The impact of liquidity on portfolio value-at-risk forecasts

ABSTRACT

Historical crisis events have highlighted the insufficiency of Value-at-Risk (VaR) as a measure of market risk because such metric does not take liquidity into account. Unlike previous studies analyzing with only a single asset, we examine the impact of liquidity on computing VaR forecasts from a portfolio level. To this end, we use multivariate GARCH-t and GJR-GARCH-t models, as compared with univariate models, to seize the liquidity property embedded in individual stock returns and evaluate their accuracy and efficiency in computing VaR forecasts for portfolios with different liquidity levels.

The empirical results indicate that computing portfolio VaR forecasts with multivariate models outperform the univariate models for full and subsample periods in terms of accuracy and efficiency evaluations, in particular for less-liquid portfolios. These results suggest the importance of liquidity in computing portfolio VaR forecasts. Ignorance of the impact of liquidity in computing portfolio VaR forecasts might result in inadequate coverage and insufficient market risk capital requirements.

KEYWORDS:

• Value-at-risk
• illiquidity
• multivariate GARCH-t and GJR-GARCH-t models
• accuracy and efficiency

JEL CLASSIFICATION:

• C32
• C52
• C53

Acknowledgments

Professor Hung acknowledges the financial support from the Ministry of Science and Technology of Taiwan, R.O.C. (MOST 105-2410-H-034-002).

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ Weiß and Supper (2013) constructed an equally-weighted portfolio with five individual stocks listed in NASDAQ 100 index and compute the liquidity-adjusted VaR forecasts. The NASDAQ 100 index includes 100 of the largest non-financial companies listed on NASDAQ.

² Previous studies used bid-ask (quoted) or effective spread based on microstructure or high-frequency transaction data to measure market liquidity. Although this kind of measure is much ideal and widely used in financial literature, it has drawbacks that microstructure data for all individual stocks might not be readily available and cover long research period as well. Thus, this study uses the illiquidity measure of Amihud (2002) based on daily frequency data to measure market liquidity.

³ In the green zone, the multiplier value is 3 when the exceptions are between 0 and 4; in the yellow zone, the multiplier values for 5 through 9 exceptions are 3.4, 3.5, 3.65,3.75 and 3.85, respectively; in the red zone, the multiplier value is 4 as exceptions are above 10.

⁴ There are totally 150 component stocks listed in Taiwan top 50 and mid-cap 100 indices, but only 103 component stocks subsist and are available during our research period. We rank the remaining 103 individual stocks by their market capitalizations and choose the top 100 stocks as the research sample.

⁵ The window size used for estimation of VaR models contains 1238 observations. This study also uses 500 observations as the window size, and the results are similar with the window size of 1238 observations.

⁶ The aggregate illiquidity is computed by equally weighted Amihud illiquidity measure of each individual stocks for every portfolio decile.

⁷ The mean and skewness are respectively regressed on the aggregate illiquidity without controlling other effects for full sample period and two sub-sample periods. The regression results are omitted in this study, and they are available upon request.

⁸ To reduce possible estimation uncertainty that might compromise the predictive ability of multivariate model as the dimension of the portfolio increases, we use a two-stage maximum likelihood method (Engle 2002) to estimate the parameters for multivariate models.

⁹ Consistent with the quantitative standards prescribed by the Basel Committee the 99% confidence level is used for VaR computation. Thus, this study only computes portfolio VaR forecasts with 99% confidence level and one-day horizon.

¹⁰ Chen and Tu (2013) argued that the unconditional and conditional coverage tests developed by Kupiec (1995) and Christoffersen (1998) may not provide robust results because these two statistical tests are based on the frequency of violations, the small number of violations may induce biased conclusion.

¹¹ To examine the relation between market capitalization and the percentage number of violations, Dias (2013) regressed the percentage number of VaR violations on the market capitalization of portfolios, which takes values from 1 to 10 corresponding to the first and the tenth deciles. This study argues that the liquidity of portfolio is not proportionately increasing from the first to the tenth deciles as indicated by the aggregate illiquidity in Table 1. Thus, this study regresses the actual failure rate on aggregate illiquidity of portfolio to analyze the relation between the actual failure rate and illiquidity of portfolio. The regression results are omitted in this study, and they are available upon request.

¹² Previous studies used efficiency evaluation for VaR model selection can referred to Sarma, Thomas, and Shah (2003), Hung, Lee, and Liu (2008), Su and Hung (2011), Su (2014) and Su, Lee, and Chiu (2014).

¹³ To save space, we only provide the graphs for the most-liquid and the least-liquid portfolios as a comparison, and the others are available upon request.

¹⁴ We generate m = 10,000 simulated returns in this study.

Additional information

Funding

This work was supported by the Ministry of Science and Technology of Taiwan[MOST 105-2410-H-034-002].