Asset Class Co Movement And The Macro Economy

Published Date: 02 Nov 2017

Asset Class Co-movement and the Macro-economy

Abstract

This paper analyses the co-movement of stocks, government bonds and gold in the US, UK, Germany and Japan by applying Engel’s (2002) dynamic conditional correlation estimation method and regressing against macroeconomic variables and implied stock volatility. Building on the current literature this paper shows that real interest rates represent a significant and positive factor in stock-bond correlation, while higher implied stock volatility has a negative effect on both stock-bond and stock-gold correlations. This highlights the value of bonds and gold as safe havens for investors and their importance to the financial system in cushioning falling asset values during crises.

Word count: xxxx

Contents

Introduction

Literature review

Asset class co-movement

Asset data

Correlation overview

Correlation measurement

Theoretical background

Stock pricing

Bond pricing

Gold pricing

Implications for co-movement

Data

Econometrics estimation

Discussion of results, weaknesses and potential further research

Results

Potential improvements and further research

Concluding remarks

I have just read Cosmo's first draft and discussed it with him. 

He has a a good draft with nice results, but he can improve it significantly.

If he makes the changes we talked about so as to improve the discussion surrounding the motivation and contribution, write an introduction, relate his results to that of the literature, make the theory section more clear, and generally makes the text flow better he will have a very good dissertation.

1 Introduction

This paper examines the dynamics of asset class co-movement, with a focus on the impact of macroeconomic factors and stock market uncertainty on the correlations between stock, bond and gold returns. Analysis focuses on factors that may cause or indicate significant changes in co-movement. Understanding the dynamics of asset correlations is important for both portfolio analysis and monetary policy.

Much of portfolio composition theory centres on three subjects: expected return, volatility and correlation. Information on and predictions of the varying correlations across asset classes are crucial for optimal portfolio composition (Wainscott, 1990). However, until the last two decades, little attention was given to asset class co-movement. Shiller and Beltratti (1992) report an early analysis of stock and government bond co-movement, but not until Li (2002) and Gulko (2002) was dynamic correlation between stock and bond markets formally considered.

The importance of asset prices, in particular stock prices, in the transition mechanism is highlighted by Mishkin (2001). Monetary policy makers considering policies such as quantitative easing that affect bond markets should account for the economic effects of subsequent stock-bond co-movement. Asset-class correlations are also important in determining financial robustness in crises. Hartmann, Straetmnas and Vries (2004, p.313) emphasise that "for the assessment of financial system stability the widely disregarded cross-asset perspective is particularly important." They highlight how a flight-to-quality [1] or a lack thereof during crises impacts on the resilience of the financial system by affecting average asset price stability.

This paper contributes to the current literature along two significant tracks. First, stock-bond correlations are examined against GDP indicators, inflation, real interest rates and implied volatility. This is broader than previous analyses and leads to different results. Second, stock-gold and stock-bond correlations are similarly analysed. The use of implied volatility indices to test gold’s safe haven [2] properties contrasts with previous studies which have been constrained to examining particular incidences of extreme stock market volatility or price falls.

Concerning stock-bond correlation, the results support the broad conclusions of the literature with regard to stock market volatility, which impacts negatively on co-movement; real interest rates, which impact positively; and real GDP, which has an insignificant effect. Contrary to the literature reviewed, inflation rates are shown to have an insignificant rather than a positive effect. A negative relationship is found between stock-gold correlations and implied volatility. This is consistent with the evidence in the literature suggesting that gold acts as a safe haven for stocks in extreme market environments.

The remainder of this paper is presented as follows. Section 2 reviews the current literature on asset-class correlations. Section 3 describes the technique used to estimate co-movement, the asset data, and the estimated time-series themselves. Section 4 examines asset pricing theory to assist the selection of macroeconomic variables that may impact on correlations, makes theoretical predications of their effects and sets out the data used to analyse these variables. Section 5 reports on the empirical analysis and discusses the final results. Section 6 offers concluding remarks.

