Value-at-Risk of Brazilian ETFs with Extreme Value Theory Approach

Yuri Sampaio Maluf; Otávio Ribeiro Medeiros

doi:10.7444/180

Value-at-Risk of Brazilian ETFs with Extreme Value Theory Approach

Yuri Sampaio Maluf, Otávio Ribeiro Medeiros

Resumo

OBJECTIVE
Investigate how investors in Brazil are exposed to risks via Exchanged Traded Funds (ETF) compared with their respective indexes.

METHODOLOGY
It compares the risks of Bovespa Index ETF and the Bovespa index from May09 to jul13. The level of risk was calculated with the VAR (Value at Risk) and ES (Expected shortfalls) methods, using the bootstrap technique. The characteristics of heteroskedasticity and fat tails that are typical in financial time series were incorporated, having a good fit with the generalized Pareto distribution.

RESULTS AND CONCLUSIONS
The data indicate that the indirect investment in the market portfolio with ETFof Bovespa is more risky to the agents than the direct investment of assets comprising the portfolio of the Bovespa index.

PRACTICAL IMPLICATIONS
The greatest risk of ETF relative to the Bovespa index itself represents a cost to the fund in relation to direct investment in stocks that comprise the index. This cost associated with additional risk should be added to the administration fee charged by managers and administrators of ETF.

KEYWORDS
ETF, Value-at-Risk, Extreme Value Theory.

OBJETIVO
Investigar como os investidores no Brasil estão expostos aos riscos através dos Exchanged Traded Funds (ETF) compa-rado com seus respectivos índices.

METODOLOGIA
Foram comparados os riscos do ETF de Ibovespa e do pró-prio Ibovespa, de mai09 a jul13. O nível de risco foi calculado com os métodos VAR (Value at Risk) e ES (Expected Shortfalls), empregando a técnica de bootstrap. Foram incorporadas as características de heterocedasticidade e de caudas pesadas típicas em séries financeiras, tendo um bom ajustamento com a distribuição de Pareto generalizada.

RESULTADOS E CONCLUSÕES
Os dados apontam que o investimento indireto na carteira de mercado com o ETF do Ibovespa oferece mais risco aos agentes do que o investimento direto dos ativos que compõe a carteira do índice Ibovespa.

IMPLICAÇÕES PRÁTICAS
O maior risco do ETF de Ibovespa em relação ao próprio ín-dice representa um custo do fundo em relação ao investimento direto nas ações que compõem o índice. Esse custo associado ao risco adicional deve ser adicionado à taxa de administração cobrada pelos gestores e administradores do ETF.

PALAVRAS-CHAVE
ETF, Valor em Risco, Teoria Valores Extremos.

Referências

ANBIMA. (2011). Fundo de investimento: Relatório de taxas de administração. São Paulo: Associação Brasileira das En-tidades dos Mercados Financeiros e de Capitais.

ARTZNER, P.; DELBAEN, F.; EBER, J. M.; HEATH, D.; Co-herent measure of risk. Mathematical Finance, v. 9 , p. 203-228, 1999.

BASLECOMMITEE. Overview of the amendment to the capi-tal accord to incorporate market risks. Bank of International Settlements. 1996.

BORGES, E. C.; EID JR, W.; YOSHINAGA, C. E. Exchange traded funds versus fundos indexados no brasil. Revista de Finanças Aplicadas, v.1, p. 1 – 15, 2012.

CHERRY, J. The limits of arbitrage: Evidence from exchange traded funds. Working Paper, University of California-Berkeley, 2004.

CHIANG, W. Indexing for maximum investment results. Working Paper. Chicago, Ilinois, USA, 1998.

CHOUDHRY, M. An introduction to value at risk. John Wiley, 2006.

CONT, R. Empirical properties of asset returns: stylized facts and statistical issues. Quantitative Finance, v.1, p.223-236, 2001.

DIMITRAKOPOULOS, D. N.; KAVUSSANOS, M. G.; SPYROU, S. I. Value at risk models for volatile emerging markets equity portfolios. The Quarterly Review of Econom-ics and Finance, v.50, p. 515-526, 2010.

DOLVIN, S. D. Etfs: Arbitrage opportunities and market forecasting. Journal of Index Investing, v.1, p.107-116, 2009.

DOWD, K. A value at risk approach to risk-return analysis. The Journal of Portfolio Management, v.25, p.60-67, 1999.

EFRON, B.; TIBSHIRANI, R. J. An introduction to the boot-strap. CHAPMAN HALL/CRC, 1993.

