Estimating Default Probabilities for Emerging Markets Bonds

Transcription

1 Estimating Default Probabilities for Emerging Markets Bonds Stefania Ciraolo (Università di Verona) Andrea Berardi (Università di Verona) Michele Trova (Gruppo Monte Paschi Asset Management Sgr, Milano) EXTENDED ABSTRACT In the last decade, emerging markets have experienced numerous financial 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. All these events have given rise to significant contagion effects among emerging markets. Estimating the default probability priced in emerging market bonds 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 offered by Brady/Global bonds with respect to those obtainable investing in US Treasury bonds 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 market losses caused by frequent downgrading and subsequent bonds price volatility. In this paper, we aim to extrapolate default probabilities implicit in the prices of bonds issued by emerging market countries and to forecast the dynamics of such probabilities in order to implement efficient portfolio strategies. The paper is organised as follows. In the first part, we develop and estimate a reduced form type model for the calculation of default probabilities. In the second part, a logit specification based on the use of specific financial variables is applied to predict the dynamics between rating classes of the bonds. Finally, the out-of-sample forecasts of the logit model are exploited to implement a trading strategy for portfolios of emerging markets bonds, which are then analysed under the Risk/Return profile (adjusted to account for transaction costs). 1. Estimating default probabilities As is well known, there are several models to compute default probabilities and, in general, to evaluate financial instruments subject to default risk. In general, these can be classified into three main groups (for a comprehensive review, see Duffie and Singleton (2001)): Merton s (1974) option-based approach, structural models (see, for example, Longstaff and Schwartz (1995)) and reduced-form models (see, among the others, Jarrow, Lando and Turnbull (1997)). We choose reduced-form models as sufficiently representative of the dynamics characterising the Brady/Global bonds market and extrapolate probabilities of default of developing countries from their bond market prices. The theoretical model assumes that the market price of a defaultable asset should be a function of the default probability structure, along with the cash flows and the term structure of interest rates

2 As in Izvorski (1998) and Trova (2000), we assume that the probability that default occurs between two dates is constant over all time maturities and changes only for the effect of changes in the reference currency s term structure and of macroeconomic and/or political events. Moreover, we assume that, once a country defaults on some issue, the issuer, in all subsequent payments, will pay only a fraction (the recovery rate) of coupon and principal. Finally, the recovery rate is assumed to be fix and independent of the time of default. Given these assumptions, the following equilibrium relationship between the market price of a defaultable bond, V t, and its expected cash flows can be derived: V t = N i= 1 c ti [ ] ti i i ( 1+ r ) ( 1 p) + δ( 1 ( 1 p) ) ti where: t i, i = 1,,N, indicates the time to i-th maturity; c ti the i-th cash flow; r ti the risk-free yield for the i-th maturity; p=p i, the probability that default occurs between time t i e t i-1 ; δ the recovery rate. 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 hyperparameter of the model, δ, that we put equal to 20%, based on bond managers experience. As we consider only US Dollar denominated emerging markets global bonds, USD Libor and swap rates are used to fit the risk-free term structure in correspondence of the payments dates. A two-factor version of the Cox, Ingersoll and Ross (1985) model is employed to build the term structure. Estimation is carried out applying a cross-sectional maximum likelihood technique. We apply the model to weekly data of prices of long-term Global Bonds, with a plain vanilla structure, issued by several emerging markets: Argentina, Brazil, Colombia, Mexico, Venezuela, Panama, Ecuador, South Korea, Philippines, China, South Africa, Russia, Turkey and Slovakia. The sample period ranges between February 1997 and July Figure 1 shows default probabilities estimated for some of these countries for the period. Figure 1. Estimated default probabilities 8% 7% 6% Argentina Russia Turkey Venezuela 5% 4% 3% 2% 1% 07/01/00 07/07/00 07/01/01 07/07/01 Applying a principal components analysis to the default probabilities estimated for the fourteen countries in the sample, we can show that a contagion effect seems to hold, as just two factors can explain almost 70% of the total variability of default probabilities