2 Literature Review

The literature has focused principally on stock-bond correlation. Shiller and Beltratti (1992) and Campbell and Ammer (1993) find positive co-movement between stocks and bonds, although Shiller and Beltratti’s estimations of correlation are significantly higher. Neither study examines correlation as a changing variable. Li (2002) seeks to explain changes and trends in stock and bond returns over a 40-year period through macroeconomic factors. He finds that uncertainty about expected inflation is particularly important and positively related to stock-bond correlation, while the relationship with unexpected inflation and real interest rate uncertainty is significant and positive but less so. As inflation uncertainty is often correlated with asset volatility, Li’s (2002) results raise the possibility of decreasing diversification benefits when their importance is increasing. In agreement, Ilmanen (2003) finds that variable inflation pushes stock-bond correlations positive. He finds that economic growth and asset volatility shocks put negative pressure on co-movement, concluding that deflationary recessions, equity weakness and high-volatility can lead to negative stock-bond correlations. D’Addona and Kind (2006) find, in accordance with Li (2002) that real interest rate volatility increases stock-bond correlation, but determine that inflation shocks impact negatively on co-movement. This result is in opposition to the findings of Li (2002), but is likely to be a result of d’Addona and Kind’s (2006) pricing model. Yang, Zhau and Wang (2009) lend support to Li (2002) by interpreting their finding that higher inflation is positively linked with stock-bond correlation with the observation that higher inflation uncertainty is typical of higher inflation levels. In line with most of the literature, Andersson, Krylova and Vӓhӓmaa (2008) find that stock-bond co-movement is linked positively with inflation expectations and periods of negative stock-bond correlation coincide with reduced inflation expectations. However, in contrast to Ilmanen (2003), Andersson et al. (2008) find economic growth expectations have virtually no effect on stock-bond correlation.

With a focus on crises, Gulko (2002) finds that during US stock market crashes the correlation with Treasury bonds tends to turn negative providing an effective avenue for diversification. In apparent contrast, Hartmann et al. (2004, p.313) conclude, that ‘stock-bond contagion is approximately as frequent as flight to quality from stocks into bonds.’ This discrepancy could be due to Gulko’s focus on stock market crashes and Hartmann et al.’s broader view. Baur and Lucey (2009) support this explanation, finding that flights often occur during crises but that high bond market volatility makes cross-asset contagion more likely. The importance of co-movement behaviour in crises is highlighted by Cappiello, Engle and Sheppard (2006) who find that international stock correlation rises during financial turmoil, increasing the value and uniqueness of the diversification benefits that decreasing stock-bond correlation can offer to an international portfolio. It is demonstrated empirically by Baur and Lucey (2009) that flights, by improving diversification, improve the stability and resilience of the financial system in crisis times.

Shifting attention from specific crises and market crashes to the level of market volatility allows for more general and continuous analysis of stock-bond co-movement in response to uncertainty. Connolly, Stivers and Sun (2005) examine the link between stock-bond correlation and implied stock volatility. They argue that the implied volatility measures, such as the CBOE Volatility Index (VIX) for the S&P 500 Index, reflect general market, financial, and economic uncertainty. A negative relationship was found between stock-bond co-movement and implied stock market volatility by Connolly et al. (2005) for the US. Andersson et al. (2008) also use implied stock volatility measures and additionally broaden the view to the US, UK and Germany. Their finding that high stock market uncertainty results in negative correlation between stocks and bonds accords with the results of Connolly et al. (2005). The conclusions drawn from implied volatility analysis are consistent with the idea of flights to quality; both imply a negative impact of crises on stock-bond correlation.

Commodities are rarely examined in the context of asset class co-movement. This could be a significant oversight. Although not as prominent in portfolio composition as stocks and bonds, the importance of commodities, especially gold, for investment is increasing. The body of academic research on the use of gold in investment is still small relative to its importance (Lucey, 2011), but the growing use of gold as a perceived safe haven investment led Baur and Lucey (2010) to examine the relationship between stock, bond, and gold returns in the US. They determine that gold is a safe-haven asset against stocks in times of extreme negative returns on equities, although it cannot be used in the same way against bonds. Baur and McDermott (2010) examine the stock-gold relationship internationally and find similar results for Europe and the US but not for Australia, Canada, Japan and large emerging markets.

Comparison of asset class co-movement internationally is vital, since portfolios are largely global and increasingly so. Andersson et al. (2008) find that from the early 90s the US, UK, and Germany present similar patterns of stock-bond co-movement, with periods of negative correlation largely common across nations. However, Yang et al. (2009), studying a 150 year period for the US and UK, observe that stock-bond correlation patterns are different over the business cycle. Li (2002) examines all G7 countries from 1958 to 2001. He reports that the countries’ stock-bond correlations often move together and that broad trends appear to hold across countries, with some exceptions. Co-movement in Japan is most unique over the period, with Italy also deviating from some of the broad cross-country trends. The comparison is closest in recent years between the US, UK, France, and Germany. Consistently across the literature, the findings on the determinants of stock-bond correlation are broadly consistent across countries, demonstrating that conclusions drawn for one country should be of use to others, their investors, and policy makers.

