Short-term Dynamics in the Cyprus Stock Exchange

Abstract

This paper investigates the short-term dynamics of stock returns in an emerging stock market namely, the Cyprus Stock Exchange (CYSE). Stock returns are modelled as conditionally heteroscedastic processes with time-dependent serial correlation. The conditional variance follows an EGARCH process, while for the conditional mean three nonlinear specifications are tested, namely: (a) the LeBaron exponential autoregressive model; (b) the Sentana and Wadhwani positive feedback trading model; and finally (c) a model that nests both (a) and (b). There is an inverse relationship between volatility and autocorrelation consistent with the findings from several other stock markets, including the US. This pattern could be the manifestation of a certain form of noise trading namely positive feedback trading or, momentum trading strategies. There is little evidence that market declines are followed with higher volatility than market advances, the so-called ‘leverage effect’, that has been observed in almost all developed stock markets. In out of sample forecasts, the nonlinear specifications provide better results in terms of forecasting both first and second moments of the distribution of returns.

Keywords:

• Cyprus Stock Exchange
• positive feedback trading
• stock return dynamics
• EGARCH
• GED
• exponential autoregression
• forecasting

Notes

1. At the same time, this emerging market is not yet as liquid and efficient as other developed markets, with prices potentially influenced by feedback trading strategies, a ‘herd’ mentality or rumours.

2. All hypotheses testing in this paper is done at the 5% level for simplicity and uniformity.

3. A negative δ is consistent with the so-called ‘leverage hypothesis,’ whereby negative returns increase the debt/equity ratio. As a result, negative returns are followed by higher volatility than positive returns of an equal size (see also, Nelson, 1991).

4. If all investors had the same demand function given by (6), then in equilibrium , which is the dynamic Capital Asset Pricing Model proposed by Merton (1973).

5. If ρ<0 there would be negative feedback trading.

6. It should be noted that it is the interaction of risk-averse utility maximizers and positive-feedback traders that produces negative autocorrelation that rises in magnitude as volatility rises. Negative feedback trading would produce positive time-varying autocorrelation instead. However, if all investors followed positive-feedback trading strategies then returns would exhibit positive autocorrelation.

7. The density function of the GED is given by

where Γ (.) is the gamma function, and ν is a scale parameter capturing the degree of deviation from normality (fat tails or excess kurtosis) to be estimated endogenously. This parameter controls the shape of the distribution allowing the GED to nest several other densities. For example, if ν=2, f(·) yields the normal distribution, while for ν=1 it yields the Laplace or, double exponential distribution (see also, Nelson, 1991).

8. The sample log-likelihood can be expressed as follows: .

9. Several sets of initial values were used to ensure that the final estimates are robust to the choice of initial values.

10. This is obviously true for the evaluation of derivative securities, such as options and options on futures, where ex ante volatility measures are critical inputs.

11. The choice of the AR1 specification for the benchmark model is based on the need to have nested models so that meaningful statistical inferences can be applied. For example, with suitable parameter restrictions the three models used for the conditional mean can be reduced to the AR1 model. Likewise, the choice of the EWMA specification for the benchmark conditional variance was made due to the popularity and wide use of the model as well as it being nested within the GARCH(1,1). It should be noted that the results were almost identical when the GARCH(1,1) model was used.

12. The version of the Diebold-Mariano test used here is the sign test based on the residuals obtained from the null (i.e. benchmark) and the alternative models.