Linking the interest rate swap markets to the macroeconomic risk: The UK and us evidence

International Review of Financial Analysis 22 (2012) 38–47

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International Review of Financial Analysis

Linking the interest rate swap markets to the macroeconomic risk: The UK and us evidence A.S.M. Sohel Azad a,⁎, Victor Fang a, Chi-Hsiou Hung b, 1 a b

School of Accounting, Economics and Finance, Faculty of Business and Law, Deakin University, 221 Burwood Highway, Burwood, Vic-3125, Australia Durham Business School, Mill Hill Lane, Durham University, Durham DH1 3LB, UK

a r t i c l e

i n f o

Article history: Received 15 February 2012 Received in revised form 27 February 2012 Accepted 5 March 2012 Available online 13 March 2012 JEL Classifications: E43 G12 Keywords: Interest Rate Swaps Low-frequency Volatility Macroeconomic Risk

a b s t r a c t In this paper we aim to link the volatility of interest rate swap (hereafter, IRS) markets to the macroeconomic risk/uncertainty of the UK and the US. In doing so, we obtain the low-frequency volatility of IRS using a recently developed Asymmetric Spline GARCH (ASP-GARCH) model of Rangel and Engle (2012). Our findings suggest a strong relationship between uncertainties of macroeconomic fundamentals and the fluctuation in swap market volatility. The association between the two is robust with respect to the choice of different alternative measures of volatility that are used in the literature on GARCH modelling. From the perspectives of practical implications, the findings suggest that policy makers should use low-frequency volatility in order to examine market responses to key macroeconomic policies, and that market participants may rely on lowfrequency volatility to extract trading signals. Using such signals, hedgers could make forecast of whether they need to increase (decrease) IRS usage to hedge risk originating from macroeconomic uncertainty. © 2012 Elsevier Inc. All rights reserved.

1. Introduction Financial economists have keen interests in guaging the macroeconomic driving forces of the risk and returns on assets, and seek to identify the causal relationship between the financial market and macroeconomic risk or uncertainty (Chen, Roll and Ross (1986), among others). 2 Prior research shows that macroeconomic risk plays an important role for hedging or speculation purposes with the use of derivatives. Beber and Brandt (2009), for example, conjecture that market participants use derivatives to hedge or speculate on macroeconomic risk. Cowen (2009) argues that underestimation of macroeconomic risk is one of the major sources of global financial crises. Among derivative market instruments, interest rate swaps (IRS) has a forward looking feature and has received extensive attention (see, for instance, Beber and Brandt (2009) and Azad, Fang and Wickramanayake (2011)).

⁎ Corresponding author. Tel.: + 61 392446873; fax: + 61 392446283. E-mail addresses: [email protected], [email protected] (A.S.M.S. Azad), [email protected] (C.-H. Hung). 1 Tel.: + 44 1913345498; fax: + 44 1913345201. 2 Influential prior research includes: Officer (1973), Schwert (1989), Hamilton and Lin (1996), Diebold and Yilmaz (2008), Lettau, Ludvigson and Wachter (2008), Genberg and Sulstarova (2008), Engle and Rangel (2008), Beber and Brandt (2009) and Azad et al. (2011). Beber and Brandt (2009) define macroeconomic risk as the market participants being unsure about the current state of the economy. We use the terms macroeconomic risk, macroeconomic uncertainty, macro-risk and macroeconomic volatility interchangeably in this paper. 1057-5219/$ – see front matter © 2012 Elsevier Inc. All rights reserved. doi:10.1016/j.irfa.2012.03.001

The recent BIS (2011) survey indicates that the outstanding ‘notional principal’ in swaps trading has grown from virtually nothing in the early 1990s to more than US $450 trillion in 2011, which has also surpassed that of the US Treasury debt. The phenomenal growth is also reflected in the Derivatives Usage Survey 2009 of ISDA, in which it shows that ranging from 70 to 94 percent of the world's largest corporations use swaps and other derivative products to manage their business and macroeconomic risks. This paper tests the hypothesis that there is a high (less) incentive for the hedgers to use swaps when macroeconomic risk or uncertainty is high (low). We decompose volatility into two components: (1) high-frequency or short-term volatility and (2) low-frequency or long-term volatility. One important advantage of this volatility decomposition is that, in contrast to the high-frequency component, low-frequency volatility generates a parsimonious volatility term structure that can be modelled as a function of macroeconomic risk to discover the macroeconomic sources of variation in volatility term structure. In addition to examining the responses of low-frequency IRS volatility to changes in macroeconomic risks, this paper contributes to the literature by examining the lead-lag relationship between IRS and macroeconomic risk. In regards to the benefits of using low-frequency volatility, Engle and Lee (1999), Adrian and Rosenberg (2008), Engle and Rangel (2008) and Azad et al. (2011) show that the low-frequency component represents the slow moving trend that varies systematically with fundamental economic variables. They find that the use of the low-frequency component indicates a stronger relationship between macroeconomic risk and the volatility of the financial market. To our best knowledge, our paper is

A.S.M.S. Azad et al. / International Review of Financial Analysis 22 (2012) 38–47

the first that uses Asymmetric Spline GARCH (hereafter ASP-GARCH) model of Rangel and Engle (2012) to estimate and decompose the aggregate volatility shocks in IRS markets into high and low-frequency components. Our approach is also in line with that of Azad et al. (2011). Azad et al. (2011) point out that the economically and statistically insignificant (albiet positive) relationship between macroeconomic risk and volatility in stocks, bonds and derivatives markets reported in the extant research is largely due to misspecification of volatility. For example, many studies use aggregate volatility shocks as a proxy for financial market volatility (see, e.g., Schwert (1989), Hamilton and Lin (1996), Diebold and Yilmaz (2008)). Our sample covers the major international swap markets in the UK and the US for different maturities. The two markets together represent around 40% of the total swap market during the period from June 1998 to June 2010. Data for the empirical analysis span from October 1989 to April 2010 meaning that almost the entire history of swap is incorporated into the empirical analysis. Importantly, we find a positive and statistically significant relationship between interest rate swaps and most of the macroeconomic variables. We also find that some macroeconomic variables (CPI volatility and money supply in the UK; interest rate volatility and industrial production volatility in the US) are negatively correlated with the US swap market. The explanations of the mixed findings are provided in the result section. In terms of the explanatory power, the results for the UK show the best fit. There is also a bi-directional causality between macroeconomic risk variables and low-frequency IRS volatility for both markets. Interestingly, our findings suggest that swap market volatility leads macroeconomic risk variables, which implies that swap market volatility contains a fair amount of information in predicting macroeconomic risk/uncertainty. Schwert (1989), Engle, Ghysels and Sohn (2008) and Azad et al. (2011) also report similar findings in different financial markets. We conduct robustness tests including the use of alternative measures of volatility: the benchmark long-term volatility obtained from C-GARCH model of Engle and Lee (1999) and the model-free realised volatility. These alternative volatility measures are then regressed on the macroeconomic risk proxies. The evidence suggests that, compared with these two alternative measures, the low-frequency volatility obtained from using Rangel and Engle's (2012) approach gives a strong link between the swap market and the macroeconomy. Moreover, the use of low-frequency volatility results in higher adjusted R-squared statistics compared to the alternative measures. The rest of this paper is organised as follows. Section 2 describes the data, variables and a summary of directional hypotheses of macroeconomic risk. We give the methodology in Section 3, and critically

