GARCH vs. Traditional Methods of Estimating Value-at-Risk (VaR) of the Philippine Bond Market

Transcription

1 GARCH vs. Traditional Methods of Estimating Value-at-Risk (VaR) of the Philippine Bond Market

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3 INTRODUCTION

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5 Value-at-Risk (VaR)

6 Value-at-Risk (VaR) summarizes the worst loss over a target horizon that will not be exceeded with a given level of confidence (Jorion, 2007)

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8 GLOBAL FINANCIAL CRISIS

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10 Fat tail Distribution Market Volatility

11 Generalized Auto Regressive Conditional Heteroskedasticity

12 Do GARCH-based models better estimate VaR of the Philippine Bonds than the usual approaches?

13 To produce VaR estimates for Philippine bond market using classical and GARCHbased model approaches To evaluate the methods to determine which can produce the best VaR estimates through certain backtesting procedures

14 Few studies on the topic in the Philippines Sustain the growth and stability in the market despite unexpected market conditions Help policymakers in knowing what measures to utilize in order to absorb shocks and undesirable market conditions Make academicians more aware of econometric tools in measuring risks, specifically VaR

15 Standard Value at Risk (VaR) iboxx Asian Bond Fund Index Family (Asian Development Bank) Classical VS GARCH-based Backtesting Procedures: Proportion of Failure, Independence and Interval Forecast Test

16 REVIEW OF RELATED LITERATURE

17 Filtered historical simulation, a modified version of the usual historical simulation, provided the best results for bonds and interest rate swaps in the United States. Liu et al. (2012) With the three classical approaches for VaR estimation of Dutch bond portfolios, the combination of variance-covariance and Monte Carlo method provided the best results. Vlaar (2000) GARCH models performed better than the usual approaches and RiskMetrics in estimating the VaR in different assets, specifically stock indices in different stock markets in different parts of the world. Nyssanov (2013), Hafezian et al. (2015), Thapar (2006), Demireli (2010), So & Yu (2006) and Cera & Cera (2013)

18 EGARCH outperformed other GARCH-based models in estimating the VaR of asset portfolios, with a highlight on the usage of student-t distribution in many of the findings. Angelidis et al. (2004), Bucevska (2013), Johansson & Jowa (2013), Ivo & Rippel (2011) and Tagliafichi (n.d.) Asymmetric GARCH-based models, in general, provide better estimates of VaR as changes or the dynamic character of the financial data are better captured. Berggren & Folkelid (2010), Brooks & Persand (2003) and Thupayagale (2010)

19 GARCH VaR measures were more accurate during crisis period in the US Financial Crisis. GARCH-based methods covered for the mishaps of the risk models during the pre-crisis period of GARCH (1,1) model outperformed other GARCH models and RiskMetrics in measuring VaR during the Financial Crisis in the Iranian Stock Exchange.

20 THEORETICAL FRAMEWORK, EMPIRICAL METHODOLOGY & CONCEPTUAL FRAMEWORK

21 Value-at-Risk worst expected loss over a specific time interval at a given confidence level maximize returns Markowitz s Mean-Variance Framework portfolio diversification minimize losses

22 VaR s Three Key Elements Level of Loss in Value Definite Time Horizon when the risk is measured Confidence Level

23 There is a 1% probability that the investor will lose PHP3.6 million in a day.

24 Source: Rashid, Z. Tata Consultancy Services

25 To produce VaR estimates for Philippine bond market using classical and GARCH-based model approaches

26 Classical Approaches GARCHbased model Approaches

27 Historical Simulation Classical Approaches Variance-Covariance Method Monte Carlo Simulation

28 It uses the past returns in order to predict the future returns It assumes that the asset returns are normally distributed and that the portfolio value changes are linearly dependent on the risk factor returns. It involves producing a model for future asset prices and running multiple hypothetical trials through the model. It generates values randomly unlike historical simulation that bases its calculation from historical returns. Historical Simulation Variance-Covariance Method Monte Carlo Simulation

29 GARCH(1,1) IGARCH EGARCH GJR-GARCH GARCH-based model Approaches APARCH

30 indicator function taking the value one if the residual is smaller than zero and the value zero if the residual is not smaller than zero expresses fat tail distributions, excess kurtosis and leverage effects information about the volatility during the previous period assumes that the sum of persistent parameters is going to be one captures the asymmetric effect of the news; long run conditional variance GARCH IGARCH EGARCH GJR-GARCH APARCH