3.1 Measuring asset class co-movement

To measure the time-varying correlation the dynamic conditional correlation (DDC) model, suggested by Engel (2002) [3] , is applied to daily data. Backward looking 22-day averages of the DCC model estimates are taken on the 15th of each month to generate monthly data for the analysis in this paper. DCC overcomes several key disadvantages of the simple 22-day rolling window correlation (RWC) [4] for use as a measure of co-movement. The RWC is, to an extent, arbitrary in length and highly positive or negative observations do not fade out but, instead, drop out abruptly. Further, the trade off between responsiveness to change and extra noise is particularly stark and a 22-day RWC creates a noisy time series, in which it is difficult to see trends and important shocks. Importantly, periods of high volatility in one of the assets biases the RWC upwards in magnitude as a measure of co-movement due to the impact of variance on the simple correlation equation. This problem is demonstrated by a stark example in Forbes and Rigobon (2002). Except for the issue of abrupt drop outs of data, the problems also apply when using an exponentially smoothed window.

This paper attempts to avoid these problems by assuming that the dynamic covariance between the assets is given by the following DCC(1,1) specification, a simplified multivariate generalized autoregressive conditional heteroskedasticity (GARCH) model given by:

(1)

where ri,t is the return on asset i at time t, σi,t is the conditional standard deviation of asset i at time t, σij,t is the conditional covariance between assets i and j at time t, zi,t = ri,t/σi,t and ρij,t is the dynamic conditional correlation (DCC) between assets i and j at time t. [5] 

Thus, by estimating the changing variance, the DCC measure does not suffer from the aforementioned bias of the RWC. Further, the weight placed on the more recent return data is determined through maximum likelihood estimation rather than arbitrarily. Finally, the final output is more intelligible, appearing smoother without losing responsiveness to shocks.

3.2 Asset Data

The US, UK, Germany and Japan were chosen for analysis due to their large, developed and globally important financial markets. Together, the four countries represent approximately 40% of global nominal GDP (IMF, World Economic Outlook Database, 2012), 65% of outstanding public debt (World Federation of Exchanges, 2012) and 75% of the weight in the MSCI World Index (2013). Further, due to their strong recent history of developed and relatively transparent financial markets, available data is of good quality and length compared to that concerning many other countries.

The US is the largest and most internationally important country of the sample by almost any economic or financial measure. The US dollar’s (USD) place as the primary global reserve currency is also an important differentiating factor, for example resulting in higher demand for US government bonds. Further, gold’s relationship to the other asset classes could be different due to the USD’s role as its international pricing currency. The UK or, more specifically, London acts as a global financial centre and is set apart from other large nations of Europe by both its currency and its economic structure. Germany is the largest eurozone nation and has internationally important stock and bond markets. German bonds often act as the reference point for other eurozone debt. The availability of data for Japan is relatively poor for this study but its value lies in its stark differences from the other three nations and therefore it supports the generality of any results that are consistent across the four countries. Japan’s deviation is evident in the asset class correlations (observable in Figures 1, 2 and 3) and in its economic story over the last three decades of fast growth followed by decline, low interest rates and very low/negative inflation.

The stock returns are calculated from broad, value-weighted price indices from MSCI. The sample runs from the beginning of 1980 to February 2013. The bond indices used are 10-year clean price benchmark indices from Datastream and cover the same time span, except for Japan, where the series starts in 1984. The gold bullion prices in USD/troy ounce (from Datastream) are converted for the UK, Germany and Japan into their local currencies for use in this paper.

3.3 Correlation Overview

Figure 1: Stock-bond correlation

Table 1: Summary statistics for stock-bond correlation

No. of observations

Mean

Standard deviation

Minimum

Maximum

US

397

0.084

0.364

-0.687

0.652

UK

397

0.087

0.348

-0.656

0.745

Germany

397

0.063

0.391

-0.737

0.726

Japan

349

-0.114

0.297

-0.673

0.699

Until the last 10 to 15 years, the literature and debate concerning stock-bond correlation was interested principally in whether it was positive or negative and to what extent. The consensus in the 90s was that the correlation is positive (Shiller and Beltratti, 1992). Looking back 20 years later, however, it is clear that the data no longer supports that hypothesis. Since 1998, the correlations for the countries in this sample have been negative on average and their sample means (Table 1) are very close to zero and negative in the case of Japan. Over the period, the US, UK and Germany followed similar trends. Until 1998, their co-movement remained broadly positive with a slight positive trend. It then broke down into negative territory and followed a mild negative trajectory, albeit with increased instability. Japan’s series, meanwhile, departs markedly from the others with a prolonged period between 1992 and 2004 where little similarity to other nations can be observed.