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analyse the empirical findings in Section 4. Section 5 shows robustness checks and Section 6 concludes. 2. Data and variable description 2.1. Data We use the swap rates and macroeconomic variables in the UK and the US. We estimate low-frequency volatilities of IRS from daily closing mid-rates on swap maturities of 5 and 10 year. These maturities represent shorter to longer maturities, respectively, and are relatively more liquid than other maturities. Swaps data are collected from DataStream. Since our macroeconomic variables are in monthly observations, while the swap rates are in daily observations, we need to obtain a measure of monthly low-frequency IRs volatilities. The procedure is explained in the methodology section. Data for macroeconomic variables are collected from different sources, which are discussed in Table 1. Empirical analysis covers the period from October 1989 to April 2010. As noted, this sample represents almost the entire history of swap. 2.2. Variable description The dependent variables are the low-frequency swaps volatilities, while the explanatory variables are the proxies for macroeconomic risk and variables related to economic policies as in Azad et al. (2011). Azad et al. (2011) explain the reasons why those macroeconomic variables are chosen, particularly in swap markets. Taking the same variables also helps us making a cross-country comparison of empirical findings. Since volatilities are not directly observable in each country and for each swap maturity, we estimate the daily low-frequency volatility by using the Asymmetric Spline-GARCH of Rangel and Engle (2012) which is an improvement over that of Engle and Rangel (2008). We then take the average of the daily low-frequency volatilities for the respective month considering 21 trading days in a month. For robustness checks, we also consider two alternative measures of low-frequency volatilities: the benchmark long-term volatility from Engle and Lee's (1999) additive volatility decomposition, and the model-free realised volatility. We obtain these three measures of volatilities for each swaps maturity. Further, since the theory does not indicate an entirely one-way relationship between financial markets and macroeconomy, we expect a lead-lag/feedback relationship between the two, following Chen et al. (1986), Schwert (1989) and Azad et al. (2011). Studying this relationship has several benefits. First, one can investigate whether policy makers implicate the market reactions (feedback effects) into the

Table 1 Macroeconomic Variables, Proxies and Predicted Signs. This table summarises the macroeconomic risk variables, relevant proxies and their predicted signs, and the source of data. We take the conditional volatility from GARCH (1,1) to proxy for the volatility of innovations on macroeconomic fundamentals, similar to Bansal and Yaron (2004) and Wachter (2006). Macroeconomic Variables

Proxies/transformations

Pred. Sign on Low-frequency IRS Volatility

Source

Volatility of industrial production Volatility of CPI

Conditional volatility from a GARCH (1,1) model obtained from industrial production index Conditional volatility from a GARCH (1,1) model obtained from seasonally adjusted consumer price index Conditional volatility from a GARCH (1,1) model obtained from short-term bond index yield (3-month) Option implied volatility, obtained from the real effective exchange rate

+/−

DataStream

+

DataStream

+

DataStream

+

DataStream

Difference between long-term and short-term Treasury Bond (TB) yield Changes in seasonally adjusted unemployment rate (Volume or percentage) changes from the previous month in average amounts outstanding/money stock

+/− +/− +

DataStream DataStream Central banks, DataStream

Volatility of interest rate Foreign exchange volatility Slope of the yield curve Unemployment rate Money supply (M2)

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A.S.M.S. Azad et al. / International Review of Financial Analysis 22 (2012) 38–47

subsequent policy decisions and, hedgers (speculators) can hedge (speculate) to reduce the impact of macroeconomic uncertainty on their interest rate risk exposure. Second, the notion that market volatility (IRS volatility in this paper) helps predict the movement of macroeconomic variable is also captured (Schwert (1989)). That is, the degree of responses of macroeconomic risk to a change in low-frequency IRS volatility can be ascertained. 3. Estimation methodology This section explains the methodologies to estimate and decompose the aggregate IRS volatility into two components namely, highand low-frequency volatility components. Having obtained this, we model low-frequency volatility for each country as a function of macroeconomic risk.

a company across the domestic and international markets [Nishioka and Baba (2008)]. A negative c in Eq. (3) implies the presence of leverage effect, that is, negative shocks have a larger effect than the positive shocks on the high-frequency volatility component. 3.2. Linking irs volatility to macroeconomic uncertainty Following Adrian and Rosenberg (2008), Engle and Rangel (2008) and Azad et al. (2011), we model low-frequency IRS volatility as a function of macroeconomic and related policy variables that have relationships with the IRS markets.3 Specifically, we run the following timeseries OLS regression for each swap maturity of the UK and the US: Lowvoli;t ¼ ci;0 þ θi;1 cpivolt þ θi;2 ipvolt þ θi;3 irvolt þ θi;4 f xvolt þ θi;5 slopet þ θi;6 unemt þ θi;7 m2t þ μ i;t

ð4Þ

3.1. Estimating and decomposing aggregate irs volatility We use the Asymmetric Spline-GARCH of Rangel and Engle (2012) to estimate aggregate IRS volatility and to decompose that volatility into high-frequency and low-frequency components as follows: Δr i;t ¼

qffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffi hi;t εi;t ¼ g i;t :τi;t εi;t ; εi;t Φt−1 eN ð0; 1Þ

 ε2i;t−1 c g i;t ¼ 1−α i −βi − i þ α i 2 τi;t−1 0 τi;t

¼ γ 0;i exp@γ1;t t þ

k X j¼1

! þ ci

! ε2i;t−1 þ βi g i;t−1 I τ i;t−1 ri;t−1b0

1   2 A ωj;i t−t j−1 þ

ð1Þ

ð2Þ

ð3Þ

where Δri, t(=ri, t −μi, t) indicates the swap rates changes for maturities i=1, 2 (i.e., 5 and 10 years) on day t for each country (UK and US). The aggregate volatility hi, t is decomposed into (i) gi, t and (ii) τi, t, where, gi, t and τi, t characterise the high- and low-frequency volatility components, respectively, on day t for swap maturities i. High-frequency volatility is quickly mean-reverting, while low-frequency volatility is slowly meanreverting (Engle and Rangel (2008) and Adrian and Rosenberg (2008)). Despite its persistence, gi, t does not have a long-term impact on hi, t. It is the term, τi, t, which has a persistent impact on hi, t. Therefore, for subsequent analysis that investigates the relationship between macroeconomic risks and swap market volatility), we only consider low-frequency volatility τi, t. Φt − 1 denotes an extended information set including the history of swap rates changes up to day t−1. Given the estimates for γ=(γo, γ1)' and ωj(j=1 to k) a sequence of {tj}jk= 1 (where t1 >1 and tk ≤T, denotes a division of the time horizon T in k equally spaced intervals) can be estimated. The spline fits a smooth curve to a sequence of points {τtj}jk= 1 that are unobserved and based on the spline parameters. For each maturity, following parameters for the above ASP-GARCH model: α,β, c,γ=(γo γ1)' and ωj(j=1 to k) are estimated. To choose an ‘optimal’ number of knots k, we use the Bayesian Information Criteria (BIC). k governs the cyclical pattern in τi, t. Large values of k imply more frequent cycles. The coefficient, {ωj}, measures the ‘sharpness’ (i.e., the duration and strength) of each cycle. The term Iri, t − 1 b 0 in (3) is an indicator function of negative shocks (asymmetry in volatility). This function is included to accommodate the leverage effects. Why should such leverage effect be entertained by the GARCH specification? Statistically, it is found that a negative shock (or an unexpected drop in price, i.e., bad news) to financial time series increases the predictable volatility more than a positive shock (or an unexpected increase in price, i.e., good news) of similar magnitude. In the case of equity returns, for instance, a drop in equity price causes the firm's debt to equity ratio to rise dramatically. This leads the investor's future cash flow to be more unstable and risky. In swaps, it is linked to skewness risk, which can originate from the credit spread differential of