31 VaR = σ t+1 q(p) Where: σ t+1 standard deviation q(p) quantile of a particular probability distribution GARCH IGARCH EGARCH GJR-GARCH APARCH

32 To evaluate the methods to determine which can produce the best VaR estimates through certain backtesting procedures

33 Kupiec s Proportion of Failure Test Christoffersen s Independence Test Christoffersen s Interval Forecast Test

34 p = p = x T Number of violations Failure rate Number of observations This measures if the number of violations corresponds to the confidence level. Proportion of Failure Test Independence Test Interval Forecast Test

35 LR POF = 2ln 1 p T x p x + 2ln 1 x T T x x T x p = (1 c) Expected failure rate Under the null hypothesis, the POF statistic given by equation follows a 2 distribution with one degree of freedom. Proportion of Failure Test Independence Test Interval Forecast Test

36 0 if VaR is not breached Indicator I t = ቊ 1 otherwise Possible Outcomes: 00, 01, 10, 11 T i,j (i = 0, 1; j = 0, 1) Proportion of Failure Test Independence Test Interval Forecast Test

37 π 0 = I t 1 = 0 I t 1 = 1 I t = 0 T 00 T 10 T 00 + T 10 I t = 1 T 01 T 11 T 01 + T 11 T 00 + T 01 T 10 + T 11 Deviation Indicator Outcomes T 01 T 00 + T 01, π 1 = T 11 T 10 + T 11, π = T 01 + T 11 T 00 + T 01 + T 10 + T 11 LR Ind = 2ln 1 π (T 00 +T 10 ൯π T 01+T ln 1 π T 00 0 π T π T 10 1 π T 11 1 Proportion of Failure Test Independence Test Interval Forecast Test

38 LR CC = LR POF + LR Ind 2 distribution with 2-degrees of freedom Proportion of Failure Test Independence Test Interval Forecast Test

39 Source: Author

40 RESULTS & DISCUSSIONS

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42 Classical Methods

43 Daily Returns (in percentage) 1 Jul 08 1 Jul 09 1 Jul 10 1 Jul 11 1 Jul 12 1 Jul 13 1 Jul 14 1 Jul 15 VaR Estimates Period: July December Return HS VaR (99%) HS VaR (95%) VCV VaR (99%) VCV VaR (95%) MS VaR (99%) MS VaR (95%) Source: Author s estimates

44 Daily Returns (in percentage) VaR Estimates Period: January December Jan 12 3 Mar 3 May 3 Jul Sep 12 3 Nov 12 3 Jan 13 3 Mar 3 May 3 Jul Sep 13 3 Nov 13 3 Jan 14 3 Mar 3 May 3 Jul Sep 14 3 Nov 14 3 Jan 15 3 Mar 3 May 3 Jul Sep 15 3 Nov Return HS VaR (99%) HS VaR (95%) VCV VaR (99%) VCV VaR (95%) MS VaR (99%) MS VaR (95%) Source: Author s estimates

45 GARCH-based Methods

46 Estimation Period: January June 2008 GARCH-type GARCH (1,1)-N 0.00*** 0.51*** 0.68*** - GARCH (1,1)-T 0.00*** 0.26*** 0.82*** - IGARCH-N *** 1.00*** - IGARCH-T *** 1.00*** - EGARCH-N -1.94*** 0.86*** 0.88*** -0.12*** EGARCH-T -0.46*** 0.28*** 0.97*** 0.01 GJR-GARCH-N 0.00*** 0.36*** 0.68*** 0.25*** GJR-GARCH-T 0.00** 0.25*** 0.81*** 0.02 APARCH-N *** 0.67*** 0.12 APARCH-T *** 0.84*** 0.04 Source: Author s estimates Note: *- significant at 10% level ** - significant at 5% level *** - significant at 1% level

