. History continues with another period of calm before (and after in this case) the storm. Another nancial crisis was getting ready to a ect Latin America once again: the Brazilian crisis of December February The currency (the Real) was devalued after speculative attacks based on the nancial and scal fragility of the Brazilian economy. As a result, the default probability peaked (even if at lower levels than the preceding ones) once more. As other countries, including Brazil, recovered late in 1999, this last crisis was the beginning of the end for Ecuador whose implied probability continued to increase up to 45% in October, when default was nally declared. The critical situation of the nancial sector (especially the banking sector, with its huge amount of non-performing loans, and its links, both direct and indirect, with the political forces governing the country), the high level of the in ation rate, the political uncertainty, and the unmatched requests formulated by the World Bank and the International Monetary Fund for critical but necessary reforms, were the motivations leading Turkey in the severe crisis dated spring The markets, worried about the capability of the Turkish economic authorities to deal with the disappointing political and economic situation, and about the capability of the Turkish government to roll out the increasing public debt as well, increased the risk appreciation versus Turkish bonds, as shown by the time path of the default probability estimated by our model. After the recovery, subsequent to new loans by the IMF (granted as counterpart of a plan of huge reforms involving the banking sector as well as the new exchange rate management and the setting of in ation target policies), the re-appreciation of the risk implied by the presence of Turkish bonds in institutional investor s portfolios (early summer 2001) was probably due (besides some doubts concerning the e ectiveness of the planned reforms) to the contagion e ect induced by the outbreak of the Argentine crisis. Argentina s troubles began as an e ect of the recession glooms involving the most important trading (and supporting) partner: the United States, as well as of the continuous political uncertainty concerning the government of the country itself. The bond markets, once again, called for higher risk premiums (and therefore higher implied default probabilities), starting from June 2001 and spreading from the domestic market to the Eurobonds and the 9

12 Brady Bonds markets. On the other hand, the International Monetary Fund (once again) called for more structural reforms involving the currency peg (a oating exchange rate could allow for a sort of amortization of some of the negative e ects of the current account situation, and the decreasing growth in gross domestic product, allowing for an upswing of the export sector), the banking system and more stability in the political situation 7. Looking at the interrelation between default probabilities estimated for the di erent countries, we observe that a regional contagion e ect holds. Table 3 shows the high correlation degree, calculated over the entire sample period, between the estimated risk-neutral default probabilities across countries belonging to the same economic region. This is particularly true for the most economically homogeneous region in our sample, Latin America, with correlations around 70-80%. Applying a principal components analysis to the default probabilities estimated for the twelve countries in the sample, we can show that just two factors can explain almost 70% of the total variability of default probabilities. Looking more closely at the distributional properties of implied riskneutral default probabilities, in particular observing the distances of minimum and maximum values from the sample means and medians in table 2, we can notice that the shape of such distributions looks far from being symmetric and is characterised by right fat tails. This intuition is reinforced by the estimation of a non-parametric empirical probability density function of the estimates. A normal kernel has been used to obtain the probability density functions (pdf s) plotted in Figure 2. Using the estimated default probabilities along with the tted US riskfree term structure, we can exploit equation (3) of the reduced-form model to recover, for each country, the implicit term structure of credit spreads, which re ects market s medium-long term expectations about bonds default probability. Figure 3 shows the time series estimates for some countries, whereas table 4 contains some summary statistics on the whole sample. In general, we observe relatively at term structures, which can become very steep during high volatility periods and downward sloping in the weeks following the end of a crisis. 7 Estimates for Argentina s default probability in the period August January 2002 are presented in the Appendix. 10