Where, Lowvoli, t Low-frequency volatility for swap maturities i for period t is obtained from Eq. (3) cpivolt Volatility of consumer price index ipvolt Volatility of industrial production irvolt Volatility of short-term interest rate fxvolt Volatility of foreign exchange rate slopet Slope of the term structure unemt Unemployment rate m2t Money supply To reiterate, the choice of the explanatory variables is guided by economic theory and their importance and relevance supported by prior literature (on swap markets as well as on low-frequency volatility). In order to have robust results, the study selects those macroeconomic variables for which data are available in monthly frequency. For instance, since the gross domestic product (GDP) data are only available at a quarterly frequency while the analysis is monthly, the study uses industrial production growth as a proxy for the growth rate of GDP. Further, since there is no intensive study linking macroeconomic risk to the behaviour of swaps markets, this study relies on the literature that focuses on volatility decomposition and that investigates the impact of macroeconomic risk on financial markets. Previous studies suggest that both the levels as well as volatilities of macroeconomic variables can be used to proxy for macroeconomic risk. We expect that a statistically significant relationship exists between those macroeconomic risk proxies and the low-frequency IRS volatility. Since we take monthly observations for macroeconomic volatility/risk, it is essential to have a measure of monthly lowfrequency IRS volatility, which can be calculated using Eq. (5): vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N i;t u 1 X Lowvoli;t ¼ t τ Ni;t d¼1 i;d;t

ð5Þ

where, Lowvoli, t stands for low-frequency volatility of swap in month t swap for maturity i (=5 and 10). Ni, t is the number of trading days in a month for maturity i. τi, d, t is the daily low-frequency volatility observed for maturity i of swap quote day d at year t. Macroeconomic risks, other than Slope, UNEM and M2, are proxied by the conditional volatility of GARCH (1,1) model. 3 High-frequency volatility or skewness risk is more of an idiosyncratic risk (company related factor). This is why prior empirical literature did not focus on the highfrequency component to investigate its linkage with macroeconomic risks (see also Azad et al. (2011) for a review of literature).

A.S.M.S. Azad et al. / International Review of Financial Analysis 22 (2012) 38–47 2.4

Table 2 Estimation Results of ASP-GARCH for Different Swap Maturities.

LVOL_5 HVOL_5

This table shows the estimation results of ASP-GARCH model of Rangel and Engle (2012). The model specification is provided in Eqs. (1)–(3). The sample covers the daily observations from October 1989 through April 2010. α and β are the ARCH and GARCH effects, respectively, while the coefficient c measures whether there is any asymmetric effect. ωj(j = 1 to k) are the coefficients that measure the duration and strength of business cycles. * and ** indicate level of significance at 5% and 1% respectively. Standard errors of the estimated coefficients are in parentheses.

2.0

Parameters

0.8

α β c ω1 ω2 ω3 ω4 ω5 ω6 ω7 ω8 ω9 ω10 ω11 ω12

UK

41

US

1.6

1.2

5-year swap

10-year swap

5-year swap

10-year swap

0.0649*** (0.0041) 0.9083*** (0.0057) − 0.0238*** (0.0052) 0.0346*** (0.0014) − 0.0785*** (0.0015) 0.0926*** (0.0009) − 0.0789*** (0.003) 0.03815*** (0.006) − 0.0075 (0.0074) − 0.0077 (0.0081) 0.0257*** (0.0086) − 0.0398*** (0.0093) 0.0262** (0.0106) 0.0329** (0.0128) − 0.1167*** (0.020)

0.0403*** (0.0031) 0.9577*** (0.0024) − 0.0175*** (0.0038) 0.0403*** (0.0011) 0.9577*** (0.0018) − 0.0175 (0.0015) − 7.9402 (0.0018) 1.6587 (0.0030) __

0.0411*** (0.0053) 0.9293*** (0.0078) − 0.0109** (0.0051) 0.0092*** (0.0009) − 0.0128*** (0.0015) 0.0093*** (0.0011) − 0.0146*** (0.0011) 0.0337*** (0.0015) __

0.4

__

__

__

__

__

__

__

__

0.0468*** (0.0063) 0.9154*** (0.0112) − 0.0235*** (0.0064) 0.0001 (0.0044) 0.0109* (0.0066) − 0.0143*** (0.0045) − 0.0003 (0.0039) 0.0115*** (0.0034) − 0.0088*** (0.0032) − 0.0166*** (0.0036) 0.0526*** (0.0045) − 0.0833*** (0.0070) __

__

__

__

0.4

__

__

__

4. Estimation results and discussion 4.1. Asymmetric spline-garch results and summary stats This sub-section reports the estimation results of the ASP-GARCH model of Rangel and Engle (2012) for 5- and 10-year swap maturities of the UK and the US. For each swap maturity, we use its daily swap rate changes and estimate the ASP-GARCH model. Table 2 reports the parameter estimates, where α and β indicate the ARCH and GARCH effects, respectively. It is noticeable that asymmetric effect (measured by c) in the high-frequency component appears in both the countries. The additional parameters, γ =(γo γ1)' and ωj(j =1 to k), also need to be estimated for the ASP-GARCH model. For optimal knot points, k, which indicates the cyclical effects in the series, we try up to 20 knot points using BIC. As noted in the methodology section, the large values of k imply more frequent (business) cycles. The coefficients ωj measure the ‘sharpness’ (i.e., the duration and strength) of each cycle (Engle and Rangel (2008)). The results show that the maximum knot points are observed with 5-year UK swap rate followed by the 10-year US swap rate. The variation in the number of knots is attributed to the market volatility patterns of the respective swap maturity and market as well as to their responses to business cycle risks during the sample period. The coefficients ωj are highly significant for most knot points. This suggests that the swap market could be highly responsive/indicative to business cycle risk. Figs. 1–4 provide a visual inspection of the two volatility measures: daily high- and low-frequency volatilities, respectively, for the UK and the US. The analysis represents only 5-year and 10-year swap maturities. The high-frequency component is associated with

0.0 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008

Fig. 1. HV and LV of 5-year UK swap.

2.2 HVOL_10 LVOL_10

2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6

1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008

Fig. 2. HV and LV of 10-year UK swap.

the short-run conditional volatility, and the low-frequency component is associated with the slow-moving trend that characterises the unconditional volatility, which is deemed to be driven by macroeconomic risk (Engle and Rangel (2008)). It is evident that the sterling swaps market was highly volatile during the early stages of swap market development including the 1990s. Similar findings are also reported by Gupta and Subrahmanyam (2000), who find that the swap market was volatile during 1991 – 93. Further, we find that volatility increases during the middle and last parts of our sample periods. The US swap market was less volatile during the 1990s. With the beginning of the new century volatility started to decline and began to rebound from 2004. The global financial crisis struck both economies. Overall, the low-frequency component reveals the facts that the volatilities of the swaps market are 3.5 3.0

LVOL_5 HVOL_5

2.5 2.0 1.5 1.0 0.5 0.0 89 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09

Fig. 3. HV and LV of 5-year US swap.

