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A New Method for Estimating Value-at-Risk of Brady Bond Portfolios

A New Method for Estimating Value-at-Risk of Brady Bond Portfolios. Ron D'Vari & Juan C. Sosa State Street Research & Management CIFEr, New York March 30th, 1999. Objectives. Estimate short-term spread-driven VaR statistics for Brady Bond portfolios

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A New Method for Estimating Value-at-Risk of Brady Bond Portfolios

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  1. A New Method for Estimating Value-at-Risk of Brady Bond Portfolios Ron D'Vari & Juan C. Sosa State Street Research & Management CIFEr, New York March 30th, 1999

  2. Objectives • Estimate short-term spread-driven VaR statistics for Brady Bond portfolios • Model accurately the dynamics of country spread time series: time-varying volatility and persistent shock-events • Allow for exogenous factors: contagion, sentiment indicators, macroeconomic variables VaR of Brady Bonds - Ron D'Vari, et al.

  3. Methodology Requirements • Accuracy • Robustness • Feasible automation and maintenance VaR of Brady Bonds - Ron D'Vari, et al.

  4. Modeling Alternatives • Rolling Variance-Covariance • (Multivariate) GARCH • We suggest a hybrid approach • Univariate GARCH with Persistent Jumps • Rolling white noise correlation matrix • Exogenized jump frequencies VaR of Brady Bonds - Ron D'Vari, et al.

  5. Data Set • JP Morgan’s EMBI database of country-representative Brady Bond indices • Current countries: Argentina, Bulgaria, Brazil, Ecuador, Mexico, Panama, Peru, Poland, and Venezuela • Longest daily data sets start in 1992 VaR of Brady Bonds - Ron D'Vari, et al.

  6. Approximating Returns • Brady Bond portfolio returns can be decomposed into • US Term Structure Movements • Country Risk Changes • Bond Issue Specifics • We are concerned only about the second VaR of Brady Bonds - Ron D'Vari, et al.

  7. Spread Returns • For a N-country portfolio, our return formula is given by • rp = w1r1+ w2r2+…+ wNrN • » - w1d1Ds1 - w2d2Ds2 -…- wNdNDsN • di and Dsi are the duration and spread change for country i bonds over the return horizon • wi is the weight of country i bonds in the portfolio VaR of Brady Bonds - Ron D'Vari, et al.

  8. Rolling Var-Covar Vart(rp) = (w1d1 ... wNdN)S(w1d1 ... wNdN)` where Sis the sample var-covar matrix of the spread change vector over the past 3-months VaR of Brady Bonds - Ron D'Vari, et al.

  9. Rolling GARCH (univariate) • We consider the popular GARCH(1,1) version of the model • Model parameters are reestimated daily using all previously available spread change data • VaR estimates are produced via simulation VaR of Brady Bonds - Ron D'Vari, et al.

  10. Rolling GARCH-PJ (univariate) • We consider a variation of GARCH(1,1) that features Bernoulli-style jumps Dst = a0 + et, where et = sqrt(ht)ut + jt, with ut~ N(0,1) i.i.d. ht = g0 + g1 e2t-1 + g2ht-1 jt ~ N(mj,sj2) with probability p 0 with probability 1-p VaR of Brady Bonds - Ron D'Vari, et al.

  11. Rolling GARCH-PJ (univariate) cont’d • Jump occurrences in this model will induce a volatility spike in subsequent days • Bernoulli, rather than Poisson jumps, simplify and speed up the parameter estimation procedure • VaR estimates are also produced via simulation VaR of Brady Bonds - Ron D'Vari, et al.

  12. Rolling Exogenized GARCH-PJ (univariate) • Jump frequencies are also allowed to depend on exogenous or past data • We consider a contagion variable: the average implicit jump probability across all countries in the sample over the past month VaR of Brady Bonds - Ron D'Vari, et al.

  13. Brazil: Daily Series of 1-day spread changes, Jan/01/98-Jan/22/99 3 and 90%&99% Var-Covar VaR estimates 2 1 0 -1 -2 -3 0 25 50 75 100 125 150 175 200 225 250 VaR of Brady Bonds - Ron D'Vari, et al.

  14. Brazil: Daily Series of 1-day spread changes, Jan/01/98-Jan/22/99 4 and 90%&99% GARCH(1,1) VaR estimates 3 2 1 0 -1 -2 -3 0 25 50 75 100 125 150 175 200 225 250 VaR of Brady Bonds - Ron D'Vari, et al.

  15. Brazil: Daily Series of 1-day spread changes, Jan/01/98-Jan/22/99 and 90%&99% GARCH-PJ(1,1) VaR estimates 4 3 2 1 0 -1 -2 -3 0 25 50 75 100 125 150 175 200 225 250 VaR of Brady Bonds - Ron D'Vari, et al.

