The Stock-Bond Relationship and.asset Allocation October 2009

Transcription

1 The Stock-Bond Relationship and.asset Allocation October 2009 The relationship between stocks and bonds has important implications for asset allocation and risk diversification. This Research Bulletin examines the recent history of this relationship in the G5 economies. It also uses the multi-asset class platform of the Barra Integrated Model (BIM) to consider some of the possible drivers behind the evolution of this relationship. In addition, it is shown that scenario testing is useful in determining the impact on the stock-bond correlation from possible future scenarios. An inflation surprise accompanied by quicker-than-expected Fed hikes, for instance, would likely imply an increase in the optimal allocation to global equities at the expense of global bonds. Introduction The relationship between equities and fixed income is a critical one for portfolios that contain both asset classes. Even though bonds typically yield a lower rate of return than equities in the long run, the inclusion of bonds and other fixed income instruments in a portfolio may be justified by the diversification effect resulting from the low correlation between bonds and stocks. However, the correlation between the two is not stable, and changes in this number potentially have important implications for investors in determining the diversification benefits of bonds and the asset allocation between these two classes. The stock-bond correlation is important in asset allocation, since a higher correlation would imply a higher allocation to equities, given that bonds generally have lower expected returns. Most portfolio optimization exercises assume a positive correlation, but as we show later, the correlation may move from being positive to negative and vice versa. These changes may have a material effect on the optimization outcome. For example, a change in correlation from 0.5 to +0.5 would significantly increase the optimal allocation of equities from 36% to 67% based on expected returns of 12% for equities and 4% for bonds. 1 The Stock-Bond Relationship in the G5 Countries The Barra Integrated Model (BIM) is useful for investors examining the relationship between equities and bonds, because it has both equity and fixed income factors at the country level. In addition, the model separates different aspects of the term structure, including government rates and credit spreads. The former is further divided into factors such as the shift and twist of the sovereign yield curve (shift factors capture parallel movements, and twist factors capture changes in slope). We consider the relationship between stocks and bonds in Figure 1, which shows the correlation between the respective national stock market factors and the sovereign shift factors in the G5 countries. 2 Our first observation is that these correlations are unstable and may be positive or negative, depending on the period examined. Second, there are clear inter-country differences in these correlations. Japan is the obvious outlier, especially in the first half of the sample period. Given the variability of these correlations, our next step is to consider the various drivers that may cause them to vary. 1 These figures are based on the historical volatilities of 14% and 7% for equities and bonds, respectively. The optimization problem maximizes expected portfolio return with a given level of risk. 2 Only government bonds are covered in this Research Bulletin. Corporate and other non-sovereign bonds may behave very differently. For instance, Briand and Owyong (2009) have shown that both stocks and non-sovereign bonds suffer from the flight to quality during crises MSCI Barra. All rights reserved. 1 of 7

2 Figure 1: Stock-Bond Correlations in G5 Countries (24-month window) One such driver is the stock market cycle. Gulko (2002) has shown that stocks and treasuries tend to decouple during equity market crashes, while they are positively correlated during normal market conditions. In general, a bear market in equities is associated with a flight to quality and an increased demand for bonds, which leads to a decline in the correlation between equities and bonds. A second factor is the interest rate cycle, which directly affects the price of bonds and equities through changing their discount rates, causing bond and equity prices to be inversely related to interest rate changes. However, stock-bond correlation tends to be higher during a tightening cycle than during an easing one; the impact of changing interest rates on bonds is direct and immediate, but its effect on stocks tends to be quicker during tightening phases than easing periods MSCI Barra. All rights reserved. 2 of 7

3 The third factor that affects the stock-bond correlation is expected inflation. Higher expected inflation decreases the real value of future coupon payments, thus lowering bond prices. Stocks are also affected adversely, since real earnings growth is negatively impacted. Thus, higher inflationary expectations will also raise the stock-bond correlation. To represent equity market performance and the interest rate cycle, we used the BIM equity country factor and sovereign shift factor. Finding a variable for expected inflation is more complicated. Inflation-linked bonds are often used to provide a measure of expected inflation, but these bonds either are not available for all countries, or some of them have been traded for only part of our sample period. In addition, they are sometimes plagued by liquidity problems, as happened in October last year when the US Federal Reserve suspended their TIPS Expected Inflation estimates due to illiquidity. Surveys of consumers and professional forecasts are another source of data on expected inflation, but the comparability of survey data within and across countries is questionable due to methodological differences. As an alternative, this Research Bulletin uses changes in the slope of the yield curve to capture changes in inflationary expectations. As was shown by Ang, Bekaert, and Wei (2008), term spreads are primarily driven by changes in expected inflation. The advantage of using BIM factors to capture the various drivers is that these factors are pure versions from which other influences have been filtered. For instance, using equity indices, instead of the equity country factors from BIM, would have introduced style biases, since some countries have a disproportionate number of large caps or value stocks. Similarly, movements in the stock markets of countries with a large manufacturing sector may be overly influenced by developments in that sector. In BIM, these effects are explicitly accounted for and separated. The stock-bond correlations for the G5 countries are regressed on the three drivers identified: the stock market cycle, the interest rate effect, and expected inflation. The results are shown in Figure 2 (note that France and Germany share the same bond-related factors, which are based on the common bonds in the eurozone). Figure 2: Determinants of Stock-Bond Correlations ( ) USA UK Japan Germany France Constant *** -0.18* -0.14*** (0.229) (5.439) (-1.937) (-2.412) (-0.974) Equity Market Effect 1.50*** 2.00*** *** 1.08*** (6.628) (6.203) (1.326) (2.668) (3.465) Interest rate effect 11.97** 21.03*** *** 27.60*** 31.19* (2.160) (5.878) (-4.349) (2.710) (1.655) Inflationary Expectations 14.62*** 14.08*** ** 9.09** 4.70 (3.499) (3.847) (-2.118) (2.031) (0.822) Adjusted R-squared Note: Standard errors are in parentheses, and are corrected for autocorrelation with the Newey-West procedure. *, ** and *** represent statistical significance at the 90%, 95% and 99% confidence levels respectively. With the exception of Japan, which was mired in an equity slump since the early 1990s, the stock market cycle appears to have a positive and statistically significant effect on the correlation between stocks and bonds. This is in line with expectations, since in bull markets both equities and bonds are likely to move up together, thus raising their correlation. As for the interest rate effect, higher levels are also found to have a positive impact on the stockbond correlation. This is expected as noted earlier, since higher interest rates tend to raise the correlation between the two types of assets MSCI Barra. All rights reserved. 3 of 7