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A.S.M.S. Azad et al. / International Review of Financial Analysis 22 (2012) 38–47 4.0 LVOL_10 HVOL_10

3.6 3.2 2.8 2.4 2.0 1.6 1.2 0.8 0.4

87 88 89 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10

Fig. 4. HV and LV of 10-year US swap.

closely related to business cycle fluctuations determined by the major institutions like: (i) Office for National Statistics (UK), and (ii) National Bureau of Economic Research (NBER, US). For the subsequent analysis, the low-frequency volatilities (from swap maturities of 5-year and 10-year) are needed for the two countries. Since the study uses monthly observations for macroeconomic variables, we convert the daily low-frequency volatilities into monthly observations using Eq. (5). Tables 3 and 4 show the summary statistics and the correlation matrix, respectively, for the UK. The volatility measures for CPIVOL, IPVOL and IRVOL are obtained by using the GARCH (1,1), while the one-month option implied volatility for the FXVOL is directly observed from DataStream. The unemployment rate is taken into first difference/change as the level data are non-stationary. The money supply is the monthly change in broad money supply from the previous month. The low-frequency volatility correlations between the 5year and 10-year swaps are very high. The correlations between the low-frequency volatilities and the three macroeconomic risk proxies

(CPIVOL, IRVOL and slope) are positive, while the correlations between the low-frequency volatilities and the four macroeconomic risk proxies (IPVOL, FXVOL, UNEM and M2) are negative. The descriptive statistics and the correlation matrix for the US are reported in Tables 5 and 6, respectively. The volatility measures for CPIVOL, IPVOL, IRVOL and FXVOL are obtained by using the GARCH (1,1). The trade-weighted value of the US dollar against major currencies is used for computing the FXVOL. The slope is defined as the yield differences between the 20-year constant maturity and the 3-month Treasury bill. Similar to the UK, the unemployment rate (UNEM) is the change instead of the level as it is non-stationary. As always, the correlations of low-frequency volatility across the different maturities (5-year and 10-year swap) are very high. Of the several macro-risk proxies, the IRVOL and M2 are negatively correlated with the 5-year swap, while only M2 is negatively correlated with the 10-year swaps. The other macro-risk proxies are positively correlated with the swaps. Before we explore the relationship between swap market volatility and macroeconomic risk, we test the unit root of the macro-risk variables. The stationarity of the macro-risk variables is confirmed with the Augmented Dickey-Fuller (ADF) unit root test. Table 7 reports the ADF test statistics which indicate that the null of unit root is rejected for all the variables in the two countries. The test is conducted on the level series with the exception of UNEM, which shows unit root at level. So, we consider first differences of UNEM for both countries. 4.2. Regression results Table 8 reports the OLS regression results using Eq. (4). The analysis is based on a sample covering from October 1989 to April 2010. The model appears to have the best fit for the UK followed by the US, and in terms of maturity, it is the 10-year swaps followed by 5year swaps. However, in terms of relationship the US swaps market is highly correlated with most of the macroeconomic variables. The results also show that for the 5-year sterling swap market, variables

Table 3 Descriptive Statistics (UK). This table provides a summary statistics for the dependent and explanatory variables. The daily interest rate swap volatility is measured using Eq. (3) and converted into monthly low-frequency volatility (LVOL) using Eq. (5). Volatility of macroeconomic variables is measured by GARCH (1,1). Unemployment is a change in the unemployment rate from the previous month. The money supply is monthly change in broad money supply from the previous month. *** indicates the level of significance at 10%. The analysis covers the data for the period from October 1989 to April 2010 with 247 monthly observations.

Mean Median Maximum Minimum Std. Dev. Skewness Kurtosis Jarque-Bera

LVOL_5

LVOL_10

CPIVOL

IPVOL

IRVOL

FXVOL

SLOPE

UNEM

M2

1.4676 1.4981 1.5587 1.2638 0.0904 − 0.7242 2.2082 28.1585***

0.9163 0.9145 1.0574 0.7799 0.1062 0.0162 1.3122 29.4458***

0.1402 0.1448 0.1685 0.0600 0.0212 − 1.6310 5.8929 211.4767***

0.8248 0.7028 6.1879 0.5035 0.4153 7.3253 83.4081 99644.8800***

0.0612 0.0405 0.1793 0.0170 0.0427 1.1602 3.4861 84.0718***

8.9970 8.3000 26.5000 4.6500 3.0485 2.7608 13.2809 1049.7520***

0.0006 − 0.0300 1.2600 − 1.0400 0.3205 0.3503 4.2420 30.3315***

0.0011 0.0000 0.5000 − 0.3000 0.1182 0.6496 4.2090 47.1167***

3272.7170 2463.0000 24545.0000 − 17469.0000 3262.6250 0.9164 15.3544 2157.86***

Table 4 Correlation Matrix (UK). This table indicates the correlation among the low-frequency volatilities (LVOL) of 5- and 10-year swap maturities and the macro-risk variables. The analysis covers the data for the period from October 1989 to April 2010 with 247 monthly observations.

LVOL_5 LVOL_10 CPIVOL IPVOL IRVOL FXVOL SLOPE UNEM M2

LVOL_5

LVOL_10

CPIVOL

IPVOL

IRVOL

FXVOL

SLOPE

UNEM

M2

1 0.8686 0.2524 − 0.0741 0.9005 − 0.3862 0.0014 − 0.5205 − 0.3466

0.8686 1 0.0567 − 0.0806 0.9329 − 0.1711 0.0016 − 0.4725 − 0.4226

0.2524 0.0567 1 − 0.1471 0.2796 − 0.5003 0.0134 − 0.3544 0.0932

− 0.0741 − 0.0806 − 0.1471 1 − 0.1063 0.2120 − 0.0170 0.2409 0.0410

0.9005 0.9329 0.2796 − 0.1063 1 − 0.3085 − 0.0172 − 0.5063 − 0.3729

− 0.3862 − 0.1711 − 0.5003 0.2120 − 0.3085 1 − 0.0340 0.4727 − 0.1719

0.0014 0.0016 0.0134 − 0.0170 − 0.0172 − 0.0340 1 − 0.0305 0.0306

− 0.5205 − 0.4725 − 0.3544 0.2409 − 0.5063 0.4727 − 0.0305 1 0.0575

− 0.3466 − 0.4226 0.0932 0.0410 − 0.3729 − 0.1719 0.0306 0.0575 1

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Table 5 Descriptive Statistics (US). This table provides a summary statistics for the dependent and explanatory variables. The daily interest rate swap volatility is measured using Eq. (3) and converted into monthly low-frequency volatility (LVOL) using Eq. (5). Volatility of macroeconomic variables is measured by GARCH (1,1). Unemployment is a change in the unemployment rate from the previous month. The money supply is monthly change in broad money supply from the previous month. ** and *** indicate the level of significance at 5% and 10%, respectively. The analysis covers the data for the period from October 1989 to April 2010 with 247 monthly observations.

Mean Median Maximum Minimum Std. Dev. Skewness Kurtosis Jarque-Bera

LVOL_5

LVOL_10

CPIVOL

IPVOL

IRVOL

FXVOL

SLOPE

UNEM

M2

1.0119 1.0112 1.6729 0.8167 0.1244 1.8374 9.7941 609.0728***

0.9809 0.9784 1.2427 0.7651 0.1033 0.2991 3.3547 4.9371**

0.0292 0.0264 0.0912 0.0151 0.0113 1.7457 7.4749 328.8494***

0.4756 0.2650 9.6185 0.1435 0.9058 7.0524 59.8972 35078.25***

0.0774 0.0458 0.8723 0.0197 0.0915 4.2534 29.2547 7775.468***

3.6574 3.4760 7.7559 2.2956 0.9896 1.4642 5.5876 155.896***

2.1330 1.9600 4.4300 − 0.3300 1.3538 0.0357 1.7326 16.4487***

0.0180 0.0000 0.5000 − 0.4000 0.1563 0.5135 3.5919 14.3414***

13.1718 10.3000 200.6000 − 68.9000 28.5406 2.1414 13.4540 1302.875***

Table 6 Correlation Matrix (US). This table indicates the correlation among the low-frequency volatilities (LVOL) of 5- and 10-year swap maturities and the macro-risk variables. The analysis covers the data for the period from October 1989 to April 2010 with 247 monthly observations.

