Macro Factors and Volatility of Treasury Bond Returns 1

Transcription

1 Macro Factors and Volatility of Treasury ond Returns 1 Jingzhi Huang McKinley Professor of usiness and Associate Professor of Finance Smeal College of usiness Pennsylvania State University University Park, PA 16802, U.S.A. Phone: (814) jxh56@psu.edu Lei Lu Assistant Professor of Finance School of Finance Shanghai University of Finance & Economics Shanghai, , China Phone: +86 (21) lu.lei@mail.shufe.edu.cn 1 We would like to thank enjamin Croitoru, Hao Zhou, and seminar participants at Zhejiang University, Shanghai Jiaotong University, Southwestern University of Finance and Economics, the 2008 Chinese Finance Association annual meeting, and the 2008 Chinese Economic Association annual meeting for helpful comments. We acknowledge the financial support from the Shanghai Pujiang Program and the Shanghai University of Finance and Economics 211 Project-China

2 Macro Factors and Volatility of Treasury ond Returns Abstract This paper investigates the impact of macroeconomic variables on the volatility of Treasury bond returns. y using principal components analysis, we extract the real and monetary macro factors from the real activities and monetary variables, respectively. We find that these macro factors have a significant impact on the volatility of Treasury bond returns. In particular, we find that the real activities affect the return volatility across all maturities, while the monetary variables are significantly related to the volatility of short- and medium-term bonds only. The implication of these findings is that the policy makers can employ monetary policy to stabilize the fluctuation of short- and medium-term bonds, but need to take the real activities into account when stabilizing the fluctuation of long-term bonds. JEL classifications: E44; G12; G17 Keywords: bond volatility; real factor; monetary factor; volatility decomposition

3 1. INTRODUCTION One important issue related to the Treasury bond market is the factors that affect the volatility of Treasury bond returns. Viceira [2007] finds that the short-term nominal interest rates positively forecast bond volatility. Jones, Lamont, and Lumsdaine [1998], Christiansen [2000], and Goeij and Marquering [2006] find that the announcements of macroeconomic variables significantly affect the volatility of Treasury bond returns. Fleming and Remolona [1999] and alduzzi, Elton, and Green [2001] also study the impact of macro news on bond volatility and other features of bond markets (e.g., trading volume and liquidity) using different sets of macroeconomic announcements. Recent empirical evidence further documents that releases of macroeconomic news affect the shape of the term structure of the bond volatility. For instance, Goeij and Marquering [2006] find that releases of employment data and producer price index have an effect on the volatility of medium- and long-term bond returns, while the announcements of monetary policy only affect short-term bond volatility. However, few studies have examined whether macroeconomic fundamentals themselves can predict the volatility of Treasury bond returns. This question is interesting especially given that Ludvigson and Ng [2009] find that the macroeconomic fundamentals greatly affect bond returns and then bond risk premia. A related question is whether monetary variables (rather than their announcements) have different effects on the volatilities of bond returns with different maturities. In this paper, we provide perhaps the first attempt to answer the above two questions. Specifically, we first extract the real and monetary factors from the 1

4 macroeconomic variables using the principal components analysis. We then examine the impact of both the real and monetary factors on the volatilities of bond returns. Next, to disentangle the impacts of maturity on the volatility of bond returns from that caused by market risk, we decompose the bond volatility for each maturity into market-level volatility and maturity-dependent volatility and then rerun the regression separately using the two volatility components. We find that macroeconomic variables significantly affect the bond volatility and its two components. Specifically, the real activities affect the bond volatility of all maturities, while the monetary variables are significantly related to the volatility of short- and medium-term bonds (e.g., 1-, 2-, 5-, and 7-year) and have no influence on the volatility of long-term bonds. The implication of these findings is that the policy makers can employ monetary policy to stabilize the fluctuation of short- and medium-term bonds, while they need to take the real activities into account when stabilizing the fluctuation of long-term bonds. Moreover, our results suggest that macroeconomic variables can be good predictors for volatility of Treasury bond returns, in particular, the real activities and monetary variables differently affect the volatilities of bond returns with different maturities. This paper contributes to the literature at least in two aspects. First, existing studies (e.g., Jones, Lamont, and Lumsdaine [1998]; Christiansen [2000]; and Goeij and Marquering [2006]) focus on the effects of macroeconomic announcements on the volatility of bond returns, but none of them investigate the relationship between the macroeconomic variables and bond volatility. David and Veronesi [2008] find that investors beliefs about fundamentals (proxied by investors uncertainty about economy) 2