13 6 Predicting the dynamics of default probabilities for portfolio trading strategies In the previous section, we have estimated historical default probabilities from market prices of emerging markets bonds. For the bonds we are considering, we can observe that to an increase (decrease) in default probability corresponds a decrease (increase) in the market price of the bond one week ahead, as the average correlation between lagged default probabilities and bond prices is This means that predicting default probabilities, or, at least, the direction of default probabilities, can provide useful insights about future movements in bond prices. This would obviously represent a relevant information for portfolio allocation. In this section, we develop a forecasting model for the probability of observing an increase/decrease in future default probabilities, which is based on the use of frequently observed nancial variables. The forecasts are then used to implement e cient trading strategies for portfolios of emerging markets bonds. Because of the availability of data on the explanatory variables, the analysis in the following is restricted to seven countries, which are representative of di erent economic regions: Argentina, Brazil, Mexico, Russia, Turkey, South Korea and Philippines. First, for each country, we regress estimated default probabilities against some signi cant nancial variables, such as interest rates, bond indices and exchange rates. More precisely, as explanatory variables, we use lagged values (up to two weeks) of short and long term interest rates in local currencies, J.P.Morgan and Lehman Brothers local indexes, log changes in exchange rates and interest rate spreads calculated with respect to US rates. As shown in table 5, the nancial variables seem to contain a signi - cant amount of information for future default probabilities, with adjusted R-squared of the regressions around 75%, on average. We then use this evidence to build a logit type model for the prediction of the probability of a market downgrading or upgrading of Global bonds. From now on, we use the term downgrading to indicate either an increase in bonds default probability or a decrease in bonds price. Similarly, we use the term upgrading to indicate a decrease in bonds default probability or an increase in bonds price. In fact, as said above, an increase (decrease) in default probability is almost equivalent to a decrease (increase) in the market price of the bond. The dependent variable in the logit model assumes either value 1 for 11

14 positive weekly changes of the estimated default probability or value 0 for non-positive weekly changes. As explanatory variables, we use lagged values of the nancial variables included in the regression analysis above, that is, short and long term interest rates in local currency, J.P.Morgan and Lehman Brothers local indexes, log changes in exchange rates and interest rate spreads with respect to US rates. The model generally provides accurate predictions both for market downgrading and upgrading of bonds. Table 6 shows the percentage of correct in-sample predictions for one week ahead default probabilities and changes in bond prices. We notice that, with the only exception of South Korea, in about 75% of the cases the model correctly predicts future movements in default probabilities. As regards future changes in bond prices, the statistics are relatively satisfactory for all countries, except for South Korea and Russia (only in the downgrading case). The nal step of our empirical investigation consists in using the logit speci cation to produce out-of-sample forecasts for the dynamics of default probabilities. In this case, we recursively estimate the model using windows of three years (Argentina, Mexico, Brazil) or one year (Russia, Turkey, Philippines, South Korea) of weekly data. At each point in time, we generate one-step-ahead forecasts for the probability of having a bond market up/downgrading and use them to simulate trading strategies for portfolios of emerging market bonds. The simulations are carried out for the investment period 1 September July 2001 (48 weeks) assuming a starting equally weighted portfolio of $1,000,000 Global bonds. Portfolios of di erent bonds are considered and the following naive trading strategy is applied 8 : - upgrading signal (the probability of a decreasing default probability forecasted by the model is greater than 60%): position increased by $100,000 dollars; - downgrading signal (the probability of an increasing default probability forecasted by the model is greater than 60%): position closed; - no clear signal (the probability of a decreasing/increasing default probability forecasted by the model is between 40% and 60%): position unchanged; - minimum investment required to re-open a position on a bond: $100,000 dollars; - borrowing and lending at the USD risk-free 1 week Libor rate. We apply the strategy to 22 di erent portfolios: one containing all the 8 This strategy has been implemented after several constructive discussions with numerous traders. 12

15 bonds of the seven countries and 21 formed combining the seven bonds taking ve at a time. Table 7 shows that the simple active portfolio strategy, which is based on the signals derived from the out-of-sample forecasts obtained by the logit model for the probability of an upgrading/downgrading of the bond over the next week, provides quite satisfactory results, especially in comparison with the buy & hold strategy and the J.P.Morgan - Lehman Brothers benchmarks recalculated for the countries in the portfolios. In general, along the sample period considered in the simulations, emerging markets bonds have not performed particularly well, as the average returns on the benchmarks and the buy & hold portfolios are negative: 1:67% and 9:41%, respectively. Instead, the active portfolio strategy always produces positive returns, with an average value around 5:7%. Moreover, the variability of returns among the di erent portfolios is much lower (0:97%) than in the benchmarks (4:16%) and buy & hold (3:79%) case 9. The naive portfolio strategy based on the out-of-sample forecasts for default probabilities is also exible enough to control for the risk of the portfolio. Figure 4 shows that a VaR measure at the 95% con dence level, calculated using the J.P.Morgan RiskMetrics s methodology, satis es the capital requirements for the 7-bond portfolio formed applying the active strategy (this is true also for all the 5-bond portfolios). We observe that the active strategy provides a more suitable VaR measure than the buy & hold portfolio. In fact, it gives rise to only two breaks along the 48 weeks considered (4.2%), whereas there are ve breaks in the case of the buy & hold strategy. Moreover, as it adapts to new market conditions, the VaR measure in the active strategy case is less conservative and imposes, on average, lower capital requirements than in the buy & hold case. 7 Conclusion In this paper we have addressed two main issues: the computation of default probabilities implicit in emerging markets bonds prices and the impact on portfolio risks and returns of di erent default probability expectations. 9 In our calculations, we have not explicitly considered transaction costs. We observe a decrease of about 1% in the returns of the active portfolio strategy when a 10 basis points percentage of transaction costs is introduced. However, we believe that the returns in table 7 are not over-estimated, especially if we take the point of view of a relatively large emerging market fund. In fact, we use the mean of bid and ask quotes for bond prices, which means that, on average, transaction costs are already included in the buying and selling prices used to implement the active strategy. 13