LVOL_5 LVOL_10 CPIVOL IPVOL IRVOL FXVOL SLOPE UNEM M2

LVOL_5

LVOL_10

CPIVOL

IPVOL

IRVOL

FXVOL

SLOPE

UNEM

M2

1 0.8643 0.2996 0.0852 − 0.1327 0.5510 0.7065 0.0972 − 0.0959

0.8643 1 0.2503 0.2742 − 0.0484 0.5831 0.7340 0.2164 0.0410

0.2996 0.2503 1 0.1955 − 0.0986 0.2626 0.2095 0.2062 0.0987

0.0852 0.2742 0.1955 1 0.1957 0.3105 0.1507 0.3911 0.4360

− 0.1327 − 0.0484 − 0.0986 0.1957 1 − 0.0214 0.0858 0.1852 0.2121

0.5510 0.5831 0.2626 0.3105 − 0.0214 1 0.3661 0.2576 0.1023

0.7065 0.7340 0.2095 0.1507 0.0858 0.3661 1 0.1106 − 0.0394

0.0972 0.2164 0.2062 0.3911 0.1852 0.2576 0.1106 1 0.2229

− 0.0959 0.0410 0.0987 0.4360 0.2121 0.1023 − 0.0394 0.2229 1

related to monetary shocks (interest rate volatility, IRVOL and money supply, M2) are significant, while for the 10-year sterling swap market, CPIVOL and IRVOL are significant. That is, monetary policy variables are important driving forces for the low-frequency IRS volatility of the UK markets. The low-frequency volatility of 5-year US dollar swaps market is negatively related to industrial production volatility and interest rate volatility, but positively related to FXVOL and the slope. The 10-year US dollar swap is positively associated with IPVOL, FXVOL and the slope but negatively associated with IRVOL. The coefficient of CPI volatility (CPIVOL) is statistically significant, large in magnitude, and negative for the 10-year UK swap. This finding implies that macro-risk may help resolve uncertainty in swap markets. Brenner, Pasquariello and Subrahmanyam (2006) relate such phenomenon to ‘storm before the calm hypothesis’. The hypothesis states that macroeconomic risk may lessen the degree of confusion or information heterogeneity among market participants, thus reducing the low-frequency volatility of swap. This proposition is related to the causality test reported in Table 10 where CPIVOL appears to lead the relationship in the case of 10-year UK swap. Table 7 Unit Root Tests of Macroeconomic Risk Proxies. This table shows the Augmented Dickey-Fuller (ADF) unit test statistics and p-values for the macroeconomic risk proxies. The critical values for the ADF test are −3.4594, -2.8742 and −2.5736 at 1%, 5% and 10% respectively. Macro-risk Variables

UK ADF test stats

p-value

US ADF test stats

p-value

CPIVOL IPVOL IRVOL FXVOL SLOPE UNEM M2

− 3.94 − 17.09 − 4.37 − 3.38 − 14.01 − 3.28 − 3.83

0.002 b 0.000 b 0.000 0.013 b 0.000 0.016 0.003

− 3.54 − 6.28 − 3.07 − 3.87 − 2.95 − 4.32 − 8.41

0.0074 b0.000 0.029 0.002 0.040 b0.000 b0.000

In the US market, the coefficient of IPVOL is statistically significant and negative for the 5-year maturity but positive for the 10-year maturity. Such a varying degree of relationship is observed in the prior researches in different financial markets. As Table 9 shows macroeconomic variables have both positive and negative influences on the financial markets. As regards the IPVOL, its positive coefficient indicates that an increase in the volatility of industrial production increases the low-frequency volatility of swap. As shown in Table 9, Diebold and Yilmaz (2008) report similar results in different financial markets. Relating to negative coefficient of IPVOL, Officer (1973) argues that the drop in stock market volatility in the 1960s was induced by reduced variability in industrial production. In contrast to findings from stock markets, our empirical results have different implications. For instance, as argued by Genberg and Sulstarova (2008), the variability of GDP or industrial production raises the probability of default, which in turn increases the default risk and raises the interest rate. Thus, according to this explanation, when the macroeconomy is volatile, investors fear such volatility, and the volatility of industrial production increases the volatility of swaps markets instead of reducing it. A negative coefficient as observed for the 5-year US swaps is consistent with prior empirical studies including those of Schwert (1989), Hamilton and Lin (1996), Adrian and Rosenberg (2008) and Engle and Rangel (2008) in other financial markets. The negative influence of IPVOL can be linked to the theory of ‘irreversibility in investment’ or ‘diminishing returns to investment’ (Keynes (1936), Pindyck (1991)). This theory indicates that there is an inverse relationship between macroeconomic risk and investment. That is, an increased volatility leads to uncertainty regarding long-term profitability of investment, which in turn discourages the market participants to use IRS as a hedging instrument. Thus, according to the theory of ‘irreversibility in investment’, IPVOL pushes down the demand for IRS and its volatility. The coefficient of interest rate volatility (IRVOL) is highly significant for both the UK and the US markets. It is well known that the rise of the swaps market is attributable to the volatile interest rates

44

A.S.M.S. Azad et al. / International Review of Financial Analysis 22 (2012) 38–47

Table 8 Low-Frequency Volatility of Swap and Macroeconomic Risk. Results from the following OLS regression model (see Eq. (4) for details): Lowvoli, t = ci, 0 + θi, 1cpivolt + θi, 2ipvolt + θi, 3irvolt + θi, 4fxvolt + θi, 5slopet + θi, 6unemt + θi, 7m2t + μi, t where, the dependent variable is the low-frequency volatility (Lowvol) obtained from using Eq. (3). See Table 1 for details of the right-hand side variables (macroeconomic variables). Standard errors of the estimated coefficients are in parentheses and are corrected for autocorrelation and heteroskedasticity by using the Newey-West method. Sample covers the period from October 1989 through April 2010 for both the UK and the US with 247 monthly observations. *, ** and *** indicate level of significance at 10%, 5% and 1%, respectively. For brevity, the empirical analysis is conducted on full sample only. Azad et al. (2011) conduct an analysis of full sample and sub-samples to identify the variation in relationship during the crisis periods. Pred. sign Intercept CPIVOL

+

IPVOL

+/−

IRVOL

+

FXVOL

+

SLOPE

+/−

UNEM

+/−

M2

+

Adjusted R2 F-stat

UK

US

5-year swap

10-year swap

5-year swap

10-year swap

1.2388 − 0.5039 (0.9425) 0.0098 (0.0066) 10.9007*** (3.8414) − 0.0044 (0.0029) 0.0045 (0.0052) − 0.0579 (0.0658) − 1.41E-06* (7.79E-07) 0.8273 125.5877***

0.7386 − 1.7719*** (0.4815) 0.0003 (0.0031) 13.5994*** (1.0605) 0.0016 (0.0013) 0.0087 (0.0056) − 0.0887 (0.0874) − 8.81E-07 (8.80E-07) 0.9195 298.1233***

0.7331 1.0547 (1.7636) − 0.0100** (0.0047) − 0.1888*** (0.0526) 0.0427*** (0.0078) 0.0537*** (0.0119) − 0.0066 (0.0441) − 0.0002 (0.0002) 0.6344 61.4738***

0.7662 − 0.0132 (0.8621) 0.0093** (0.0049) − 0.1387** (0.0543) 0.0330*** (0.0091) 0.0466*** (0.0123) 0.037 (0.0257) 3.95E-05 (0.0002) 0.6638 69.8358***

markets in the early 1970s. A positive association is therefore empirically appealing for the UK. Moreover, since increasing interest rate volatility is often associated with economic uncertainty, it affects the default risk of both swap counterparties, thereby increasing the volatility in IRS market. Earlier studies, which use aggregate volatility models, report mixed results on the coefficient of IRVOL on the swap (e.g., In, Brown and Fang (2003)). A somewhat theoretically inconsistent result is obtained for the US swap market. Using different proxies of short-term interest rate (e.g., US TB 3-month and 6-month etc.), we still find negative coefficient of the IRVOL. There are two explanations for such findings.