The past 33 years have featured instability but also sustained periods of both positive and negative co-movement. In 1989, correlations for all four countries fell sharply before a long period of positive persistence for the US, UK and Germany, which ended near the beginning of 1998. Negative persistence can be observed for all countries from mid-2007 onwards.

Figure 2: Stock-gold correlation

Table 2: Summary statistics for stock-gold correlation

No. of observations

Mean

Standard deviation

Minimum

Maximum

US

397

-0.014

0.102

-0.446

0.241

UK

397

0.021

0.101

-0.304

0.262

Germany

397

0.035

0.113

-0.408

0.246

Japan

397

0.040

0.112

-0.254

0.262

Figure 3: Bond-gold correlation

Table 3: Summary statistics for bond-gold correlation

No. of observations

Mean

Standard deviation

Minimum

Maximum

US

397

-0.001

0.085

-0.253

0.242

UK

397

0.010

0.112

-0.362

0.369

Germany

397

-0.003

0.116

-0.354

0.391

Japan

349

-0.039

0.077

-0.251

0.122

Stock-gold and bond-gold correlations are far less studied in the literature than stock-bond correlation. To an extent, this is justified by gold’s less prominent place in investment portfolios compared with stocks or bonds. However, with interest in gold and related gold stocks growing in recent years and central bank purchases (by weight) in 2012 the largest since 1964 (World Gold Council, 2013), an understanding of these correlations could be valuable to investors and central banks. Too much repetition?

Compared to the stock-bond correlations, there is a far smaller range and standard deviation in the stock-gold and bond-gold correlations. Means are very close to zero and there are fewer occurrences of prolonged negative or positive co-movement. However, both trends and incidences of sharp change are discernable. Japan’s stock-gold and bond-gold series are again the most independent relative to the others. This is particularly evident after 2006, with the Japan’s correlations remaining stable relative to the other countries. The UK, US and Germany’s stock-gold correlations appear to become more closely linked in the latter half of the sample (after 1998) and exhibit similar responses to shocks since the financial crisis began. It should be noted that the stock-gold and stock-bond series appear positively linked when stock-bond correlation is high and, conversely, negatively linked when stock-bond correlation is low. This could arise mechanically due to the interdependent nature of the three correlation series and, importantly, it could be that two correlations determine the third. Both the literature (Baur and Lucey, 2010 and Ciner, Gurdgiev and Lucey, 2010) and the analysis in this paper indicate that the driving forces behind bond-gold correlation are relatively weak. It may be that stock-bond and stock-gold correlations dominate and, at least to some extent, drive the bond-gold correlation.

4 Why asset-class correlations change over time: theoretical background and relevant data

Examining pricing theory for stocks, bonds and gold assists selection of variables that may determine co-movement and can lend support to or cast uncertainty over empirical results. A change or additional uncertainty in a variable that affects the price of two different assets will promote either positive co-movement, if the measure has a directionally similar effect, or negative co-movement, if the measure impacts in opposite ways. Pricing is largely dependent on expectations. Although changes and uncertainty in the expectations of future economic variables are important for determining co-movement, they are not directly measurable. Nevertheless, uncertainty is often positively linked to levels of macroeconomic variables. Ball (1992) and Kontonikas (2004) show how higher inflation increases inflation uncertainty. Further, if a macroeconomic aggregate (such as the inflation rate, real interest rates or real GDP growth) is at a relatively high level, its actual and perceived importance in determining asset price moves is likely also to increase, compounding any underlying impact on co-movement.

4.1 Stock pricing

The price of a stock or an index can be described in many different ways, such as by a discounted dividends model (applied in Anderson et al., 2008), a discounted cash flow (DCF) model or by derivation from a yield equation (used in Li, 2002). This paper takes a macro perspective and describes the sum price of a nation’s publicly listed companies, and therefore the price of its broad, value weighted index, through the discounted sum of those companies’ cash flows. The result should be a model that is intuitive and flexible, while also clear in its conclusions. The following stock market value (SMV) model can be seen as a modification of a DCF model

(2)

where SMPτ is the stock market price at time t=τ, Eτ are market expectations at t=τ, δt is the fraction of nominal GDP that makes up publicly listed company cash generation augmented for international inflows and outflows at time t, GDPt is the level of real GDP at time t, PLt is the price level at time t, rn is the real interest rate at time t=n, πn is the inflation rate at time at time t=n and ERPn is the equity risk premium, the rate at which investors discount the cash flows due to risk aversion and the perceived relative risk compared to holding cash, at time t=n.

