انتقال نوسانات بین سهام و اوراق قرضه

A two-factor no-arbitrage model is used to provide a theoretical link between stock and bond market volatility. While this model suggests that short-term interest rate volatility may, at least in part, drive both stock and bond market volatility, the empirical evidence suggests that past bond market volatility affects both markets and feeds back into short-term yield volatility. The empirical modelling goes on to examine the (time-varying) correlation structure between volatility in the stock and bond markets and finds that the sign of this correlation has reversed over the last 20 years. This has important implications far portfolio selection in financial markets.

The world-wide downturn in equity prices in October 1987 focussed academic and practitioner attention on to the international transmission of financial market volatility. It was clear at that time that shocks were being transmitted around the global trading system. Evidence of an international volatility contagion effect was documented by King and Wadhwani (1990), who found that the correlation between market movements in different countries and general levels of volatility were positively related. Understanding the nature of linkages between financial markets, whether intra- or international, is fundamental to establishing the limits of diversification, to security pricing, and to successful asset allocation. While there is a large literature examining the international transmission of equity market volatility, and a growing literature examining the international transmission of bond market volatility, there are relatively few intra-national studies, and then usually within one asset class. By contrast, this study aims to explore the intra-national transmission of volatility between short-term risk-free yields, long-term bond yields and equity returns in the UK. During the period immediately following the 1987 equity market crash, the flow of investment funds out of the equity market and into the gilt-edged market was substantial. The Stock Exchange (1988) reported that gilt-edged market average customer turnover reached a record £3114 million per day during November 1987, following the record average customer turnover of £1342 million ser day during October 1987 in the equity market. In fact, during the second quarter of 1987, gilt-edged market turnover had declined. It was not until 1993, that turnover in either of the markets reached the levels observed during 1987. Indeed, during the intervening period, total average daily turnover values in each of the markets have been around one half of the levels experienced in the immediate post-crash period, see Stock Exchange (1994). Over the period October 1 to November 30, 1987, prices in the equity market fell at an annualised rate of nearly 600%, while prices in the gilt-edged market rose at an annualised rate of nearly 40%. These observations and the Exchange's report on turnover activity suggested a clear link between the behaviour of the two markets at that time. The more recent Asian crisis in global financial markets during the late Nineties had a similar impact in the gilt-edged market; Steeley and Ahmad (2002) document the empirical effects of the gilt-edged market becoming a safe-haven for international capital during this period. While these are both “headline” market events, the long term nature of any relationships between the behaviour of prices and returns in the two markets over a longer time span has not received the same attention. In particular, there has been no systematic documentation of the relationship between return volatility in the two markets. It is the aim of this study to examine the nature of the dynamic relationships between equity and bond price movements both in theory and practice in the UK, with particular reference to the time series behaviour of the processes capturing the volatility in each of the two markets. A number of studies have examined the interdependence of equity market volatility, typically using the framework of generalised autoregressive conditional heteroscedasticity (GARCH) time series models, for example, Hamao et al. (1990) and Koutmos and Booth (1995). Hamao et al. (1990) discovered that shocks to the volatility of financial market returns in one country could influence both the conditional volatility and the conditional mean of the returns in another country, while Koutmos and Booth observed asymmetric volatility relations between the financial markets of the USA, the UK and Japan, where the influence of negative shocks was different in both scale and direction to positive shocks. This kind of volatility asymmetry has become known as the “leverage effect” (Black (1976) and Christie (1982)), since an increase in a firm's debt to equity ratio will lead to both an increase in the risk and required return on equity that, ceteris paribus, will reduce the value of equity. Studies by Bekaert and Wu (2000) and Brailsford and Faff (1993) are representative of the global nature of this empirical phenomenon. The GARCH modelling framework has also been applied to analysing volatility spillovers between equity portfolios for a single country, sorted by market capitalisation. Studies by Conrad et al. (1991) and Kroner and Ng (1998) for the US equity market, and Chelley-Steeley and Steeley (1996) for the UK equity market have found a further form of asymmetry in the transmission of volatility. While past shocks to the volatility of large firm portfolios appeared to influence the volatility of small firm portfolios, the reverse was not found to be the case. Alli et al. (1994) have applied the same technique to examine volatility spillovers between different sectors of the US oil industry. In parallel with this analysis, an increasing number of studies have examined changes in the correlation among worldwide equity markets. Both Longin and Solnik (1995) and Chelley-Steeley and Steeley (1999) document increases in correlations among European countries’ equity markets since the 1970s. Goetzmann et al. (2001) found that international equity correlations change dramatically through time, with peaks in the late 19th Century, the Great Depression, and the late 20th Century. By contrast to studies of global equity markets, analyses of the interdependence of international bond markets are relatively few in number. Ilmanen (1995) used a linear regression model to forecast the excess returns of long-term international bonds. The excess returns were found to be highly correlated indicating considerable integration among international bond markets. Clare and Lekkos (2000) used a VAR model to measure the interaction between US, UK and German bond markers, and found that transnational factors were more important during times of instability. Driessen et al. (2003) analyze the bond markets of US, Japan and Germany using a principal components analysis. Bond markets, however, have been the setting for some of the key developments in GARCH methods, such as the ARCH-M model (Engle et al., 1987) and the Factor-ARCH model (Engle et al., 1990), and ARCH methods were also used to examine the properties of certain theoretical models of the yield curve, (see Steeley, 1990 and Chan et al., 1992). The application of these methods to the study of bond market integration has, however, been more recent (see Laopodis, 2002 and Christiansen, 2004 and Skintzi and Refenes, 2005). While Laopodis (2002) and Christiansen (2004) assume constant correlation structures, Skintzi and Refenes (2005) model a time varying (parametric) correlation structure among bond market volatilities, using a model previously applied to foreign exchange by Darber and Deb (2002). In this study, I also use a GARCH modelling framework to examine the interdependence between stock, bond and interest rate volatility. The model will include volatility spillovers and asymmetries and a time-varying (non-parametric) correlation structure, similar to that used by Berben and Jansen (in press) to study international equity market integration. The remaining sections of the paper are as follows. Section 2 works through a no-arbitrage model what provides a natural link between the volatility of stocks, bonds and short-term interest rates. Section 3 describes the GARCH modelling framework that will be employed. In Section 4, summary statistics for the data are reported, along with an analysis of the estimated coefficients of the GARCH models. Section 5 contains the conclusions of the study.

In this study, a theoretical model was used to provide the basis for examining the links between the volatility of short-term yield, long-term bond yields and stock returns. The empirical analysis used a GARCH framework that permitted richer structures than could be analysed using the theoretical model. In particular, the impact of dynamic spillovers and time-varying correlations among the volatility processes could be examined. The time-varying correlations used a non-parametric smooth transition process that allowed the correlation between market shocks to evolve across the sample period. Using data for the UK stock and bond markets, it was found that the correlation between short-term yield shocks and long term bona yield shocks was relatively stable during the sample period, while the correlation between each of these markets and the equity market reversed sign. This clearly has important implications regarding the increased hedging potential of the bond market in recent years, as the correlations among market shocks are now strongly significantly negative. It also makes apparent the importance of permitting correlation structures to evolve within empirical specifications. While this paper has considered only one country, it could easily be applied to other countries, and across countries, where modelling time varying correlation structures is also likely to be a key factor. Such applications are left for future research.