5 can improve the predictability of bond volatility by controlling macroeconomic variables, while the macro variables include the interest rates measures, the fundamental volatilities, and the NER index. In our paper, the macroeconomic variables include the real activities and monetary variables. In particular, we find that real and monetary factors have different impacts on the volatility of bond returns across various maturities. Second, to the best of our knowledge, this is the first paper to decompose the volatility of Treasury bonds into two components market-level and maturity-dependent volatility and then examine the relationship between each of the volatility components and certain macroeconomic variables. As such, our paper differs from the study by Goeij and Marquering [2006], which examines the impact of macro announcement on bond volatility using the intraday data whereas we investigate the effects of macroeconomic variables on both market-level volatility and maturity-dependent volatility using the daily bond return. The maturity-dependent volatility of bond returns has the same sprit of idiosyncratic volatility in the stock market. To some degree, our paper can be treated as a long-run predictability of bond volatility, while Goeij and Marquering [2006] predict the bond volatility in short run. 2. DATA 2.1 ond Data We examine the volatility of 1-, 2-, 5-, 7-, 10-, 20- and 30-year U.S. Treasury bonds. The data on bond returns for the period July 1961 through December 2008 are obtained 3

6 from the CRSP Daily Treasury Fixed-term File. 2 The excess returns are calculated using the bond returns in excess of the 3-month Treasury-bill rates, taken from the Federal Reserve oard of Governors. EXHIIT 1 Descriptive Statistics of Daily Excess ond Returns This exhibit presents the sample statistics of daily returns on 1-, 2-, 5-, 7-, 10-, 20-, and 30- year Treasury bonds in excess of the 3-month Treasury-bill rates for the period July 1961 through December The bond returns are obtained from the CRSP Daily Treasury Fixed-term File. The 3-month Treasure-bill rates are taken from the Federal Reserve oard of Governors. 1-year 2-year 5-year 7-year 10-year 20-year 30-year Mean (%) Median (%) Stdev (%) Exhibit 1 reports the descriptive statistics of daily excess returns. As can be seen from the table, the average daily excess return does not vary significantly across maturities and ranges from 2.5 bps for 1-year bonds to 2.9 bps for 7-year bonds. On the other hand, the bond volatility has a significant variation across maturities, ranging from 0.076% for 1-year bonds to 0.629% for 30-year bonds. We obtain the face value of outstanding debt from the CRSP Daily Treasury Master File and the bid and ask bond prices from the CRSP Daily Treasury Fixed-term File. The market capitalization of the bond market is calculated by multiplying the debt outstanding by the average of market bid and ask price. 2 According to the CRSP Daily Treasury Fixed-term File, the daily holding period return is defined as the price change plus interest, divided by last day s price. In Jones, Lamont, and Lumsdaine [1998], the daily returns are calculated from the Federal Reserve s constant maturity interest rate series. They calculate the bond yield from the interest rates and then derive the end-of-period bond price using the next day s yield augmented with the accrued interest rate, and the holding 4 period return equals the change in bond price.