ELTON, E.; GRUBER, M.; COMER, G. L. K. Spiders: Where are the bugs? journal of Business, v.75, p.453-472, 2002.

ENGLE, R. F.; SARKAR, D. Pricing exchange traded funds. Working Paper, New York University, 2002.

Fry, D. H. ETFs hedge funds. Wiley Finance, 2008.

GALLAGHER, D. R.; SEGARA, R. The performance and trading characteristics of exchange-traded funds. Working Paper, The University of New South Wales, 2004.

GASTINEAU, G. L. An introduction to exchange-traded funds (etfs). Journal of Portfolio Management and Economics, v.27, p.88-96, 2001.

GENCAY, R.; SELCUK, F. Extreme value theory and value-at-risk relative performance in emering markets. Interna-tional Journal of Forecasting, v.20, p. 287-303, 2004.

GUEDJ, I.; HUANG, J. Are etfs replacing index mutual funds? Working paper, University of Texas, 2009.

HALL, P.; HOROWITZ, J. L.; JING, B. On blocking rules for bootstrap with dependent data. Biometrika, v.82, p.561-574, 1995.

HO, L. C.; BURRIDGE, P.; CADLE, J.; THEOBALD, M. Val-ue-at-risk: Applying the extreme value approach to Asian markets in the recent financial turmoil. Pacific-Basin Fi-nance Journal, v.8, p.249-275, 2000.

HUANG, M. Y.; LIN, J. B. Do etfs provide effective interna-tional diversification? Research in International Business and Finance, v.25, p.335-344, 2011.

JARES, T. E.; LAVIN, A. M. Japan and hong-kong exchange traded fund etfs: Discounts, return and trading strategies. Journal of Financial Services Research, v.25, p.57-69,2004.

JONDEAU, E.; POON, S.; ROCKINGER, M. Financial model-ing under non-gaussian distribution. Springer, 2007.

JORION, P. Risk: Measuring the risk in value at risk. Finan-cial Analysts Journal, v.52, p.47-56, 1996.

LIN, C.; CHAN, S.; HSU, H. Pricing efficiency of exchange traded funds in Taiwan. Journal of Asset Management, v.7, p.60-68, 2005.

MALKIEL, B. The valuation of closed-end investment com-pany shares. Journal of Finance, v. 32, p.847-859, 1977.

MALUF, Y. S.; ALBUQUERQUE, P. H. M. Empirical evi-dence: Arbitrage with exchange-traded funds (etfs) on the brazilian market. Revista de Contabilidade e Finanças, v.24, p.64 – 74, 2013.

MARSHALL, B. R.; NGUYEN, N. H.; VISALTANACHOTI, N. Etf arbitrage. Working Paper, University of Auckland, New Zeland, 2010.

MCNEIL, A. J.; FREY, R. Estimation of tail-related risk measures for heteroscedastic financial time series: an ex-treme value approach. Journal of Empirical Finance, v.7, p.271-300, 2000.

PICKANDS, J. Statistical inference using extreme order sta-tistics. Annals of Statistics, v.3, p.119-131, 1975.

POON, S. H.; GRANGER, C. W. J. Forecasting volatility in financial markets: A review. Journal of Economic Literature, v.41, p.478-539, 2003.

ROMPOTIS, G. An empirical comparing investigation on ex-change traded funds and index fund performance. Working Paper, University of Athens Greece, 2005.

ROMPOTIS, G. An empirical look on exchange traded funds. Working Paper, University of Athens Greece, 2007.

SHIN, S.; SOYDEMIR, G. Exchange-traded funds, persis-tence in tracking errors and information dissemination. Journal of Multinational Financial Management, v.20, p.214 – 234, 2010.

SIMON, D. P.; STERNBERG, J. S. Overreaction and trading strategies in European ishare. Journal of Alternative Invest-ment, v.8, p.29-41, 2005.

SIRR, G.; GARVEY, J.; GALLAGHER, L. Emerging markets and portfolio foreign exchange risk: An empirical investiga-tion using a value-at-risk decomposition technique. Journal of International Money and Finance, v.30, p.1749- 1772, 2011.

SMITH, R. L. Estimating tails of probability distributions. Annals of Statistics, v.15, p.1174-1207, 1987.

WANG, C. C.; LIAU, Y. S.; YANG, J. J. W. Information spill-over in the spot and etf indices in Taiwan. Global Journal of Business Research, v.3, p.117-131, 2009.

WILD, R. Exchange-traded funds for dummies. Indianapolis, Indiana: Wiley Publishing, 2007.

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