It should be noted that the ERP in the SMV model is both time varying and not constrained to be positive. ERP is time varying to capture the possibility of investors not discounting for risk in a constant and multiplicative way. Since the ERP is relative to the risk of holding short-term cash instruments, it could, theoretically, be negative in some periods if it is perceived that the protection from the risk of inflation and low or negative real interest rates that stocks can offer outweighs cash’s benefit of certain nominal capital preservation.

The following decomposition of GDPt and PLt allows Equation 2 to be rearranged to the final stock market value (SMV) model equation in (4).

(3)

where GDPτ-1 is real GDP at time t=τ-1, gn is growth of real GDP in t=n, PLτ-1 is the price level at t=τ-1 and πn is inflation at t=n.

(4)

Several predictions can be drawn from the model. Higher real GDP growth expectations act positively on the stock market price index. Higher real interest rate expectations impact negatively, as do increases in equity risk premiums. The effect of an increase in expected inflation, however, is unclear. Any negative effect may be factored already into lower real GDP expectations, but could also act on δ expectations negatively if profits/cash flows are likely to fall as a fraction of GDP. Higher expected inflation may also negatively impact the equity risk premium (ERP) by magnifying the perceived benefit of stocks as a hedge against inflation.

4.2 Bond pricing

The price of 10-year government bonds can be derived indirectly by determining the yield of these securities. The model is simplified slightly by restricting analysis to 10 yearly periods, which is sufficient for present purposes. The 10-year government bond yield can be represented as

(5)

where BYτ is the 10-year bond yield at time t=τ, Eτ are market expectations at t=τ, rt is the real interest rate at time t, πt is the inflation rate at time t and TPt is the term premium, which represents the perceived risk of holding an asset with a fixed yield (the 10-year bond) relative to the risk of holding an asset yielding the nominal interest rate (cash instruments). This concept is similar to that of the ERP and is time varying for the same reason. Further, a negative term premium could exist if the perceived protection from uncertain nominal yields that bonds offer outweighs the benefit of certain capital preservation and the protection against inflation (assuming real rates are steady) offered by cash.

If expectations of r, π and TP are small, then Equation 6 is a good approximation.

(6)

The price of the bond can be calculated by discounting its cash flows by the bond yield.

(7)

Where BPÏ„ is the price of the 10-year government bond at time t=Ï„, Ct is the annualised coupon payment, and FV is the face value of the bond. An expectation term is not necessary since expectations have already been taken to derive the bond yield and it is assumed that the coupon and final payments are fixed and certain.

This model predicts that higher levels of expected real interest rates, expected inflation and the term premium would all impact negatively on 10-year government bond prices.

4.3 Gold pricing

The theoretical background to gold pricing is, in some ways, the most confusing and complicated of our three assets, even though the value of gold can seem entirely straightforward from other perspectives. To consider what may drive the price of gold, it may be useful to look separately at its three primary and often overlapping uses, as an investment asset, a commodity and a currency.

Holding gold as an investment, physically or as an exchange traded fund, is very different from holding stocks or bonds, because no return is generated. The gold is not lent out for use or put to work in any way. It is held, at a cost, and, when sold, is no different from the item that was originally bought. The value of gold in investment lies in its use as an inflation hedge, holding its real value over time and working as a safe haven against other investment assets. Worthington and Pahlavani (2007) offer evidence of a cointegrating relationship between gold and inflation, supporting its role as an inflation hedge. Lucey et al. (2010) find that gold acts as a safe haven against sharp losses in both stocks and bonds for the US and UK.

Gold is used as a commodity for jewellery and in industry (primarily electronics), which together make up about half of total demand. [6] Supply is from recycling and from mining, that latter of which has large fixed costs and takes time to set up, promoting short-term inelasticity.

Gold also fits the characteristics of a currency. Among other defining properties, it is universally fungible, has a long historical precedent as a currency or as the backing of currencies, and is considered a good store of value. For this reason, it has always been purchased and held by central banks alongside other reserve currencies.

Gold prices are likely to respond positively to increased inflation expectations and may act similarly to long-dated inflation-linked bonds under high inflation uncertainty. Increases in real interest rates may have a negative effect, as the opportunity cost of holding gold will increase. Market turmoil in stock or bond markets is likely to act as a positive factor on gold prices. Worsening world growth expectations may impact negatively on prices as demand for jewellery and industrial goods fall. This may offset upward price pressure from market turmoil if negative economic growth spillovers are expected.