7 2.2 Macroeconomic Variables The monthly macroeconomic variables are collected from the database of Global Insight asic Economics for the period May 1961 through December The variables we consider are classified into the two categories of real activities and monetary variables. The variables of real activities include the index of Help Wanted Advertising in Newspaper (LHEL), the unemployment rate (LHUR), the industrial production index (IPS10), and the National Association of Production Management (NAPM) production index (PMP). All of these variables except PMP are used by Ang and Piazzesi [2003] to reflect the real activities. The monetary variables consist of the Federal funds rates (FYFF), nonborrowed reserves (FMRNA), and M2 (FM2). From October 1979 to August 1982, FMRNA was chosen as the policy target, and for the rest of the sample period FYFF was chosen as the target by the Federal Reserve. Exhibit 2 describes the real activities and monetary variables used in our analysis. EXHIIT 2 Description of Macroeconomic Variables This exhibit describes the real activities and monetary variables used in the paper. In the transformation column (Trans), lv denotes the level of the series, lv denotes the difference of the level, ln denotes the first difference of logarithm, and 2 ln denotes the second difference of logarithm. Data on all series are obtained from the Global Insight asic Economics database. Series Mnemonic Description Trans Real Activities 1 LHEL Index of Help-Wanted Advertising in Newspapers ln 2 LHUR Unemployment Rate: All Workers, 16 Years & Over lv 3 IPS10 Industrial Production Index ln 4 PMP NAPM Production Index lv Monetary Variables 1 FYFF Federal Funds Rate lv 2 FMRNA Non-borrowed Reserves 2 ln 3 FM2 Money Stock: M2 2 ln 5

8 Following Stock and Watson [2002] and Ang and Piazzesi [2003], we use principle component analysis to estimate the common factors for each group of variables, respectively. First, we transform the series of variables to be stationary. Exhibit 2 summarizes all the transformations that are used. Next, we standardize each series separately to have a mean of zero and unit variance. Then consider the following specifications: X i i i i () t = f ( t) + ε ( t), i = R, M. β (1) where X R = ( LHEL, LUHR, IPS10, PMP) and X M = ( FYFF, FMENA, FM 2) denote the vectors of real activity and monetary variables, respectively. f M represent the real and monetary factors, respectively. f R and The principal component analysis indicates that the first real factor accounts for 57.0% of the variance of real activity variables. This factor loads a significant amount of information about the real variables and can be used to measure the real activities. Similarly, the first monetary factor accounts for 46.5% of the variance of monetary variables and is used as a proxy for the monetary variables. The correlations between the first real factor and the four real variables are , 0.722, , and , respectively. We should be cautious in explaining the signs of correlations. As we anticipated, as the LHEL, IPS10, and PMP increase and the LHUR decreases, the economy tends to be healthy. Therefore, the signs of the correlations have reversed economic meaning. 6

9 The correlations between the first monetary factor with the three monetary variables are , 0.697, and Similar to the explanation of signs of correlations between real factor and real activities, the signs of the correlations have reversed economic meaning for monetary factor. As the economy becomes healthy, the funds rate tends to be high and thus attracts more investors to invest in the long-term bonds. The signs of these correlations are intuitive: to maintain a level of total reserves consistent with the FOMC's target federal funds rate, increases in borrowed reserves must generally be met by a decrease in nonborrowed reserves, and therefore the FMRNA and the FYFF are negatively correlated. Moreover, the first real and monetary factors are weakly correlated with a value of EXHIIT 3 Correlations Matrix among (Real and Monetary) Factors and ond Volatility This exhibit presents the correlations between the realized volatility of 1-, 2-, 5-, 7-, 10-, 20-, and 30- year bonds and the one-month lagged real and monetary factors. The correlations among bond volatilities are also reported in the following exhibit. 1-year 2-year 5-year 7-year 10-year 20-year 30-year Real Money year 1 2-year year year year year year Exhibit 3 reports the correlations between the macro factors and the bond volatility of various maturities, from which we can gain the preliminary information about their relationship. We find that the real factor is highly correlated with the bond volatility 7