16 First, using a reduced-form model for the pricing of defaultable bonds, we have extracted default probabilities from Global bonds market prices of twelve countries. The estimated default probabilities re ect quite closely actual crisis observed in the market over the sample period comprised between February 1997 and July Then, using logit type econometric models, we have shown that weekly changes of the estimated probabilities could be predicted by means of some capital markets factors (interest rates, exchange rates and credit spreads). Finally, we have used recursive estimates of a logit model to produce out-of-sample forecasts for appreciation/depreciation of the Global bonds. The application of a naive portfolio strategy, based on the out-of-sample forecasts of the logit model for the probability of a weekly up/down movement in the market value of the bonds, has provided quite satisfactory results, both in terms of returns and in terms of portfolio risk management. This is particularly true when we compare them with those obtained by a buy & hold strategy and the J.P.Morgan - Lehman Brothers benchmarks recalculated for the countries in the portfolios. Appendix: 2002 Argentina s default What we have seen in the last six months in Argentina (and numerically evaluated with a continuously growing estimate of default probability by our model) is nothing else than the consequence of what many of the world s top economists have said for the past two years, i.e. Argentina was caught in a vicious downward spiral that would lead to political unrest and economic collapse. What led Argentina on the edge of the abyss is now clear. Argentina was hanging on too long to a currency regime that linked the value of the ArgentinepesototheUSdollar,witha xedexchangerateofoneargentinepeso per US dollar. For a long time the system worked wonders to help Argentina in the control of its notorious hyperin ation. But, unfortunately, in the past three years, the peg to the rising U.S. dollar made Argentine products too expensive on world markets, throwing the country into recession. As in other similar cases, for a while the government, the companies and the households were able to protect themselves from some of the negative consequences of a shrinking economy by borrowing increasing amounts of money from its own banks and pension funds, from foreigners and eventually from the International Monetary Fund. But the story is widely known: when the economy did not turn around as expected (on the contrary, the situation got even worse due to the men- 14

17 tioned glooms on the world s economy), lenders became more cautious and demanded ever-rising interest rates. The higher rates drained even more money from the economy, causing still more unemployment (up to 18% in November 2001) and slower growth. Over the period from October 2001 to December 2001, Argentina s economic ministry launched a desperate plan to avoid o cial devaluation and default. Government workers and pensioners were required to take cuts in pay and bene ts of about 10%, and at the same time banks and pension funds holding government bonds were required to exchange them for new bonds paying lower interest rates. Strict limits were placed on how much money Argentines could take out of their bank accounts each week. The Argentine peso began trading uno cially at a 30%, 40%, and nally 50% discount against the dollar. The consequences of this situation were really dramatic; from a social point of view, violent popular riots took place with tragic (human and economic) e ects, while on the other side, under the nancial markets point of view, the desperate attempt of Argentina s economic authorities to ferry the economy to a safe harbour was perceived as an uno cial declaration of default and consequently the prices of Argentine bonds fell to their historical lows, with the consequent upswing of the implied default probabilities increasing from about 10% in early October to more than 30% at the end of the year (according to our estimates), as shown in gure 5. A rst step towards new economic equilibria for Argentina (supported by further loans by the International Monetary Fund and the World Bank which should be discussed around the middle of February 2002) could be the o cial peso devaluation (30%) of January 7th, 2002; this could help to come back to positive economic growth rates (or at least less dramatic negative rates) by means of the international trade channel, and perhaps the rst step towards the structural reforms required by the world s economic agents to recover trust in Argentina s future, surely this will resolve in the beginning of rather hard times under the economic point of view for Argentines. References Black, F. and J. Cox (1976), Valuing corporate securities: some e ects of bond indenture provisions, Journal of Finance, 31, Cox, J.C., J.E. Ingersoll and S.A. Ross (1985), A theory of the term structure of interest rates, Econometrica, 53, Crouhy, M., D. Galai and R. Mark (2000), A comparative analysis of current credit risk models, Journal of Banking and Finance, 24,