4.4 Implications for co-movement

Based on the theory set out here, stock-bond co-movement should respond positively to real interest rates. Higher expected stock market volatility should increase the stock market premium and could result in a lower term premium, since investors are more willing to accept bond risk when stock market risk is high, characterising a flight to safety. If so, this would have a negative impact on co-movement as investors substitute between stocks and bonds. It is predicted that uncertainty in growth expectations will not impact on stock-bond co-movement, because growth expectations do not impact directly on bond prices. The potential effect of inflation uncertainty is ambiguous. While expected inflation is a negative factor for bonds, its effect on stocks is unclear in direction and magnitude.

The theory indicates that real interest rate uncertainty could impact positively on stock-gold correlation if the gold is responsive to opportunity cost. A similar flight-to-safety effect could occur under high expected stock market volatility, negatively impacting the correlation, as gold is seen as a safe haven and a store of value. Growth uncertainty is not predicted to have an effect on co-movement. The effect of inflation uncertainty is again ambiguous, due to the unclear effect of expected inflation on stocks.

Real interest rate uncertainty may impact positively on bond-gold correlation if real interest rates are perceived as a negative factor in gold pricing. Higher expected stock market volatility may act positively on co-movement if bonds and gold jointly act as safe-haven assets. Any impact of inflation uncertainty on co-movement should be negative and growth uncertainty is not predicted to have any significant effect.

In order to test these predictions and elaborate where the theory is ambiguous, the correlations will be tested against data on inflation, real interest rates, GDP growth and expected stock market volatility.

4.5 Data

All data series used are from Datastream and run monthly from 1980 to 2013 unless otherwise specified. Seasonal adjustment is made using the US Census Bureau’s X-12-ARIMA method when required.

Monthly year-on-year inflation (iny) is generated from national CPI indices for the US, Germany and Japan, while RPI is used for the UK due to data availability. Real interest rates (r3m) are generated from subtracting iny from the interbank interest rate monthly average. Japan’s series begins in 1986 due to data availability. To represent real GDP growth expectations (gdp), consumer confidence indices are used for the US, UK and Germany, while a leading diffusion index is used for Japan due to its better data quality. The US measure ranges between 25 and 145, while the series of the UK and Germany begin in 1985 and range -35 to 7, and -33 to 11 respectively. Japan’s index ranges from 0 to 110. Expected stock market volatility (vol) is represented by stock option implied volatility indices for the US, UK and Germany. No index is available for Japan. Volatility data is daily and, consistent with the correlation series, a 22-day rolling average from the 15th of each month is used to produce monthly data. The US index is the Chicago Board Options Exchange Market Volatility Index (VIX), running from 1990. The UK index, the VFTSE is produced by NYSE Euronext and runs from 2000. The German index, the VDAX, is constructed by Deutsche Börse and runs from 1992.

5 Econometric method, results and discussion

5.1 Econometric method

To assess the impact of inflation (iny), real interest rates (r3m), GDP growth indicators (gdp) and expected stock market volatility (vol) on stock-bond, stock-gold and bond-gold co-movement the regression shown in Equation 8 is used. Due to the comparatively short time period of the implied volatility data, the same regression equation with the vol term dropped is run in parallel for the US, UK and Germany. In the case of Japan, estimation is performed exclusively without the vol term, as implied volatility data is unavailable. Running estimations without vol enables the analysis of larger samples and the inclusion of Japan. This will help to check the robustness of significant results in the full regressions.

A generalized logit transformation is applied to the correlation estimates. This changes the range of the dependent variable from the restricted [-1, +1] to the unrestricted [-∞, +∞]. An AR(1) term is added to absorb serial correlation. Augmented Dickey-Fuller tests run on the variables, using the Schwarz Bayesian information criterion to determine lag length, indicated no significant problems of non-stationarity, the results are available upon request.

(8)

where ρt is the DCC estimate at time t.