10 and that the correlations are almost the same for all maturities (ranging from to 0.295), while the monetary factor is weakly correlated with bond volatility. In particular, the correlation of the monetary factor with 1- and 2-year bond volatility is higher than that with 20- and 30-year bond volatility e.g., and vs and This suggests that the real factor might be significantly related to the bond volatility of all maturities, while the monetary factor weakly affects the bond volatility and its effect can be not significant for the volatility of long-term Treasury bonds. 3 These conjectures is examined and confirmed in the following section. Exhibit 3 also reports the correlations of volatility between different maturities. It is not surprising that the correlations decrease as the difference of maturities increases, since the expectation hypothesis claims that the volatility of long-term bond yields is on average the sum of volatilities of short-term bond yields. 3. EMPIRICAL RESULTS The objective of this analysis is to investigate if the volatility of Treasury-bond returns is related to the macro factors and, in particular, if the bond volatility of different maturities is driven by different macro factors. To proceed, we first regress the bond volatility on the macro factors for each maturity. Next, we decompose the bond volatility of each maturity into the bond-market-level volatility and the maturity-dependent volatility. Then we separately regress these two sets of volatiles on the macro factors. 3 In this paper, we call 1- and 2-year bonds the short-term bonds, 5- and 7-year bonds the medium-term bonds, and 10-, 20-, and 30-year bonds the long-term 8 bonds.

11 3.1 Preliminary Analysis We use one-month lagged real and monetary factors, lagged logarithmic nominal short rate proxied by the 3-month Treasury-bill rate, and lagged volatility value to forecast the bond volatility. ecause Viceira [2007] finds that the nominal short-term interest rates positively forecast the bond volatility, we also include this variable in the regression models. Exhibit 4 presents the estimated results for the monthly volatility of Treasury bonds on the lagged real and monetary factors, the lagged log short rate, and the lagged volatility value. The first column shows that the real factor positively and significantly affects the bond volatility across all maturities. The positive impact of real factor on volatility of Treasury bonds and the negative correlations between real factor with LHEL, IPS10, and PMP imply that the higher the LHEL, IPS10, and PMP, the lower the volatility of Treasury bonds. This is intuitive: as the LHEL, IPS10, and PMP become larger, the economy tends to be healthier, the uncertainty of economy decreases, and thus the volatility of Treasury bonds is decreased. This is consistent with David and Veronesi (2008), which find that the investors uncertainty about economy can negatively predict the bond volatility. Moreover, since the volatility of long-term Treasury bonds is generally higher than that of short-term Treasury bonds, it is not surprising that the estimated coefficients of real factor are higher for the long-term bonds. It is about 0.45 for 1-year Treasury bonds and 2.10 for 30-year Treasury bonds. The second column shows that the monetary factor is strongly related to the volatility of short- and medium-term Treasury bonds (e.g., 1-, 2-, 5-, and 7-year bonds), while it is not statistically significant for long-term Treasury bonds (e.g., 10-, 20- and 30-9

12 EXHIIT 4 Estimates of Real and Monetary Factors on Total ond Volatility This exhibit reports the regression results of monthly realized volatility of 1-, 2-, 5-, 7-, 10-, 20-, and 30- year bonds on the lagged real factor Real -1, the lagged monetary factor Money -1, the lagged log short rate r -1, and the lagged bond volatility. The t-values are reported in the brackets. Real -1 Money -1 r -1 Vol -1 R 2 1-year (3.979) (13.878) (4.398) (3.688) (14.190) (3.919) (3.448) (4.960) (12.036) year (3.968) (18.889) (4.004) (21.193) (4.549) (4.581) (19.279) (4.149) (4.421) (4.538) (16.690) year (3.990) (11.573) (4.281) (2.419) (11.593) (3.782) (2.307) (3.026) (10.858) year (2.839) (14.468) (3.081) (2.049) (14.499) (2.622) (1.942) (2.662) (13.841) year (3.621) (11.593) (3.847) (1.463) (11.605) (3.468) (1.381) (1.919) (11.331) year (3.299) (14.900) (3.472) (1.539) (14.895) (3.100) (1.458) (1.992) (14.472) year (2.835) (17.169) (3.002) (1.457) (17.145) (2.737) (1.404) (1.250) (16.999) year bonds). For example, when we regress on lagged real and monetary factors and lagged bond volatility for 1-year Treasury bonds, the coefficient for monetary factor is with t-value of We need emphasize two issues with the regression results. 10