3 2. Predicting the dynamics of default probabilities The default probabilities estimated by the model are then exploited as an input for a logit type model, which is used to assess and predict the probability of a market downgrading or upgrading in the underlying bonds. As explanatory variables, the logit specification uses weekly changes in interest rates in local currency, exchange rates, J.P. Morgan Local Indexes and interest rate spreads with respect to US rates. The empirical work shows that the model generally provides relatively accurate predictions both for market downgrading and upgrading of Brady/Global bonds. Table 1 shows the percentage of correct in-sample predictions for some of the countries considered. Table 1. Percentage of correct in-sample predictions Country Downgrading Upgrading Brazil 78% 74% Mexico 76% 75% Argentina 74% 79% Russia 80% 80% Philippines 77% 72% South Korea 61% 79% Turkey 78% 79% The model also produces satisfactory out-of-sample forecasts for the dynamics of default probabilities. In particular, one-step-ahead forecasts for the probability of having a bond market up/downgrading are used to form different simulated trading strategies for portfolios of emerging market bonds. In the following, we illustrate an example. 3. Portfolio strategies: an example In this example, we consider an equally weighted portfolio of Global bonds issued by Argentina, Brazil and Mexico for the investment period September July 2001 (48 weeks) and adopt the following trading strategy: - strong upgrading signal (probability of decreasing default probability greater than 60%): position increased by X dollars; - strong downgrading signal (probability of decreasing default probability less than 40%): position closed; - no clear signal (probability of decreasing default probability between 40% and 60%): position unchanged; - minimum investment to re-open a position on a bond: X dollars; - cash in a USD risk-free deposit paying 1 week Libor rate. The signals are derived from the out-of-sample forecasts produced by the logit model for the probability of an upgrading/downgrading of the bond over the next week. Assuming an initial investment of $ 1,000,000 and a minimum investment requirement of X = $ 200,000, this strategy gives a positive return around 5.7%. Instead, both a buy & hold strategy and the JPMorgan benchmark (recalculated for the three countries) would give negative - 3 -

4 returns (-16% and -6.6%, respectively). The return of the active strategy would be even higher (8%) if a riskier X = $ 500,000 investment requirement is imposed. Table 2. Return on different investment strategies Portfolio Strategy Return Risk-free deposit 5.07% Buy & hold % Benchmark JPMorgan -6.57% Minimum investment $ 200, % Minimum investment $ 500, % It is interesting to note that the active portfolio strategy based on the out-of-sample forecasts for default probabilities is flexible enough to control for the risk of the portfolio. In fact, we observe that a VaR measure at the 95% confidence level based on RiskMetrics's methodology (see, for example, Jorion (2001)) implies only two breaks along the 48 weeks considered (4.2%), in the case of the active strategy, and four breaks (8.3%), in the case of the buy & hold strategy. Figure 2. VaR for the buy & hold portfolio VaR breaks VaR (95%) actual loss /08/01 16/06/01 29/04/01 12/03/01 23/01/01 06/12/00 19/10/00 01/09/00 Figure 3. VaR for the portfolio with minimum investment $ 200, VaR (95%) actual loss VaR breaks 03/08/01 16/06/01 29/04/01 12/03/01 23/01/01 06/12/00 19/10/00 01/09/00-4 -

5 References - Cox, J.C., J.E. Ingersoll and S.A. Ross (1985), "A theory of the term structure of interest rates", Econometrica, 53, Duffie, D. and K. Singleton (2001), Credit risk for financial institutions: management and pricing, Graduate School of Business, Stanford University. - 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, Jorion, P. (2001), Value at Risk, (2 nd ed.), McGraw-Hill, New York. - Longstaff, F. and E. Schwartz (1995), A Simple Approach to Valuing Risky Fixed and Floating Debt, Journal of Finance, 50, Merton, R. (1974), On the Pricing of Corporate Debt: The Risk Structure of Interest Rates, Journal of Finance, 29, Trova, M. (2000), "Emerging Markets, Brady Bonds and Default Probabilities - A Portfolio Selection Approach", Intesa Asset Management, working paper