Estimating the VaR of a portfolio subject to price limits and nonsynchronous trading

Price limits and nonsynchronous trading are two main features in emerging markets. Price limits cause stock returns to be restricted within a prespecified range whereas infrequent trading induces spurious autocorrelation and biased estimate of the return variance. Both factors cause traditional measures of Value at Risk (VaR) to be biased. In this paper, we propose VaR measures based on a two-limit type Tobit model incorporating Scholes and Williams' [Scholes, M., & Williams, J. (1977). Estimating betas from nonsynchronous data, Journal of Financial Economics 5, 309-328] estimator that adjusts for price limits and nonsynchronous trading. Based on the simulation design of Brown and Warner [Brown, S., & Warner, J. (1985). Measuring security price performance, Journal of Financial Economics 8, 205-258], we compare the performance of our proposed methods with two traditional methods, one based on naive OLS estimates and the other based on historical simulation. Using daily data of all stocks listed on the Taiwan Stock Exchange and the OTC markets, the simulation results indicate that all methods perform reasonably well. The only exception is that the naive OLS yields a slightly higher failure rate when the portfolio under consideration is composed of only a few stocks. Thus, despite the potential problems induced by nonsynchronous trading and price limits, their practical impacts seem limited.