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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

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

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