UK stock market predictability: evidence of time variation

Abstract

This article examines the nature of time variation within the stock return predictive regression for the United Kingdom. We consider six predictor variables but find significant in-sample evidence of predictive power for only three: the bond–equity yield ratio, the dividend yield and the price–earnings ratio, and out-of-sample evidence for the latter two. Notwithstanding this, we are able to identify substantial evidence of time variation within predictive power for all variables. However, such time variation is only linked to the state of the macroeconomy for the same three variables. Nonetheless, we are able to identify macroeconomic regimes where predictability for each of these three variables is stronger. Specifically, predictive power is stronger for the bond–equity yield ratio when output is rising and stronger for the dividend yield and price–earnings ratio when output is falling. We can use this information to build an improved prediction model by allowing for the variables, including AR terms, to enter the model according to the state of the world. However, we are still unable to beat the market in an out-of-sample forecast exercise, except with the bond–equity yield and with a mix of this variable and an AR(1). Nonetheless, the results do point to the conclusion that stock market predictability is present for the United Kingdom and that it is time-varying, the knowledge of which can improve the forecast models.

Keywords:

• stock returns
• predictability
• time variation

JEL Classification:

• C22
• G12

Notes

1 The list of citations here is far from exhaustive but merely included to introduce the interested reader to the relevant literature.

2 The results for the short-term interest rate are qualitatively unchanged if we do not log the series. The results are available upon request, and we present the logged results for consistency with the remaining variables.

3 For obvious reasons, we do not include the dividend yield, price–earnings ratio and payout ratio in the same regression. For interest, in the reported results, we include the dividend yield and payout ratio, when we include the price–earnings ratio and payout ratio, the price–earnings ratio is significantly negative and the payout ratio significantly positive.

4 For a more detailed discussion of the forecasting metrics discussed in this section, see Rapach and Wohar (2006). Also, we drop the AR(1) term from Equation 1, so we can make a direct forecasting comparison between the predictor variable and constant expected returns. As noted, this term is not significant at the 5% level, and its exclusion does not alter the nature of the results.

5 While West (1996) shows that the Diebold and Mariano (1995) and West (1996) statistic has a standard normal limiting distribution when comparing forecasts from non-nested models, McCracken (2007) shows that it has a non-standard limiting distribution when comparing forecasts from nested models. Clark and McCracken (2005) demonstrate that the MSE-F statistic has a non-standard and non-pivotal limiting distribution in the case of nested models for forecasting horizons greater than one. In such cases, Clark and McCracken (2005) recommend basing inference on a bootstrap procedure along the lines of Kilian (1999) in the case of nested models.

6 See Clements and Hendry (1998) for a textbook discussion of forecast encompassing.

7 As pointed out by Clark and McCracken (2001), the Harvey et al. (1998) statistic has a standard normal limiting distribution when comparing forecasts from non-nested models according to the theory in West (1996). However, for nested models, Clark and McCracken (2001, 2005) show that it has a non-standard limiting distribution.

8 These are multiplied by 100 to improve presentation.

9 Again, these are multiplied by 100 to ease of presentation.

10 This is notwithstanding that in the threshold regression for the dividend yield, this coefficient is significant in both regimes. However, the coefficient magnitude suggests that the majority of information is carried in the negative regime. Nonetheless, results are largely equivalent across including or excluding this coefficient in the positive regime.

11 The key aim is to examine whether predictability is enhanced with the index acting as a point of comparison and note whether a trading profit can be made. Thus, we do not include transaction costs, which in any case are variable across market participants.