4 Lastly, the correlation between stocks and bonds tends to rise as inflationary expectations rise, which is also in accordance with expectations. France s coefficient for this variable is not statistically significant, which suggests that the eurozone s inflation expectations may be more reflective of the inflation environment in Germany, the region s largest economy. As for Japan, the counterintuitive results are indicative of its deflationary situation for most of the sample period. Unlike the other countries, rises in expected inflation and interest rates in Japan were viewed as bullish for the stock market, because they raised hopes of an exit from the deflationary spiral. This explains why the coefficients to the interest rate and expected inflation variables have the opposite sign of those for the other economies. Applying Scenario Analysis to Examine the Impact on Stock-Bond Correlations One of the problems in assessing the effect of extreme events is that, by definition, these events have rarely happened. This makes it difficult to use historical data to determine their impact. Stress testing and scenario analysis help to overcome this problem by simulating hypothetical scenarios. These tools are also useful for investors in isolating one aspect of a shock so that it can be analyzed independently. In recent years, stress testing has attracted the attention of both regulators and practitioners as an important tool that complements traditional risk measurements. Increasingly, regulators such as the Basel committee and EU Commission require that practitioners incorporate stress testing into their regular risk management practice. For stress tests, the difference between uncorrelated and correlated shocks is important. With uncorrelated shocks, only those assets affected by the specified shocks are revalued, while all others are unchanged. For example, if the shock is a widening of the corporate bond spread by 25bp, equities in the portfolio would not be revalued. With correlated shocks, the cross-asset effect is considered by using a covariance matrix that captures these relationships. 3 In this paper, only correlated shocks are considered, since we are interested in capturing all relationships between bonds and equities. In the present context, we use scenario testing to analyze how the stock-bond relationship would be affected by possible future events. From the regression analysis earlier, the effect on stockbond correlation from one explanatory variable is derived by holding all other explanatory variables constant. In real-life scenarios, these factors are simultaneously variable. For instance, a rise in inflationary expectations may accompany rate hikes from the central bank, which in turn may adversely affect the stock market. All these linkages can be captured by a scenario analysis with correlated shocks. As an example, let us consider the scenario of quicker-than-expected rate hikes by the US Fed due to inflationary pressures. The rate hike in 1994 is a close historical parallel, since the economy then was also reacting to rate increases after emerging from a period of very low interest rates. The results shown in Figure 3 indicate that both bonds and equities would unambiguously decline. Therefore, this scenario would raise global stock-bond correlations, given their current, near-zero levels, and thus it would significantly lower the diversification effect of bonds, justifying a larger allocation to equities. 3 For technical details, refer to Rubandhas (2007), Stress Testing in a Multi-Factor Framework, MSCI Barra Horizon, Summer 2007, pp MSCI Barra. All rights reserved. 4 of 7

5 Figure 3: Scenario Analysis of a Quicker-than-Expected Hike by the US Fed (Based on Historical Parallel of 1994 US Rate Hike) Source: BarraOne Conclusion This Research Bulletin examines the stock-bond relationship, which has important implications for asset allocation and risk diversification. We find that the stock market cycle, interest rates, and inflationary expectations are important drivers for the correlation between stocks and bonds. This paper also shows how the effect of possible future scenarios on this correlation may be analyzed by using scenario analysis. In the scenario in which inflationary concerns lead to quicker-thanexpected hikes from the US Fed, global bonds and stocks would generally become more correlated. These findings have important implications for asset allocation, because the optimal allocation to equities would in all likelihood increase at the expense of bonds if the correlation between bonds and equities were to rise, since a higher correlation implies lower diversification benefits from bonds. References Ang, Andrew, Geert Bekaert, and Min Wei (2008). The Term Structure of Real Rates and Expected Inflation, Journal of Finance, Vol. 63, No. 2, pp Briand, Remy and David Owyong (2009). How to Kill a Black Swan: Risk and Asset Allocation in Crises, Journal of Indexes, July/August, pp Gulko, Les (2002). Decoupling, Journal of Portfolio Management, Spring 2002, pp Rubandhas, Sam (2007). Stress Testing in a Multi-Factor Framework, Horizon, Summer 2007, pp MSCI Barra. All rights reserved. 5 of 7

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