  16. Brazil: Daily Series of 1-day spread changes, Jan/01/98-Jan/22/99 and 90%&99% GARCH-PJ(1,1) w/ Exogenized Jumps VaR estimates 4 3 2 1 0 -1 -2 -3 0 25 50 75 100 125 150 175 200 225 250 VaR of Brady Bonds - Ron D'Vari, et al.

  17. Model Choice The skewness and kurtosis of the standardized innovations support GARCH-PJ Brazil 1992-1999: Skewness Kurtosis Rolling Var-Covar 5.94 99.67 GARCH 2.96 47.20 GARCH-PJ * 0.16 3.50 GARCH-PJ Exo* 0.12 3.42 *jump days excluded VaR of Brady Bonds - Ron D'Vari, et al.

  18. Model Choice (cont’d) • Pearson goodness-of-fit statistics concentrated at the 90% tails also support (Exogenized) GARCH-PJ • In this example, the Pearson goodness-of-fit statistics are distributed c2(10) VaR of Brady Bonds - Ron D'Vari, et al.

  19. Model Choice (cont’d) Pearson Goodness-of-Fit Series EMBI Argent. Bulgaria Brazil Ecuador Num Obs 2050 1465 1069 1798 923 Var-Covar 197.56 138.32 81.477 136.68 26.933 0.00% 0.00% 0.00% 0.00% 0.27% GARCH 85.165 44.587 36.82 60.475 16.441 0.00% 0.00% 0.01% 0.00% 8.77% GARCH-PJ 21.098 8.8574 6.5732 24.874 4.6923 2.04% 54.57% 76.50% 0.56% 91.08% GARCH-PJ 17.547 17.556 9.6259 17.184 9.9252 (exogenized) 6.31% 6.29% 47.39% 7.04% 44.71% VaR of Brady Bonds - Ron D'Vari, et al.

  20. Model Choice (cont’d) Pearson Goodness-of-Fit Series Mexico Panama Peru Poland Venezuela Num Obs 1798 507 444 1069 1798 Var-Covar 140.07 46.29 44.186 43.941 93.301 0.00% 0.00% 0.00% 0.00% 0.00% GARCH 83.035 13.679 34.806 37.314 70.317 0.00% 18.81% 0.01% 0.00% 0.00% GARCH-PJ 14.016 6.158 1.4454 27.212 9.7889 17.23% 80.18% 99.91% 0.24% 45.92% GARCH-PJ 18.074 5.2091 8.6527 12.17 9.2327 (exogenized) 5.37% 87.68% 56.54% 27.38% 51.02% VaR of Brady Bonds - Ron D'Vari, et al.

  21. Hit Rates (1-day 90%,95%, 97.5% and 99% VaR) Argentina Bulgaria Brazil Mexico Poland Venezuela Rolling Var-Covar 90.0% 91.5% 91.3% 90.6% 91.1% 91.4% 91.0% 95.0% 93.2% 93.9% 92.9% 94.2% 94.9% 94.3% 97.5% 94.8% 95.3% 94.9% 95.7% 96.6% 96.2% 99.0% 96.3% 97.0% 96.7% 96.6% 97.6% 97.3% GARCH 90.0% 90.9% 90.8% 91.2% 91.2% 93.7% 90.5% 95.0% 94.3% 94.6% 94.6% 94.3% 96.0% 94.3% 97.5% 96.2% 96.0% 96.1% 96.2% 97.0% 95.9% 99.0% 97.4% 97.6% 97.6% 96.9% 98.5% 97.4% GARCH-PJ (exogenized jump) 90.0% 91.0% 90.3% 89.8% 89.9% 90.2% 90.2% 95.0% 94.9% 94.4% 94.0% 94.4% 94.5% 93.9% 97.5% 97.0% 96.7% 96.6% 97.1% 96.3% 97.2% 99.0% 99.0% 99.0% 98.5% 98.9% 99.0% 98.9% VaR of Brady Bonds - Ron D'Vari, et al.

  22. Hit Rates (1-week 90%,95%, 97.5% and 99% VaR) Argentina Bulgaria Brazil Mexico Poland Venezuela Rolling Var-Covar 90.0% 88.4% 88.3% 87.0% 89.0% 90.4% 87.3% 95.0% 91.6% 91.9% 90.7% 92.8% 94.2% 91.4% 97.5% 93.4% 93.3% 93.0% 94.8% 95.7% 93.9% 99.0% 94.3% 95.7% 94.8% 95.8% 96.7% 95.4% GARCH 90.0% 86.8% 89.2% 89.8% 88.6% 93.5% 86.2% 95.0% 92.2% 93.1% 93.3% 92.7% 96.2% 90.9% 97.5% 94.6% 94.9% 95.1% 95.9% 97.3% 93.9% 99.0% 96.8% 96.6% 96.4% 97.6% 98.3% 96.1% GARCH-PJ (exogenized jumps) 90.0% 89.6% 91.5% 89.9% 91.1% 92.7% 88.7% 95.0% 94.5% 94.7% 94.7% 95.9% 96.2% 94.7% 97.5% 96.6% 96.3% 97.5% 97.7% 97.8% 96.9% 99.0% 98.3% 98.0% 98.6% 98.7% 99.1% 98.6% VaR of Brady Bonds - Ron D'Vari, et al.