Table 9 Prior Studies in Different Financial Markets. This table presents a summary of prior literature on the impact of macroeconomic variables on (low-frequency) volatility. IP = Industrial production; IRs = shortterm interest rates; SY = slope of the yield curve; CPI = Consumer Price index; PPI = Producer Price Index; UE = Unemployment rate; Ex = Exchange rates. Most studies in this table use the second moments of the macroeconomic variables with the exception of unemployment rate and slope of the yield curve. Studies

Effect of macroeconomic variables on (lowfrequency) volatility GDP

Jones, Lin and Masih (2005) Äijö (2008) Abugri (2008) Adrian and Rosenberg (2008) Diebold and Yilmaz (2008) Engle and Rangel (2008) Engle et al. (2008) Nowak et al. (2009) Azad et al. (2011)

IP

IRs

SY

CPI

+ + + − + +

UE − +

−

Ex

− + +

+ +/−

− +

+/− +

PPI + +

+

+

+/− +

+/− −

+

First, our results in a separate set of regressions (not reported for brevity) confirm that the coefficient of IRVOL was positive during the 1990s, indicating that markets responded positively towards the rise of interest rate volatility. However, since the late 1990s the coefficient becomes negative. So the negative coefficient during the latter half of the sample could influence the sign of the coefficient for the entire sample. In a study on the US swaps market, Apedjinou (2005) attributes the variations in the sign of the coefficient to structural factors and the economic environment. The change in the coefficient of IRVOL could be related to investors’ revisions of expectation. The positive coefficient in the early period (1990s) implies that investors sought protection against IRVOL and hence, trading activities in swaps increased. Later, market participants revised their expectations based on their previous knowledge on the relationship between interest rate volatility and the swaps. Consequently, when IRVOL increases, the hedging activities through IRS might have decreased temporarily and substituted by other derivatives such as interest rate forwards. Second, a feedback relationship or dynamic interaction between interest rate volatility and low-frequency IRS volatility as observed in Table 10 implies that investors implicate the policy changes into their revised investment decisions. Thus, a change in swaps users’ perception could have led to negative coefficient of IRVOL. The FXVOL has a positive and statistically significant influence on the low-frequency volatility of all swaps. The positive coefficient is consistent with the prior empirical finding of Azad et al. (2011) in Japanese market. Most international banks offer IRS to organisations that are concerned about the foreign exchange rate risk when making interest payments. Although banks charge relatively lower costs for making such arrangements, these costs eventually translate into higher swap rates because of the increased volatility of the exchange

Table 10 Pair-wise Granger Causality Tests. This table shows the pair-wise Granger causality test results between macroeconomic risk variables and low-frequency IRS volatility. In parentheses are p-values. Low-Vol stands for the low-frequency volatility of swap. Sample covers the period from October 1989 through April 2010 with 247 monthly observations. *, ** and *** indicate level of significance at 10%, 5% and 1%, respectively. Null Hypothesis

CPIVOL does not Granger Cause Low-Vol Low-Vol does not Granger Cause CPIVOL IPVOL does not Granger Cause Low-Vol Low-Vol does not Granger Cause IPVOL IRVOL does not Granger Cause Low-Vol Low-Vol does not Granger Cause IRVOL FXVOL does not Granger Cause Low-Vol Low-Vol does not Granger Cause FXVOL SLOPE does not Granger Cause Low-Vol Low-Vol does not Granger Cause SLOPE UNEM does not Granger Cause Low-Vol Low-Vol does not Granger Cause UNEM M2 does not Granger Cause Low-Vol Low-Vol does not Granger Cause M2

UK

US

5-year

10-year

5-year

10-year

3.1405** (0.0450) 3.156** (0.0444) 0.0642 (0.9379) 0.5814 (0.5599) 84.757*** (b 0.0001) 1.6275 (0.1986) 9.7939*** (0.0001) 2.9673* (0.0540) 0.0364 (0.9642) 0.0567 (0.9449) 5.9260*** (0.0031) 2.8023* (0.0627) 18.8204*** (b 0.0001) 16.3226*** (b 0.0001)

20.3934*** (b 0.0001) 1.6552 (0.1932) 0.4232 (0.6555) 0.6504 (0.5228) 103.4260*** (b 0.0001) 0.2364 (0.7896) 3.5147** (0.0318) 2.9358* (0.0557) 0.0343 (0.9663) 0.0132 (0.9869) 30.8084*** (b 0.0001) 0.9638 (0.3829) 0.0087 (0.9913) 22.7234*** (b 0.0001)

4.5240** (0.0118) 8.6529*** (0.0002) 0.2664 (0.7664) 2.8482* (0.0599) 9.3391*** (0.0001) 3.1001** (0.0469) 1.6806 (0.1884) 1.6603 (0.1923) 23.7971*** (b 0.0001) 4.3288** (0.0142) 1.3992 (0.2488) 6.5944*** (0.0016) 4.2378** (0.0155) 2.5332* (0.0815)

0.2474 (0.7810) 3.9672** (0.0202) 19.1520*** (b 0.0001) 5.4602*** (0.0048) 15.5180*** (b 0.0001) 5.5886*** (0.0042) 4.0157** (0.0193) 6.9246*** (0.0012) 1.8738 (0.1558) 7.8953*** (0.0005) 1.6981 (0.1852) 11.4422*** (b 0.0001) 2.3897* (0.0695) 3.4722** (0.0326)

A.S.M.S. Azad et al. / International Review of Financial Analysis 22 (2012) 38–47

rate. Thus, a part of foreign exchange rate risk is transmitted to IRS. Suhonen (1998) argues that when the exchange rate is highly volatile, the cross-border counterparties demand more payer positions, thereby increasing the swap rate and its volatility. Of the other macroeconomic variables, the SLOPE coefficient is positive and significant throughout all swaps maturities for the US. Azad et al. (2011) also find a positive coefficient. They argue that a positive (negative) SLOPE implies an expectation of future interest rate rises (falls), which motivates (frustrates) IRS activities. 4 Note that a positive (negative) SLOPE is also an indication of economic expansion (contraction). As a result, the positive slope causes concerns for some hedgers to hedge their interest rate risk exposure. Azad et al. (2011) argue that the relationship between the SLOPE and the swaps can be positive from the liquidity aspect. A tight liquidity is related to a flat and/or inverse slope of yield-curve. When the liquidity dries up, the swaps trading activity may decrease, which in turn causes IRS volatility to fall. Consequently, there can be a positive relationship between the slope of the yield curve and IRS volatility. Relevant to this, Azad et al. (2011) find some support for the liquidity effect (measured through money supply) showing that IRS volatility may be dominantly driven by liquidity rather than economic expansion or contraction. The coefficient of money supply (M2) is negative but insignificant with one exception. That is for the UK 5-year swap, the coefficient is negative but very small in magnitude. The unemployment rate (UNEM) shows negative but statistically insignificant influence on the lowfrequency volatility. Azad et al. (2011) find a negative and significant effect of UNEM on IRS volatility. They relate such findings to economic slowdown and investment decline. Overall if the hypothesis (the higher the macroeconomic risk, the higher the use of swaps) does work, in a volatile economy investors would require hedging and managing the risks, and vice versa. Accordingly, the low level of macroeconomic risk/uncertainty causes decline in preferences for fixed-income assets, which frustrates derivative activities (see for instance, Loeys and Panigirtzoglou (2005) and Cailleteau and Mali (2007)). For the market makers, the risk premium is also low (high) when macroeconomic risk is low (high). The above results are consistent with both the hypothesis and prior empirical findings. In terms of the explanatory power (R-squared statistics), the model specification of (4) appears to have the best fit for the UK market followed by the US markets. The results are also consistent with the notion that macroeconomic risk leads to a greater degree of hedging or speculative activities in financial markets. Since most of the macroeconomic risk proxies are positively associated (with few exceptions including IRVOL and unemployment rate) with the volatility of the swaps markets, our findings are consistent with the argument that the greater the macroeconomic risk, the greater is the use of derivatives to gain from hedging or speculating (Beber and Brandt (2009)).