5.2 Results and discussion

Table 4: The impact of iny, r3m, gdp and vol on stock-bond correlations

Country

Obs.

iny

r3m

gdp

vol

AR(1)

Adj R2

US

277

2.258*

3.260***

-0.002**

-0.008***

0.858***

0.902

(1.66)

(3.26)

(-2.10)

(-3.48)

(28.34)

US

386

0.469

0.015**

-0.000

0.912***

0.891

(0.59)

(2.03)

(-0.37)

(40.32)

UK

157

0.091

0.030***

-0.004*

-0.009***

0.786***

0.856

(0.08)

(2.87)

(-1.78)

(-4.77)

(18.74)

UK

337

0.128

0.012**

-0.001

0.945***

0.945

(0.25)

(2.49)

(-0.620)

(53.74)

Germany

253

-1.011

0.018*

-0.003**

-0.006***

0.929***

0.961

(-1.49)

(1.70)

(-2.47)

(-3.64)

(48.29)

Germany

337

0.164

0.012*

-0.002

0.961***

0.956

(0.18)

(1.69)

(-1.55)

(61.47)

Japan

318

1.810*

0.033***

0.000

0.882***

0.931

(1.77)

(3.71)

(0.15)

(33.96)

Notes: A constant term is included in the estimations. *, ** and *** indicate significance at the 10%, 5% and 1% level respectively. t-statistics are reported below coefficient estimates in brackets. The F-statistics for all estimations are significant past the 1% level.

Table 4 demonstrates that real interest rates have a significant and positive effect on stock-bond correlations. This is consistent with the theoretical predictions and the literature (Li, 2002 and D’Addona and Kind, 2006). Inflation rates did not appear to have a significant effect, which is allowed by this paper’s theoretical perspective. Interestingly, however, it runs counter to the findings of Li (2002) and Andersson et al. (2008). The GDP growth indicators are found to have a negative and weakly significant effect in the full regressions but this is not a robust result and the effect is insignificant in the other estimations. This is broadly consistent with the literature. Implied volatility, in keeping with Connolly et al. (2005) and Andersson et al. (2008), has a highly significant and negative effect on the correlation, indicating flight-to-quality behaviour, evidencing the use of bonds as a safe haven against equities.

Table 5: The impact of iny, r3m, gdp and vol on stock-gold correlations

Country

Obs.

iny

r3m

gdp

vol

AR(1)

Adj R2

USsg

277

-1.488***

-0.001

0.000

-0.001*

0.862***

0.791

(-3.37)

(-0.33)

(0.46)

(-1.79)

(29.21)

US

386

(-0.512)*

(0.004)**

(-0.000)

0.880***

0.791

(-1.83)

(2.02)

(-1.43)

(36.81)

UK

157

-0.226

-0.003

-0.001

-0.005***

0.770***

0.759

(-0.27)

(-0.52)

(-0.40)

(-3.51)

(15.86)

UK

337

-0.279

-0.003

0.001

0.834***

0.738

(-0.97)

(-1.52)

(1.37)

(27.79)

Germany

253

-0.960*

0.010**

-0.000

-0.003***

0.849***

0.852

(-1.74)

(2.19)

(-0.01)

(-3.50)

(28.27)

Germany

337

0.153

-0.003

-0.000

0.914***

0.841

(0.34)

(-1.16)

(-0.36)

(41.04)

Japan

318

-0.650*

-0.002

0.000

0.946***

0.942

(-1.89)

(-0.92)

(0.71)

(54.44)

Notes: A constant term is included in the estimations. *, ** and *** indicate significance at the 10%, 5% and 1% level respectively. t-statistics are reported below coefficient estimates in brackets. The F-statistics for all estimations are significant past the 1% level.

Table 5 indicates that neither real interest rates nor growth indicators have a significant effect on stock-gold correlations. This runs against the prediction that real interest rates may have a joint effect on stocks and gold, resulting in positive co-movement. Inflation is found to have a significant and negative effect in the US across both estimations, in Germany in its full equation and in Japan. This may be evidence of a relatively weak relationship that is specific to individual country characteristics. Expected stock market volatility is shown to have a significant and negative effect in the US, UK and Germany. This result expands on the findings of Baur and Lucey (2010) and Baur and McDermott (2010) that gold acts as a safe haven on the worst days of stock returns, by showing that the effect is robust for the continuous variable, implied volatility.

Table 6: The impact of iny, r3m, gdp and vol on bond-gold correlations

Country

Obs.

iny

r3m

gdp

vol

AR(1)

Adj R2

US

277

-0.216

-0.015***

0.001***

0.001*

0.781***

0.766

(-0.57)

(-3.77)

(2.91)

(1.82)

(21.04)

US

386

0.460*

-0.001

0.000

0.879***

0.793

(1.96)

(-0.82)

(0.07)

(36.15)

UK

157

0.025

-0.004

-0.000

0.002*

0.855***

0.786

(0.03)

(-0.65)

(-0.05)

(1.84)

(19.31)

UK

337

-0.789***

-0.007***

-0.001

0.823***

0.820

(-2.59)

(-3.04)

(-0.75)