  23. Hit Rates (1-month 90%,95%, 97.5% and 99% VaR) Argentina Bulgaria Brazil Mexico Poland Venezuela Rolling Var-Covar 90.0% 80.6% 80.4% 79.4% 83.4% 82.7% 80.8% 95.0% 85.8% 85.7% 84.3% 88.2% 88.2% 85.3% 97.5% 88.2% 88.6% 86.8% 91.0% 91.8% 88.7% 99.0% 91.3% 91.8% 89.4% 93.5% 94.4% 91.5% GARCH 90.0% 83.5% 87.1% 84.4% 87.6% 94.2% 80.9% 95.0% 88.6% 90.8% 89.1% 91.5% 94.9% 88.1% 97.5% 92.0% 92.5% 91.8% 93.9% 95.9% 92.4% 99.0% 94.5% 95.2% 93.9% 95.9% 96.8% 94.5% GARCH-PJ (exogenized jumps) 90.0% 89.0% 90.5% 89.9% 92.4% 93.7% 91.1% 95.0% 93.0% 93.2% 94.6% 95.0% 96.7% 94.4% 97.5% 95.7% 95.9% 97.2% 96.7% 98.1% 96.8% 99.0% 97.6% 97.8% 99.0% 97.5% 99.1% 98.0% VaR of Brady Bonds - Ron D'Vari, et al.

  24. Multivariate ARCH Issues • Multivariate ARCH models suffer from estimation problems, deriving from the inclusion of correlation parameters • Our ad-hoc approach: a 3-month sample correlation matrix estimated from (non-jump) standardized innovations VaR of Brady Bonds - Ron D'Vari, et al.

  25. Portfolio VaR • We consider 3 equally-weighted sample portfolios • LatAm: Argentina, Brazil, Mexico, Venezuela • Global (EastEurope): Bulgaria, Mexico, Poland • Global (LatAm): Argentina, Brazil, Bulgaria • Current spread durations were used VaR of Brady Bonds - Ron D'Vari, et al.

  26. Portfolio VaR Hit Rates Rolling Var-Covar 90% 95% 97.50% 99% LatAm 1-day 90.60% 93.70% 94.90% 96.50% 1-week 87.80% 91.70% 93.50% 95.20% 1-month 80.30% 85.90% 88.00% 90.50% Global 1-day 91.10% 94.00% 95.70% 96.50% (East Europe)1-week 87.70% 91.50% 93.50% 95.00% 1-month 81.80% 86.50% 90.00% 91.80% Global 1-day 91.30% 94.50% 95.90% 96.80% (LatAm)1-week 88.40% 91.90% 93.80% 95.90% 1-month 82.20% 87.70% 90.40% 92.70% VaR of Brady Bonds - Ron D'Vari, et al.

  27. Portfolio VaR Hit Rates GARCH 90% 95% 97.50% 99% LatAm1-day 91.50% 94.70% 95.90% 97.40% 1-week 87.70% 92.10% 95.00% 96.60% 1-month 85.20% 91.00% 93.80% 94.50% Global1-day 91.60% 94.80% 96.50% 98.00% (East Europe)1-week 88.70% 92.80% 94.70% 96.20% 1-month 86.50% 92.30% 94.10% 95.10% Global 1-day 91.80% 95.10% 96.30% 97.30% (LatAm)1-week 89.90% 93.80% 95.30% 96.60% 1-month 90.10% 93.80% 94.90% 96.00% VaR of Brady Bonds - Ron D'Vari, et al.

  28. Portfolio VaR Hit Rates GARCH-PJ (exogenized jumps) 90% 95% 97.50% 99% LatAm1-day 89.30% 94.00% 96.80% 99.00% 1-week 90.00% 95.00% 96.80% 97.90% 1-month 91.90% 94.70% 96.10% 97.60% Global 1-day 90.40% 94.30% 97.20% 98.80% (East Europe)1-week 90.60% 94.70% 96.60% 98.20% 1-month 93.50% 95.30% 96.50% 97.30% Global 1-day 90.20% 94.10% 96.40% 98.70% (LatAm)1-week 90.60% 94.70% 96.50% 97.80% 1-month 95.00% 95.90% 96.40% 97.50% VaR of Brady Bonds - Ron D'Vari, et al.

  29. Conclusions and Comments • GARCH-PJ’s fit to Emerging Market spread data is superior to that of GARCH and Var-Covar approaches • Hybrid univariate GARCH fit/empirical correlation matrix VaR approach is flexible, accurate, fast, robust and easily automated • Application of methodology in other contexts is straightforward VaR of Brady Bonds - Ron D'Vari, et al.

  30. Fin VaR of Brady Bonds - Ron D'Vari, et al.

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