13 First, the positive impact of monetary factor on bond volatility has the same intuition as that for real factor: the higher the monetary factor, the lower the fund rate (because of the negative correlation with monetary factor), the worse the economy, and thus the higher the bond volatility. Second, since the correlation between real and monetary factors is negative, the estimation coefficients of real factor become larger when we include the monetary factor into the regressions. The above results confirm our preliminary results that the real factor significantly and positively affects the bond volatilities of all maturities, while the monetary factor is only related to the bond volatility of short- and medium-term bonds as illustrated in Exhibit 3. Our results are consistent with Viceira [2007], who finds that the nominal short rate significantly affects the stock and bond volatility up to a 60-month horizon. In our paper, we analyze the 1-month excess bond returns and find that the nominal short rate has significant effect on the volatility of bonds for all maturities, while its influence on the volatility of 30-year bonds is relatively limited. Our findings are also consistent with those of Evans and Marshall [1998] and Goeij and Marquering [2006]. Evans and Marshall [1998] find that a contractionary monetary policy shock induces a pronounced positive but transitory response in short-term interest rates and has a smaller effect on medium-term rates and almost no effect on long-term rates. Goeij and Marquering [2006] find that the announcements of monetary policy only affect the volatility of short-term bonds. However, this paper focuses on the connection between bond volatility and monetary variables. 11

14 3.2 Empirical Analysis Campbell, Lettau, Malkiel, and Xu [2001] decompose the stock volatility into three components market-level, industry-level and firm-specific volatilities, and they find that these three components have different patterns over time. Following their method, we decompose the volatility of government bonds into bond-market-level and maturitydependent volatility. Maturity is denoted by subscript i, and the excess bond return with maturity i is denoted by r i. The bond market capitalization for maturity of one year or greater is calculated on the basis of all seven categories of Treasury bonds. The weight of maturity i in the total bond market is denoted by w i, and the excess bond market return is r 7 = = i 1 w r i i. In the next step, we decompose the excess bond return on each maturity by using the CAPM 4 given by r ( t) = + β ( t) r ( t) v ( t). α (2) i i + i Following French, Schwert, and Stambaugh [1987] and Schwert [1989], we use the daily bond returns to calculate the realized monthly volatility. ecause r () t and ( t) v i are orthogonal, the variance of bond returns is therefore Var ( r ( t) ) Var ( t) r ( t) ( ) Var v ( t) = β ( ), (3) i i + i 4 Viceira [2007] uses the stock market returns to calculate the realized bond CAPM beta as a proxy for bond risk. 12

15 where Var ( ), ( r ) r i Var β, and ( ) i v i Var are called the total bond variance, the riskadjusted variance of the bond-market, and the maturity-dependent bond variance, respectively. To differentiate from the risk-adjusted variance of the bond market, we call ( r ) Var the variance of the bond market. Moreover, we denote the total bond volatility of maturity i, the risk-adjusted volatility of the bond-market-level, the volatility of the bond- market-level, and the maturity-dependent volatility by Var( r ) σ β Var( β r ), Var( r ) i i v σ, and σ Var( v ) i i, respectively. σ, In calculating the two components of total bond volatilities, we follow Fama and French [2005] and Ang and Chen [2007] to assume that the CAPM betas vary over time. To calculate the time-varying CAPM betas for each month, we regress the daily excess bond returns of maturity i on the daily bond-market returns like Equation (2) to gain the series of monthly betas. To well understand the maturity-dependent bond volatility, we calculate the ratio of v maturity-dependent bond volatility, to the total bond volatility,, for each maturity. σ i We find that the ratios are higher for the 1- and 2- year Treasury bonds than for the others. This ratio is on average and for 1- and 2-year bonds, and and for 20- and 30-year bonds, respectively. This means that the maturity-dependent volatility is more important in explaining the total volatility of short-term bonds than of long-term bonds. In the previous section, we studied the impact of real and monetary factors on total bond volatility of each maturity. The next step is to investigate the impacts of real σ i i i 13