47 Daily Returns (in percentage) Rolling Forecast Period: July 2008 December Jul 1 Sep 08 1 Nov 08 1 Jan 08 1 Mar 09 1 May 09 1 Jul 09 1 Sep 09 1 Nov 09 1 Jan 09 1 Mar 101 May 10 1 Jul 101 Sep 10 1 Nov 10 1 Jan 101 Mar 111 May 111 Jul 111 Sep 111 Nov 111 Jan 111 Mar 121 May 12 1 Jul 121 Sep 12 1 Nov 12 1 Jan 121 Mar 131 May 13 1 Jul 131 Sep 13 1 Nov 13 1 Jan 131 Mar 141 May 14 1 Jul 141 Sep 14 1 Nov 14 1 Jan 141 Mar 151 May 15 1 Jul 151 Sep 15 1 Nov % possible loss using EGARCH-N (99%) -0.9 Return GARCHNVAR95 GARCHNVAR99 GARCHTVAR95 GARCHTVAR99 IGARCHTVAR95 IGARCHTVAR99 EGARCHNVAR95 EGARCHNVAR99 EGARCHTVAR95 EGARCHTVAR99 GJRGARCHNVAR95 GJRGARCHNVAR99 GJRGARCHTVAR95 GJRGARCHTVAR99 APARCHNVAR95 APARCHNVAR99 APARCHTVAR95 APARCHTVAR99 Source: Author s estimates

48 Daily Returns (in percentage) Rolling Forecast Period: July 2008 December Jul 1 Sep 08 1 Nov 08 1 Jan 08 1 Mar 09 1 May 09 1 Jul 09 1 Sep 09 1 Nov 09 1 Jan 09 1 Mar 101 May 10 1 Jul 101 Sep 10 1 Nov 10 1 Jan 101 Mar 111 May 111 Jul 111 Sep 111 Nov 111 Jan 111 Mar 12 1 May 12 1 Jul 121 Sep 12 1 Nov 12 1 Jan 121 Mar 131 May 13 1 Jul 131 Sep 13 1 Nov 13 1 Jan 131 Mar 141 May 14 1 Jul 141 Sep 14 1 Nov 14 1 Jan 141 Mar 151 May 15 1 Jul 151 Sep 15 1 Nov Return GARCHNVAR95 GARCHNVAR99 GARCHTVAR95 GARCHTVAR99 IGARCHTVAR95 IGARCHTVAR99 EGARCHNVAR95 EGARCHNVAR99 EGARCHTVAR95 EGARCHTVAR99 GJRGARCHNVAR95 GJRGARCHNVAR99 GJRGARCHTVAR95 GJRGARCHTVAR99 APARCHNVAR95 APARCHNVAR99 APARCHTVAR95 APARCHTVAR99 Source: Author s estimates

49 Estimation Period: January 2006 December 2011 GARCH-type GARCH (1,1)-N 0.00*** 0.33*** 0.71*** NA GARCH (1,1)-T 0.00** 0.32** 0.76** NA IGARCH-N *** 1.00*** NA IGARCH-T *** NA EGARCH-N -1.24*** 0.56*** 0.92*** 0 EGARCH-T -0.84*** 0.43*** 0.95*** -0.07* GJR-GARCH-N 0.00*** 0.33*** 0.71*** 0.02 GJR-GARCH-T 0.00** 0.20** 0.78*** 0.15** APARCH-N *** 0.71*** 0.01*** APARCH-T *** 0.74*** 0.15 Source: Author s estimates Note: *- significant at 10% level ** - significant at 5% level *** - significant at 1% level

50 Daily Returns (in percentage) Rolling Forecast Period: January 2012 December E Jan 12 2 Mar2 May 2 Jul Sep 12 2 Nov 12 2 Jan 13 2 Mar2 May 2 Jul Sep 13 2 Nov 13 2 Jan 14 2 Mar2 May 2 Jul Sep 14 2 Nov 14 2 Jan 15 2 Mar2 May 2 Jul Sep 15 2 Nov % possible loss using EGARCH-N (99%) Return GARCHNVAR95 GARCHNVAR99 GARCHTVAR95 GARCHTVAR99 IGARCHTVAR95 IGARCHTVAR99 EGARCHNVAR95 EGARCHNVAR99 EGARCHTVAR95 EGARCHTVAR99 GJRGARCHNVAR95 GJRGARCHNVAR99 GJRGARCHTVAR95 GJRGARCHTVAR99 APARCHNVAR95 APARCHNVAR99 APARCHTVAR95 APARCHTVAR99 Source: Author s estimates

