رابطه بین تغییرات در قیمت سهام و بازده اوراق قرضه در کشورهای G7: تجزیه و تحلیل موج ضربه ای

The purpose of this paper is to shed a new perspective on the relationship between changes in stock prices and bond yields in the G7 countries. Theoretical studies argue that this relationship may be negative or positive. To investigate the relationship, we model a newly developed time-series technique: wavelet correlation analysis. The key empirical results show that the correlation between changes in stock prices and bond yields can differ from country to country and can also depend on the time scale. Furthermore, wavelet analysis reveals that changes in stock prices and bond yields do not move together in most G7 countries, except in Japan.

The movements of real stock prices and interest rates are important for institutional and individual investors in the management of their portfolios. Many investors use a tactical asset allocation strategy whereby they shift their investments between stocks and interest rates in different anticipated capital market conditions. If stock prices and bond prices move together, this tactical strategy is not a good general strategy. The importance of the relationship between stock and interest rates has led to it being studied in two ways. First are studies that examine the relationship between short-run stock returns and short-term interest rates (Fama and Schwert, 1977, Campbell, 1987, Breen et al., 1989 and Ferson, 1989, among others). These studies find that short-term interest rates have a power to forecast short-term stock returns and short-term risk premiums. For example, Campbell (1987) uses the short-end of the yield curve to predict monthly excess stock returns. He finds that the spread of the 2-month and 6-month bills over the 1-month bill has a predictive power. The drawback of this approach is that it only considers short-term interest rates, ignoring information on long-term interest rates. The second approach is to use the term spread (difference between long-term and short-term interest rates) to forecast stock returns or stock risk premiums. This approach includes the studies of Fama and French (1989), Fama (1990), Schwert (1990), Shiller and Beltratti (1992), Campbell and Ammer (1993) and In et al. (2003).1 For example, Campbell and Ammer (1993) examine the predictive power of term spreads to forecast short-horizon stock returns with a linear vector-autoregressive (VAR) approach. They find that real interest rates have very little impact on stock returns. Another example is the study of Shiller and Beltratti (1992). They examine the relationship between changes in stock prices and the changes in long-term interest rates using a simple rational expectations present-value model and find that the relationship between changes in stock prices and bond yields is more negative than expected. In this paper, we focus on the relationship between changes in stock prices and long-term bond yields, particularly in the G7 countries. Since stocks are considered to be a long-term investment, we are interested in the multiscale relationship between changes in stock prices and bond yields for two reasons. First, from a practical point of view, many investors hold stocks over long periods. Therefore, it is important to know the manner in which changes in stock prices move with changes in long-term bond yields as the holding horizons increases. Second, the relationship between changes in stock prices and bond yields at long horizons is of particular interest given that at short horizons, the true long-run relationship could be obscured by short-term noise, which might derive, for instance, from agents trading for portfolio rebalance or unexpected immediate consumption needs (Harrison and Zhang, 1999). The main purpose of this paper is to examine the relationship between changes in stock prices and long-term bond yields in both the short run and long run. To investigate the relationship, we adopt a newly developed time-series technique: wavelet correlation analysis. Wavelet analysis possesses the ability to perform non-parametric estimations of highly complex structures without knowing the underlying functional form (Ramsey, 1999). The major aspects of wavelet analysis are the ability to handle non-stationary data, localization in time, and the resolution of the signal in terms of the time scale of analysis (Gençay et al., 2002a). Among these aspects, the most important property is decomposition by time scale. Economic and financial systems, like many other systems, contain variables that operate on a variety of time scales simultaneously, so that the relationships between variables may well differ across time scales (Ramsey, 1999). Wavelet analysis has been adopted in few studies in the finance literature. To the best of our knowledge, applications include examination of the following: foreign exchange data using waveform dictionaries (Ramsey and Zhang, 1997); decomposition of economic relationships of expenditure and income (Ramsey and Lampart, 1998a and Ramsey and Lampart, 1998b); the multiscale hedge ratio (In and Kim, 2006); systematic risk (Gençay et al., 2003); the multihorizon Sharpe ratio (Kim and In, 2005); and the relationship between financial variables and real economic activity (Kim and In, 2003), among others. What should the relationship between changes in stock prices and bond yields be? One argument has been that there should be a simple negative relationship using present-value models. For example, an increase in expected future discount rates should lead both stock prices to fall and long-term interest rates to rise.2 However, a positive relationship is also possible because movements in long-term interest rates might be related to information about the future dividend stream on stocks (Shiller and Beltratti, 1992). For this argument, two papers are worth noting for their theoretical models for testing the relationship between stock and bond markets. Based on a standard consumption-based asset pricing model, Barsky (1989) analyses the effects of change in risk and real economic productivity growth on the joint behavior of stock and bond prices. He concludes that these prices may or may not move together, depending on the degree of risk-aversion of agents. Bekaert and Grenadier (2001) develop a general multi-factor arbitrage-free model for stock and bond pricing, and show that stock and bond returns may or may not move together, depending on the parameterization of the model.3 The main results from the empirical analysis show that the correlation between changes in stock prices and bond yields can differ from country to country and can differ depending on the time horizon. From the correlations over the wavelet time domain, changes in stock prices and bond yields do not move together in most G7 countries, except in Japan. Japan shows a positive relationship up to the fourth scale. We find a negative relationship between changes in stock prices and changes in bond yields in most countries, except in Japan. In brief, over the short and long horizons, a negative relationship between changes in stock prices and bond yields is dominant. The remainder of the paper is organized as follows: Section 2 presents the data and discusses the empirical results of the long-horizon regression. Section 3 summarizes wavelet analysis relevant to our study and discusses the results. In Section 4, concluding remarks are presented.

This paper provides a new perspective on the relationship between changes in stock prices and bond yields in the G7 countries. To test the relationship, the long-horizon regression and wavelet analysis are adopted. In the long-horizon regression, the relationship between changes in stock prices and bond yields depends on which country is being investigated, as well as the time scale we adopt. For example, while Japan shows a positive relationship in all horizons, the other countries show a negative value regardless of the time horizon. The key empirical results using wavelet analysis indicate that in most countries, the variances of changes in stock prices are more volatile in all time scales than those of changes in bond yields, except in Japan. In addition, we find that the wavelet variance has a highest value in the first scale, indicating that an investor with a short investment horizon has to respond to every fluctuation in realized returns, while for an investor with a much longer horizon, the long-run risk is significantly less. From the analysis of the correlation over the wavelet time domain, changes in stock prices and bond yields do not move together in most G7 countries, except in Japan. Japan shows a positive relationship up to the fourth scale. Our results indicate that tactical asset allocation does not hold in most countries because changes in stock prices and bond prices move together, while it can hold in Japan up to the fourth scale. Overall, our study confirms the negative relationship between changes in stock prices and bond yields as found in the present-value model (Shiller and Beltratti, 1992) in most G7 countries, except Japan. In short, over the short and long horizon, the negative relationship between changes in stock prices and bond yields is dominant.