Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
권호 표지
DOI QR코드

DOI QR Code

Properties of alternative VaR for multivariate normal distributions

다변량 정규분포에서 대안적인 VaR의 특성

  • Hong, Chong Sun (Department of Statistics, Sungkyunkwan University) ;
  • Lee, Gi Pum (Department of Statistics, Sungkyunkwan University)
  • Received : 2016.09.19
  • Accepted : 2016.11.02
  • Published : 2016.11.30
Download PDF
⟨ Previous Next ⟩

Abstract

The most useful financial risk measure may be VaR (Value at Risk) which estimates the maximum loss amount statistically. The VaR tends to be estimated in many industries by using transformed univariate risk including variance-covariance matrix and a specific portfolio. Hong et al. (2016) are defined the Vector at Risk based on the multivariate quantile vector. When a specific portfolio is given, one point among Vector at Risk is founded as the best VaR which is called as an alternative VaR (AVaR). In this work, AVaRs have been investigated for multivariate normal distributions with many kinds of variance-covariance matrix and various portfolio weight vectors, and compared with VaRs. It has been found that the AVaR has smaller values than VaR. Some properties of AVaR are derived and discussed with these characteristics.

가장 선호하는 금융위험 측정 방법은 통계적으로 최대손실금액을 추정하는 VaR (Value at Risk)이다. 포트폴리오를 구성하는 여러 산업에 대한 VaR (Value at Risk)는 분산공분산 행렬과 특정한 포트폴리오가 포함되어 변환된 일변량 위험을 이용하여 추정한다. Hong 등 (2016)은 다변량 분위벡터를 바탕으로 Vector at Risk를 정의하였으며, 특정한 포트폴리오가 설정되면 Vector at Risk 중의 한 점을 최적의 VaR 즉, 대안적인 VaR (AVaR)로 제안하였다. 본 연구에서는 다변량 정규분포에 대하여 AVaR의 특성을 탐색한다. 여러 종류의 분산공분산 행렬과 다양한 포트폴리오 가중값 벡터인 경우의 이변량과 삼변량의 정규분포를 따르는 모의실험 자료와 실증예제를 이용하여 대안적인 최대손실금액인 AVaR을 구하고 VaR과 비교 분석한다. 다변량 분위벡터를 이용한 AVaR는 VaR보다 작게 추정함을 발견하였으며, 이런 특징과 함께 AVaR의 특성을 토론한다.

Keywords

References

  1. Andersson, F., Mausser, H., Rosen, D. and Uryasev, S. (2001). Credit risk optimization with condition value-at-risk. Mathatical Programming B, 273-291.
  2. Barone-Adesi, G., Giannopoulos, K. and Vosper, L. (1999). VaR without correlations for portfolios of derivative securities. Journal of Futures Markets, 19, 583-602. https://doi.org/10.1002/(SICI)1096-9934(199908)19:5<583::AID-FUT5>3.0.CO;2-S
  3. Berkowitz, J., Christoffersen, P. and Pelletier, D. (2011). Evaluating Value-at-Risk models with desk-level data, Managent Science, 57, 2213-2227. https://doi.org/10.1287/mnsc.1080.0964
  4. Heo, S. J., Yeo, S. C. and Kang, T. H. (2012). Performance analysis of economic VaR estimation using risk neutral probability distributions. Korean Journal of Applied Statistics, 25, 757-773. https://doi.org/10.5351/KJAS.2012.25.5.757
  5. Hong, C. S., Han, S. J. and Lee, G. P. (2016). Vector at risk and alternative value at risk. The Korean Journal of Applied Statistics, 29, 689-697. https://doi.org/10.5351/KJAS.2016.29.4.689
  6. Hong, C. S. and Kwon, T. W. (2010). Distribution fitting for the rate of return and value at risk. Journal of the Korean Data & Information Science Society, 21, 219-229.
  7. Jorion, P. (2007). Value at risk: The new benchmark for market risk, 1st Ed., McGraw-Hill, New York.
  8. Ko, K. Y. and Son, Y. S. (2015). Optimal portfolio and var of kospi200 using one-factor model. Journal of the Korean Data & Information Science Society, 26, 323-334. https://doi.org/10.7465/jkdi.2015.26.2.323
  9. Krokhmal, P., Palmquist, J. and Uryasev, S. (2002). Portfolio optimization with conditional Value-at-Risk objective and constraints. Journal of Risk, 4, 11-27.
  10. Kupiec, Paul H. (1995). Techniques for verifying the accuracy of risk measurement models. The Journal of Derivatives, 3, 73-84. https://doi.org/10.3905/jod.1995.407942
  11. Longin, F. M. (2000). From value at risk to stress testing: The extre value approach. Journal of Banking & Finance, 24, 1097-1130. https://doi.org/10.1016/S0378-4266(99)00077-1
  12. Longin, F. M. (2001). Beyond the VaR. Journal of Derivatives, 8, 36-48. https://doi.org/10.3905/jod.2001.319161
  13. Lopez, J. A. (1998). Methods for evaluating value-at-risk estimates. Economic Policy Review, 4, 119-124.
  14. Morgan, J. P. (1996). Riskmetrics technical document, Morgan Guaranty Trust Company, New York.
  15. Park, S. R. and Baek, C. R. (2014). On multivariate garch model selection based on risk management. Journal of the Korean Data & Information Science Society, 25, 1333-1343. https://doi.org/10.7465/jkdi.2014.25.6.1333
  16. Rockafellar, R. T. and Uryasev, S. (2000). Optimization of conditional value-at-risk. Journal of Risk, 2, 21-41. https://doi.org/10.21314/JOR.2000.038
  17. Yeo, S. C. and Li, Z. (2015). Performance analysis of volatility models for estimating portfolio value at risk. Korean Journal of Applied Statistics, 28, 541-599. https://doi.org/10.5351/KJAS.2015.28.3.541
  18. Hwang, S. Y. and Park, J. (2005). VaR (value at risk) for Korean financial time Series. Journal of the Korean Data & Information Science Society, 16, 283-288.

Cited by

  1. 다변량 경험분포함수와 시각적인 표현방법 vol.28, pp.1, 2017, https://doi.org/10.7465/jkdi.2017.28.1.87
  2. 이변량 왜도, 첨도 그리고 표면그림 vol.28, pp.5, 2016, https://doi.org/10.7465/jkdi.2017.28.5.959