Model Selection for Estimating Portfolio VAR in Korean Stock Market

Abstract

Value-at-Risk (VaR) is the most popular methodology in risk management because it is easy to communicate and easy to comprehend. The importance of VaR is rapidly increasing because the international agreement in banking industry, the Basel Accord, uses VaR methodology extensively.

However, Bedder (1995) and Hendricks (1996) warned of limitations of the VaR approach in risk management; the VaR methodology requires distributional assumptions for the relevant risk factors. Moreover, the VaR estimate depends on not only the assets class constituting portfolio, but also the model used to estimate the volatility of those assets. In this regard, it is valuable to investigate which volatility model produces superior risk measurement for a given portfolio.

In this study we sought to determine the best among various models in estimating 99% VaR and 99.5% VaR for the long and short position of a portfolio in the Korean stock market. Models were evaluated in terms of both accurate probabilities of extreme events and independent occurrence of exceptions. We used the conditional coverage test proposed by Christofferson (1998) to test those properties jointly.

We compared five univariate models and three multivariate models using the hypothetical portfolio consisting of twenty stocks whose market value ranks in the top 20th in the Korean stock market; the five univariate models are the Simple Moving Average (SMA) model, the Exponentially Weighted Moving Average (EWMA) model, the Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) model with a normal distribution, the GARCH model with a t-distribution, and the Historical Simulation (HS) model. The three multivariate GARCH models are the Constant Conditional Correlation (CCC) model, the Dynamic Conditional Correlation (DCC) model, and the Orthogonal GARCH (O-GARCH) model.

We can summarize our analysis of empirical results as follows. First, we found the overall performances of multivariate models were better than those of univariate models in evaluating VaR for the our hypothetical portfolio. Second, the performance of the DCC model was better than that of the other multivariate models such as the CCC model and the O-GARCH model. However, the CCC model as well as the DCC model passed conditional coverage tests for many cases Third, the SMA model and the HS model which are the most commonly used models in Korean financial institutes failed to pass the tests, which means those models are relatively less appropriate in evaluate VaR for a portfolio similar to our portfolio with respect to the conditional coverage perspective. This might be caused by the fact that those models failed to efficiently incorporate new information into the VaR evaluation.

This paper is organized as follows: we will review the VaR concepts, which will be followed by a review of the various methods to evaluate VaR. After that, we will move to the back-testing procedure for the model selection criteria. The empirical result of the models will be presented and discussed. Then, we will draw some conclusions and implications.

This paper is different from existing studies in two areas: the number of assets in the portfolio and models compared. Most past research used a portfolio consisting of two, three, or at most, five stocks. But, in this paper we use a hypothetical portfolio consisting of 20 stocks to test the performances of the multivariate models. One other point is little study has been done comparing the multivariate VaR estimation methods with the univariate VaR estimate methods in the VaR literature; especially little study has been done using the DCC model and the CCC model. So, the most distinctive point of this paper is that comparison. This will allow us to determine the value of conditional correlation estimation in this VaR application.

Keywords: VaR, DCC, CCC, Conditional coverage test

JEL Classification: C52, G32