18 Du e, D., L.H. Pedersen and K.J. Singleton (2000), Modeling sovereign yield spreads: a case study of russian debt, working paper, Stanford University. Du e, D. and K. Singleton (1997), An econometric model of the term structure of interest rate swap yields, Journal of Finance, 52, Du e, D. and K. Singleton (1999), Modeling term structures of defaultable bonds, Review of Financial Studies, 12, Du e, D. and K. Singleton (2001), Credit risk for nancial institutions: management and pricing, Graduate School of Business, Stanford University. Gordy, M.B. (2000), A comparative anatomy of credit risk models, Journal of Banking and Finance, 24, Izvorski, I. (1998), Brady bonds and default probabilities, International Monetary Fund, working paper 98/16. Jarrow, R., D. Lando and S. Turnbull (1997), A markov model for the term structure of credit risk spreads, Review of Financial Studies, 10, Jarrow, R. and S. Turnbull (2000), The intersection of market and credit risk, Journal of Banking and Finance, 24, Lando, D. (1998), Cox processes and credit-risky securities, Review of Derivatives Research, 2, Longsta, F. and E. Schwartz (1995), A simple approach to valuing risky xed and oating debt, Journal of Finance, 50, Merrick, J.J. (2001), Crisis dynamics of implied default recovery ratios: evidence from Russia and Argentina, Journal of Banking and Finance, 25, Merton, R. (1974), On the pricing of corporate debt: the risk structure of interest rates, Journal of Finance, 29, Saa-Requejo, J. and P. Santa-Clara (1997), Bond pricing with default risk, working paper, Anderson School of Management, University of California Los Angeles. Schonbucher, P.J. (1998), Term structure modelling of defaultable bonds, Review of Derivatives Research, 2, Trova, M. (2000), Emerging markets, Brady bonds and default probabilities: a portfolio selection approach, working paper, Intesa Asset Management, Milan. Xu, D. and F. Nencioni (2000), Introducing the J.P.Morgan implied default probability model: a powerful tool for bond valuation, working paper, JPMorgan, New York. 16

19 Table 1 Main features of Global bonds This table shows the main features of the Global bonds included in the sample. The sample contains weekly market values of prices ranging from 14 February 1997 to 27 July All bonds pay the coupon semi-annually and are not collateralised. Issuer Maturity Coupon Argentina 19 Sept % Brazil 15 May % Colombia 15 Feb % Mexico 15 May % Panama 30 Sept % Venezuela 15 Sept % Russia 24 July % South Africa 19 May % Turkey 15 June % China 22 Oct % Philippines 15 Jan % South Korea 15 Apr % 17

20 Table 2 Summary statistics on estimated default probabilities This table shows summary statistics on estimated default probabilities. These are weekly estimates from equation (2), where we consider long-term US Dollar denominated Global bonds (see table 1) for a sample period ranging between 14 February 1997 and 27 July USD Libor (all maturities between 1 month and 12 months) and swap rates (all maturities between 2 and 10 years and the 15, 20 and 30 years maturities) are used to t the riskfree term structure in correspondence of the payments dates. The risk-free term structure of interest rates is obtained estimating a two-factor version of the Cox, Ingersoll and Ross (1985) model using a maximum likelihood - Kalman lter technique. Values are expressed in percentage terms. Country No. obs. Mean Median St. Dev. Max Min Argentina Brazil Colombia Mexico Panama Venezuela Russia South Africa Turkey China Philippines South Korea

21 Table 3 Regional contagion e ect This table shows the correlation between estimated default probabilities of twelve emerging markets bonds over the sample period ranging between 14 February 1997 and 27 July Country Brazil Colombia Mexico Panama Venezuela Argentina Brazil Colombia Mexico Panama 0.78 Country S.th Africa Turkey China Philippines S.th Korea Russia S.th Africa Turkey China Philippines