financial market volatility helps predict macroeconomic volatility or risk is also captured (Schwert (1989)). Table 10 shows the results of pair-wise Granger causality tests between macroeconomic risk proxies and low-frequency IRS volatility. The analysis for the UK swaps market shows that IRVOL leads the relationship for both maturities. This result supports empirical findings in Table 8, which shows that the coefficient of IRVOL as a determinant of swaps volatility is very high. For the 5-year swap, a bi-directional causality exists between low-frequency volatility and four macrorisk factors namely, CPIVOL, FXVOL, UNEM and M2. For the 10-year swaps, low-frequency volatility of swaps leads the relationship with M2, while three macro-risk proxies namely, CPIVOL, IRVOL and UNEM lead the relationship with low-frequency volatility of swap. The empirical result of the US market shows that, for the 5-year swaps, a bi-directional causality exists between low-frequency volatility of swaps and four macro-risk variables namely, CPIVOL, IRVOL, SLOPE and M2. That is, in contrast to the UK markets, the feedback effect is stronger in the case of the 5-year US market. It seems that the interaction between the markets and the policy makers is stronger in the US swaps market than in the other swaps markets (including that of Japan in Azad et al. (2011)). As can be seen, for the 10-year swaps, the feedback effect remains stronger with four macroeconomic risk proxies, namely, IPVOL, IRVOL, FXVOL and M2. With the remaining macroeconomic risk proxies including CPIVOL, SLOPE and UNEM, the swaps lead the relationship. That is, the reverse causality is found stronger for the 10-year dollar swaps. These findings are consistent with the argument that derivatives are forward-looking instruments. Hence, low-frequency volatility can be used to predict the movements of macroeconomic variables or policy changes at the macroeconomic level. Interestingly, when alternative specifications of IRS volatility are used, we detect little evidence of causal relationship between macroeconomic risk and swaps market volatility. 5 This result is consistent with that of Engle et al. (2008). Notably, alternative specifications that are used in this study include: (i) long-term volatility 6 from the additive decomposition and (ii) realised volatility. These alternative specifications and the results are discussed in Section 5. 5. Robustness tests In this section we examine whether our empirical findings based on low-frequency volatility are robust to alternative volatility specifications. We first use the benchmark additive specification of Engle and Lee (1999), and then the realised volatility. Engle and Lee's (1999) component GARCH model has two volatility components: (i) short-run/transitory volatility,   2 g i;t ¼ ðα i −βi Þg i;t−1 þ α i εi;t−1 −hi;t−1

4.3. Causality between low-frequency irs volatility and macroeconomic risk This sub-section reports the results of the pair-wise Granger causal relationship between macroeconomic risk proxies and the lowfrequency IRS volatility to examine which of the two leads the relationship. Testing the causal link is important as Chen et al. (1986) and Schwert (1989), among others, argue that there is no satisfactory theory that indicates an entirely one-way relationship between financial markets and macroeconomy. Rather, there is a lead-lag relationship between the two. Studying this relationship also facilitates investigating as to whether policy makers implicate the market reactions (feedback effects) into the subsequent policy decisions. In addition, the notion that

ð6Þ

(ii) long-term/permanent volatility,   2 τi;t ¼ ωi þ ρτi;t−1 þ ϑi εi;t−1 −hi;t−1

ð7Þ

where, volatility innovation, (εi,2 t − 1 − hi, t − 1), drives both the shortterm and long-term components. To recall, the short-term volatility in Eq. (6) is similar in spirit to that of high-frequency volatility in Eq. (2), while the long-term volatility in Eq. (7) is similar in spirit to that of low-frequency volatility in Eq. (3). After obtaining the daily

5

The results can be obtained from authors on request. It is to be noted that both the low-frequency volatility and long-term volatility proxy the permanent component of volatility. Two different terms are used to distinguish between the models (multiplicative decomposition and additive decomposition) of volatility. 6

4 Fang and Muljono (2003) use the SLOPE as proxy for anticipated future interest rates.

45

46

A.S.M.S. Azad et al. / International Review of Financial Analysis 22 (2012) 38–47

long-term volatility, τi, t, from Engle and Lee's (1999) component GARCH model, the average of the daily long-term volatility in month t is obtained using the following equation: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u Ni;t u 1 X Longvoli;t ¼ t τ Ni;t d¼1 i;d;t

ð8Þ

where, Longvoli, t stands for average daily long-term volatility of swap for maturity i (= 5 and 10) at month t. Ni, t is the number of trading days in a month at year t for maturity i. τi, d, t is the daily long-term volatility observed for maturity i, of swap quote day d at year t. Thus, the long-term volatility (in a month), Longvoli, t is modelled as a function of the same macroeconomic risk proxies, which are used in Eq. (4). The empirical setting is as follows (the same equation is used for each country): Longvoli;t ¼ ci;0 þ θi;1 cpivolt þ θi;2 ipvolt þ θi;3 irvolt þ θi;4 f xvolt þ θi;5 slopet þ θi;6 unemt þ θi;7 m2t þ μ i;t

ð9Þ

Table 11 presents the estimation results of Eq. (9) based on longterm volatility from Engle and Lee's (1999) additive volatility decomposition. The results indicate that the adjusted R-squared falls considerably for both the markets. Another noticeable finding is that in the sterling swap, the coefficient of FXVOL becomes significant for both maturities, while the coefficients of IPVOL and SLOPE coefficient become significant for 10-year swap. In the case of the dollar swaps market, the coefficient of IPVOL becomes positive for 5-year swaps. No other notable changes are observed in the case of the dollar swaps market. Another test used for robustness check is the model-free realised volatility of IRS as a dependent variable. The realised volatility, representing the overall realisation of volatility, is noisy in the sense that it

does not separate the short-term component. The realised volatility can be calculated as: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u Ni;t uX Realvoli;t ¼ t r2i;t;d

ð10Þ

d¼1

where, Realvoli, t stands for the realised volatility of swap for maturity i (=5 and 10) in month t. Ni, t is the number of trading days in a month at year t for maturity i, and ri,2 t, d denotes the daily squared changes in swap rates observed for swap maturity i at day d of year t. For the two countries, the OLS equation involving realised IRS volatility as a function of same macroeconomic risk proxies can now be specified: Realvoli;t ¼ ci;0 þ θi;1 cpivolt þ θi;2 ipvolt þ θi;3 irvolt þ θi;4 f xvolt þ θi;5 slopet þ θi;6 unemt þ θi;7 m2t þ μ i;t