(26.66)

Germany

253

1.392***

-0.007*

-0.000

0.001

0.912***

0.890

(3.06)

(-1.74)

(-0.28)

(1.32)

(38.36)

Germany

337

1.060***

-0.009***

-0.000

0.900***

0.907

(2.93)

(-3.39)

(-0.19)

(41.53)

Japan

318

-0.215

-0.005***

0.000

0.924***

0.934

(-0.93)

(-2.87)

(0.07)

(45.45)

Notes: A constant term is included in the estimations. *, ** and *** indicate significance at the 10%, 5% and 1% level respectively. t-statistics are reported below coefficient estimates in brackets. The F-statistics for all estimations are significant past the 1% level.

Table 6 shows that none of the indicators have an effect that is significant and consistent across countries on bond-gold correlations. However, counter to the theory, real interest rates are a significant and negative factor in Germany and Japan. This could be explained if higher real interest rates indicate greater domestic currency instability, as depreciations reduce foreign demand for bonds while increasing the price of gold in the domestic currency and vice versa. Implied volatility has a weakly significant and positive effect on correlation in the US. This is consistent with flight-to-safety behaviour and supports the idea of the two assets acting simultaneously as safe havens against stocks during crises.

Repeating a similar analysis with use of global or US (a proxy for global) GDP indicator in addition to a domestic indicator may add relevance due to the importance of international trade for the countries’ economies and firms, especially the UK, Germany and Japan. However, given the relative insignificance of domestic growth expectations found by this paper and others and the similarity of business cycles between developed nations this would be unlikely to yield starkly different results.

Research using the absolute deviation of the GDP indicators from their mean may better capture times when real GDP growth expectations are more prominent in price determination and likely to impact on co-movement significantly.

Economic forecast data used in similar analyses is not freely accessible so was not used. Since asset pricing in largely determined by expectations and co-movement by changes or uncertainty in these expectations, economic forecast data on inflation, interest rates and GDP could improve the precision and directness of the analysis. Another approach that may be more direct is to try and estimate future uncertainty from past data, for example, by calculating the volatility of a rolling window of recent data. This approach has the benefit of focusing on uncertainty but it lacks use of any information on expectations.

Constructing an implied volatility index for Japan and extending the UK index would be useful for the analysis. It is possible as long as there is suitable option price data available, Anderson et al. (2008) constructed an implied volatility index in this way for the UK. Failing this, similar to above, calculating the volatility of a rolling window of stock returns could be useful.

Further analysis looking at uncertainty in the bond market, through implied bond price volatility indices or otherwise, would shed light on whether gold can act as safe haven for bonds.

Although pricing gold in the UK, Germany and Japan’s domestic currencies is consistent with the perspective of a domestic investor or central bank, further research could examine how the results might differ when gold is priced in USD. For a non-US investor this is the equivalent of buying gold and selling an equal value of USD and will result in different investment properties.

Gold stocks and not just physical gold often used in investment to gain exposure to the perceived benefits of gold. Repeating similar analysis using the returns on a basket of gold stocks instead of the returns on physical gold could be relevant to investors.

By examining a relatively broad base of developed nations, highly significant results are likely to apply across the developed world’s financial markets and are of use to investors and policy makers outside the four countries studied. However, as emerging market economies are not included in this analysis and have been shown in other papers to have distinct tendencies and characters (Baur and McDermott, 2010) caution and/or further study should be used before applying the conclusions of this paper more broadly.

6 Concluding remarks

This paper shows that the effect of implied stock volatility is significant and negative for both stock-bond and stock-gold correlations. The positive impact of real interest rates found in this paper is more prominent than in older studies. This may be due to the more recent data used and the unusual interest rate environment in recent year, with sharp central bank rate cuts followed by prolonged low or negative real rates. Compared to implied volatility, real interest rates have a high persistence, staying stable at levels substantially both above and below the mean. This allows for the characterisation of the real interest rate as the principal long-run driver of stock-bond co-movement, with implied volatility most prominent over the short and medium runs.

The findings of this paper could be of use to both investors and policy makers. Investors could make use of the additional information and analysis on the ability of bonds and gold to protect portfolio values in crisis times. Greater understanding of the impact of the real interest rate on co-movement could be used to adjust asset class weightings in a portfolio for improved mean-variance properties over the long term. Better understanding of asset class co-movement, in particular stock-bond correlation could assist monetary policy makers by allowing more accurate estimation of the monetary transition mechanisms. Anticipating the effect of crises on asset class correlations could help to inform regulation and improve predictions of financial system resilience.