51 Daily Returns Rolling Forecast Period: January 2012 December Jan 12 2 Mar 2 May Jul 12 2 Sep 12 2 Nov 12 2 Jan 13 2 Mar 2 May Jul 13 2 Sep 13 2 Nov 13 2 Jan 14 2 Mar 2 May Jul 14 2 Sep 14 2 Nov 14 2 Jan 15 2 Mar 2 May Jul 15 2 Sep 15 2 Nov Return GARCHNVAR95 GARCHNVAR99 GARCHTVAR95 GARCHTVAR99 IGARCHTVAR95 IGARCHTVAR99 EGARCHNVAR95 EGARCHNVAR99 EGARCHTVAR95 EGARCHTVAR99 GJRGARCHNVAR95 GJRGARCHNVAR99 GJRGARCHTVAR95 GJRGARCHTVAR99 APARCHNVAR95 APARCHNVAR99 APARCHTVAR95 APARCHTVAR99 Source: Author s estimates

52 Historical Simulation Variance-Covariance Method Monte Carlo Simulation GARCH (1,1)-N GARCH (1,1)-T IGARCH-T EGARCH-N EGARCH-T GJR-GARCH-N GJR-GARCH-T APARCH-N APARCH-T Source: Author s estimates No. of violations Jul 2008 to Dec 2015 Jan 2012 to Dec % 99% 95% 99%

53 Historical Simulation Variance-Covariance Method Monte Carlo Simulation GARCH (1,1)-N GARCH (1,1)-T IGARCH-T EGARCH-N EGARCH-T GJR-GARCH-N GJR-GARCH-T APARCH-N APARCH-T Source: Author s estimates No. of violations (in %) Jul 2008 to Dec2015 Jan 2012 to Dec % 99% 95% 99%

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55 Period: July 2008 to December 2015 Method Historical Simulation Variance- Covariance Method Monte Carlo Simulation Confidence Level Proportion of Failure Test Risk for 1977 observations Independence Test Interval Forecast Test Test Result Source: Author s estimates

56 Period: July 2008 to December 2015 Method Confidence Level Proportion of Failure Test Risk for 1977 observations Independence Test Interval Forecast Test Test Result GARCH (1,1)-N GARCH (1,1)-T IGARCH-T EGARCH-N EGARCH-T GJR-GARCH-N GJR-GARCH-T APARCH-N APARCH-T Source: Author s estimates

57 Period: January 2012 to December 2015 Method Historical Simulation Variance- Covariance Method Monte Carlo Simulation Confidence Level Proportion of Failure Test Risk for 1055 observations Independence Test Interval Forecast Test Test Result Source: Author s estimates

58 Period: January 2012 to December 2015 Method Confidence Level Proportion of Failure Test Risk for 1055 observations Independence Test Interval Forecast Test Test Result GARCH (1,1)-N GARCH (1,1)-T IGARCH-T EGARCH-N EGARCH-T GJR-GARCH-N GJR-GARCH-T APARCH-N APARCH-T Source: Author s estimates

59 Method Jul 2008 to Dec 2015 Jan 2012 to Dec % 99% 95% 99% Historical Simulation Variance-Covariance Method Monte Carlo Simulation GARCH (1,1)-N GARCH (1,1)-T IGARCH-T EGARCH-N EGARCH-T GJR-GARCH-N GJR-GARCH-T APARCH-N APARCH-T

60 CONCLUSIONS & RECOMMENDATIONS

61 Do GARCH-based models better estimate VaR of the Philippine Bonds than the usual approaches? YES

62 GARCH-based models outperform the classical models in estimating the VaR estimates for the Philippine Bond Market Index Returns Estimation window (January 2006 to June 2008): GARCH (1,1) and GJR-GARCH with normal distribution Estimation window (January 2006 to December 2011): EGARCH with normal distribution In measuring VaR, the length of the data set affects the accuracy of the VaR figures. Inclusion of the effects of the Global Financial Crisis provided an edge to the asymmetric GARCH models to become the better VaR methods

63 Christoffersen s Interval Forecast Test is the most significant backtesting procedures used. Captures both the unconditional coverage and independence properties of the VaR estimates. Despite being not fully developed, the Philippine Bond Market possesses the characteristics of a usual financial market specifically in terms of the returns. Proves the usefulness and validity of the GARCH models in analyzing the market especially the returns of the assets

64 FUTURE STUDIES Utilization of other local and foreign asset indices Comparative study on VaR performance of ASEAN financial markets Exploring on the other types of VaR (e.g. Component VaR and Conditional VaR) Adding other GARCH models Working on mean-var efficient frontier

65 INVESTORS Similar research studies using company-specific data POLICYMAKERS Calculation of local bond index

66 Thank You!

67 GARCH vs. Traditional Methods of Estimating Value-at-Risk (VaR) of the Philippine Bond Market