ð11Þ

Table 12 demonstrates the results based on realised volatility. Some transmigrations across the coefficients of the macro-risk variables are observed for the sterling swap market. The CPIVOL coefficient becomes significant for the 5-year swap but insignificant for the 10-year maturity. IRVOL remains to be the most significant factor. The coefficient of FXVOL becomes significant, while that of money supply becomes insignificant. Interestingly, for the dollar swap market, no significant changes are observed with the exception of IPVOL. The coefficient of IPVOL becomes positive and significant for the 5-year swap but insignificant for the 10-year swap. We complete the robustness check with the comparison of adjusted R-squared that we obtain from using different volatility specifications. Table 13 presents the adjusted R-squared statistics and their averages for two swap maturities. For both the UK and US markets, as expected, the highest adjusted R-squared statistics are obtained by using lowfrequency volatility from multiplicative volatility decomposition of Rangel and Engle (2012), followed by long-term volatility from

Table 11 Long-Term Volatility of Swap and Macroeconomic Risk. Results from the following OLS regression model: Longvoli, t = ci, 0 + θi, 1cpivolt + θi, 2ipvolt + θi, 3irvolt + θi, 4fxvolt + θi, 5slopet + θi, 6unemt + θi, 7m2t + μi, t where, the dependent variable is the long-term volatility of swap. See Table 1 for details of macroeconomic variables that are used on the right-hand side of the above equation. Standard errors of the estimated coefficients are in parentheses and are corrected for autocorrelation and heteroskedasticity by using the NeweyWest method. Sample covers the period from October 1989 through April 2010 with 247 monthly observations. *, ** and *** indicate level of significance at 10%, 5% and 1%, respectively. Predicted sign Intercept CPIVOL

+

IPVOL

+/−

IRVOL

+

FXVOL

+

SLOPE

+/−

UNEM

+/−

M2

+

Adjusted R2 F-statistic

UK

US

Table 12 Realised Volatility of Swap and Macroeconomic Risk. Results are based on the following OLS regression model: Realvoli, t = ci, 0 + θi, 1cpivolt + θi, 2ipvolt + θi, 3irvolt + θi, 4fxvolt + θi, 5slopet + θi, 6unemt + θi, 7m2t + μi, t where, the dependent variable is the realised volatility. See Table 1 for details of macroeconomic variables. Standard errors of the estimated coefficients are in parentheses and are corrected for autocorrelation and heteroskedasticity by using the Newey-West method. Sample covers the period from October 1989 through April 2010 with 247 monthly observations. * and *** indicate level of significance at 10% and 1%, respectively. Predicted sign

5-year swap 10-year swap 5-year swap 10-year swap 0.6798 − 3.5754 (4.8574) 0.0222 (0.0153) 8.8511*** (2.5561) 0.0104** (0.0046) 0.0216 (0.0140) − 0.0073 (0.4779) − 1.79E-06 (4.99E-06) 0.3304 13.8279***

0.5378 − 2.7791 (3.2430) 0.0200* (0.0108) 9.1900*** (2.6788) 0.0102* (0.0055) 0.0222* (0.0132) − 0.1625 (0.4425) − 2.93E-06 (b 0.0000) 0.3709 16.3287***

0.4777 0.7263 (1.3879) 0.0106* (0.0062) − 0.4255*** (0.0887) 0.0356*** (0.0119) 0.0408*** (0.0130) − 0.0456 (0.0386) − 0.0002 (0.0003) 0.5530 44.1226***

0.3896 0.5223 (0.8118) 0.0171*** (0.0063) − 0.3575*** (0.0634) 0.0301** (0.0131) 0.0528*** (0.0077) 0.0033 (0.0451) 0.0002 (0.0005) 0.4447 28.9096***

Intercept CPIVOL

+

IPVOL

+/−

IRVOL

+

FXVOL

+

SLOPE

+/−

UNEM

+/−

M2 Adjusted R F-statistic

+ 2

UK

US

5-year

10-year

5-year

10-year

0.2289 − 0.7887* (0.4455) 0.0044** (0.0022) 1.7879** (0.7075)** 0.0026 (0.0013) 0.0050 (0.0076) 0.0252 (0.0428) − 3.69E-07 (5.40E-07) 0.2173 8.2190***

0.2048 − 0.5879 (0.4091) 0.0040* (0.0021) 1.6925** (0.7562) 0.0023* (0.0012) 0.0033 (0.0067) − 0.0129 (0.0390) − 7.28E-07 (5.00E-07) 0.2186 8.2752***

0.1633 0.0749 (0.2744) 0.0055*** (0.0019) − 0.0521*** (0.0171) 0.0061** (0.0026) 0.0130*** (0.0018) 0.0178 (0.0121) − 9.66E-06 (8.93E-05) 0.3738 21.8059***

0.1620 0.2326 (0.2132) 0.0029 (0.0022) − 0.0642*** (0.0135) 0.0051* (0.0031) 0.0120*** (0.0019) 0.0154 (0.0119) 7.52E-06 (8.44E-05) 0.3300 18.1703***

A.S.M.S. Azad et al. / International Review of Financial Analysis 22 (2012) 38–47 Table 13 Comparison of Adjusted R-Squared Statistics under Different Models. This table provides a comparison of adjusted R-squared statistics obtained from different models. LFV stands for low-frequency volatility based on the ASP-GARCH model of Rangel and Engle (2012), C_LTV stands for long-term volatility based on the C-GARCH model of Engle and Lee (1999) and RV indicates model-free realised volatility. The adjusted R-squared statistics for LFV (low-frequency volatility) is based on Eq. (4), for long-term volatility (C_LTV) is based on Eq. (9) and for realised volatility is based on Eq. (11). UK LFV

US C-LTV

RV

LFV

C_LTV

RV

2

0.3738 Adjusted R for 5-year swap 0.8273 0.3304 0.2173 0.6344 0.553 Adjusted R2 for 10-year 0.9195 0.3709 0.2186 0.6638 0.4447 0.33 swap 0.8734 0.3507 0.2179 0.6491 0.4988 0.3519 Average Adjusted R2

additive volatility decomposition of Engle and Lee (1999) and finally realised volatility. The results from two-component GARCH specifications clearly yield higher adjusted R-squared, which falls sharply when we use realised volatility. This signifies the importance of using a better measure of risk proxy for the financial markets concerned. 6. Conclusions Prior researches show that macroeconomic risk plays an important role for hedging or speculating purposes with the use of derivatives. The purpose of those studies is to guage the macroeconomic driving forces of the risk and returns on assets, and to identify the causal relationship between the financial market and macroeconomic risk or uncertainty. In line with those studies, this paper investigates whether macroeconomic risk plays any role in driving the low frequency or long-term component of swap market volatility. The main finding of the paper shows that for both the UK and the US markets, the low frequency volatility of both longer (10-year) and shorter (5-year) maturities of swaps have strong associations with macroeconomic risk proxies. This relationship is strong in terms of the explanatory power of the model. The association between low-frequency volatility and macroeconomic risk is robust with respect to the choice of different alternative measures of volatility that are used in the literature on GARCH modelling. From the perspectives of practical implications, the findings suggest that policy makers should use low-frequency volatility in order to examine market responses to key macroeconomic policies, and that market participants may rely on low-frequency volatility to extract trading signals. Using such signals, hedgers could make forecast of whether they need to increase (decrease) IRS usage to hedge risk originating from macroeconomic uncertainty. Acknowledgement We would like to thank anonymous referee(s) and the editor Jonathan Batten for comments and suggestions on earlier versions. We specially thank Jose Gonzalo Rangel for sharing his computer program of Asymmetric Spline-GARCH model. Any remaining errors are our responsibility. References Abugri, B. A. (2008). Empirical relationship between macroeconomic volatility and stock returns: Evidence from Latin American markets. International Review of Financial Analysis, 17(2), 396–410.

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