22 Table 4 Estimated term structures of credit spreads This table shows average estimated credit spreads for di erent maturities. These are implicitly derived from estimated default probabilities and US risk-free term structure. The sample period varies for each country and ranges between 14 February 1997 and 27 July Values are expressed in percentage terms. Standard deviation in parentheses. Country No. obs. 1 year 5 year 10 year Argentina (1.017) (0.980) (0.917) Brazil (1.924) (1.794) (1.607) Colombia (1.068) (1.037) (0.994) Mexico (0.736) (0.720) (0.699) Panama (0.488) (0.476) (0.462) Venezuela (5.429) (3.749) (2.473) Russia (5.987) (5.083) (3.801) South Africa (0.268) (0.265) (0.262) Turkey (0.938) (0.918) (0.878) China (0.342) (0.340) (0.337) Philippines (0.716) (0.699) (0.676) South Korea (1.056) (1.031) (0.998) 20

23 Table 5 Predictive ability of nancial variables for default probabilities This table shows the predictive ability of nancial variables for default probabilities. Estimated default probabilties are regressed against lagged values (up to two weeks) of short and long term interest rates in local currencies, J.P. Morgan and Lehman Brothers local indexes, log changes in exchange rates and interest rate spreads calculated with respect to US rates. The sample period varies for each country and ranges between 14 February 1997 and 27 July Country No. of obs. R 2 Argentina Brazil Mexico Russia Turkey Philippines South Korea

24 Table 6 Percentage of correct in-sample predictions This table shows the percentage of correct in-sample predictions of a market downgrading (weekly increase in default probability or decrease in bond price) or upgrading (weekly decrease in default probability or increase in bond price) in the underlying bonds. These are obtained estimating a logit model, where the dependent variable assumes either value 1 for positive weekly changes of default probability or value 0 for non-positive weekly changes. As explanatory variables, short and long term interest rates in local currencies, J.P. Morgan and Lehman Brothers local indexes, log changes in exchange rates and interest rate spreads calculated with respect to US rates are used. The sample period varies for each country and ranges between 14 February 1997 and 27 July Values are expressed in percentage terms. Change in def. prob. Change in bond price Country No. obs. Downgr. Upgr. Downgr. Upgr. Argentina Brazil Mexico Russia Turkey Philippines South Korea

25 Table 7 Return on di erent investment strategies This table shows the returns given by di erent investment strategies on portfolios of Global bonds. Simulations are carried out for the period 1 September July 2001 (48 weeks) assuming that the portfolios are initially equally weighted. The active portfolio strategy is based on the buy/sell signals provided by the out-of-sample forecasts for the dynamics of default probabilities obtained through the logit model. An initial investment of $1,000,000 is assumed. On the active strategy, a minimum investment requirement of $100,000 is imposed to re-open a position. No constraints on borrowing and lending at the USD 1 week risk-free Libor rate are imposed. All values are in percentage terms. Bonds used to form portfolios are those of table 1 for Argentina (A), Brazil (B), South Korea (K), Mexico (M), Philippines (P), Russia (R) and Turkey (T). Portfolios Active portfolio Benchmark Buy&hold A, B, K, M, P 4:58 0:24 9:45 A, B, K, M, R 6:75 0:85 7:41 A, B, K, M, T 5:34 6:37 13:73 A, B, K, P, R 5:81 0:59 8:21 A, B, K, P, T 4:41 6:61 14:53 A, B, K, R, T 6:58 6:08 12:48 A, B, P, R, T 5:64 6:77 14:34 A, B, M, P, R 5:82 0:11 9:26 A, B, M, P, T 4:41 7:05 15:58 A, B, M, R, T 6:58 6:53 13:54 A, K, M, P, R 6:73 3:22 5:19 A, K, M, P, T 5:32 4:18 11:51 A, M, P, R, T 6:56 4:32 11:32 A, K, P, R, T 6:56 3:87 10:27 A, K, M, R, T 7:49 3:61 9:47 B, K, M, P, R 5:06 8:43 1:24 B, K, M, P, T 3:65 0:64 7:56 B, M, P, R, T 4:89 0:54 7:37 B, K, P, R, T 4:89 1:00 6:32 B, K, M, R, T 5:82 1:26 5:52 K, M, P, R, T 5:80 3:58 3:30 A, B, K, M, P, R, T 6:44 1:70 9:41 Average 5:69 1:67 9:41 Standard deviation 0:97 4:16 3:79 23