16 and monetary factors on the two components of total volatility: the bond-market-level v volatility, σ, and the maturity-dependent volatility,. σ i EXHIIT 5 Estimate of Real and Monetary Factors on ond Market Level Volatility This exhibit reports the regression results of monthly bond-market-level volatility on the lagged real factor Real -1, the lagged monetary factor Money -1, the lagged log short rate r -1, and the lagged bond volatility. The t-values are reported in the brackets. Real -1 Money -1 r -1 Vol -1 R (2.677) (22.738) (2.915) (1.967) (22.737) (2.623) (1.904) (1.551) (22.346) Exhibit 5 presents the regression results of real and monetary factors on the bond-market-level volatility. For all combinations of explanatory variables, the coefficients of the real factor are positive, and the t-values demonstrate that the real factor significantly affects the bond-market-level volatility. When we regress on lagged real factor and lagged bond volatility, the coefficient of real factor is with the t- value of y including monetary factor and short rate, the coefficients become and with t-values of and 2.623, respectively. The second column reports the regression results for the monetary factor. In general, we find that the monetary factor is not significant or marginal significant, although it is still negatively correlated with the bond-market-level volatility. When we regress on real and monetary factors and lagged bond volatility, the t-value for monetary factor is 1.967, while it insignificant with t-value of when including short rate. The possible reason is that the effect of the monetary factor on the maturity- EXHIIT 6 14

17 Estimates of Real and Monetary Factors on Maturity Dependent ond Volatility This exhibit reports the regression results of monthly maturity-dependent volatility on the lagged real factor Real -1, the lagged monetary factor Money -1, the lagged log short rate r - 1, and the lagged bond volatility. The t-values are reported in the brackets. Real -1 Money -1 r -1 Vol -1 R 2 1-year (3.929) (11.013) (4.187) (2.561) (11.229) (3.619) (2.225) (5.507) (9.109) year (4.260) (16.327) (4.486) (2.025) (16.366) (4.132) (1.819) (5.592) (13.399) year (4.713) (11.138) (4.976) (2.364) (11.228) (4.430) (2.182) (4.289) (9.936) year (4.035) (15.384) (4.387) (3.205) (15.663) (3.911) (2.873) (5.959) (12.486) year (3.404) (17.882) (3.282) (-0.817) (17.866) (2.741) (-1.089) (5.048) (15.360) year (3.294) (9.179) (3.327) (0.494) (9.181) (2.543) (0.246) (4.986) (7.560) year (3.897) (6.825) (4.057) (1.582) (6.892) (3.568) (1.460) (2.617) (6.528) dependent volatility of short- and medium-term Treasury bonds has been removed leaving the effect of the real factor on the volatility of bond-market-level. Exhibit 6 presents the estimates of real and monetary factors on the maturitydependent volatility. This analysis further investigates the effects of macroeconomic variables on the volatilities of treasury bonds with various maturities. The first column 15

18 shows that the real factor positively and significantly affects the maturity-dependent volatility of all maturities with most of the t-values greater than 3. Th economic explanation is the same as that for total bond volatility of each maturity (e.g., see Exhibit 4). The second column reports the regression results for monetary factor. We find that its coefficient is positively and statistically significant for Treasury bonds with maturity up to seven years, while it becomes insignificant for Treasury bonds with maturity of 10 years or greater. It has the same regression results and economic intuition for total bond volatility. 3.3 Robustness Check In this section, we provide the robustness check to examine the relationship between macroeconomic factors with volatility of Treasury bonds. Constant etas: In Campbell, Lettau, Malkiel, and Xu [2001], the CAPM betas are assumed to be constant. We use the whole samples to run model (2) and thus we can calculate the bond-market volatility and maturity-dependent bond volatility, respectively. The regression results show that this does not change our conclusions qualitatively. Stock Market Index: Viceira [2007] uses the stock market returns to calculate the realized bond CAPM beta as a proxy for bond risk. As a robustness check, we replace the index of bond market returns by the stock market index (e.g., daily returns on the valueweighted portfolio of all stocks traded on the NYSE, the AMEX, and the NASDAQ) and run the regression models, we have the similar estimation results for real and monetary factors. Equally-Weighted Index: In this section, we use the equally-weighted bond 16

19 returns across various maturities to replace the value-weighted bond returns and run the regression models, we find that the monetary factor is significantly related to the return volatility of short-term bonds (e.g., 1- and 2-year) and weakly related to the volatility of medium-term bonds (e.g., 5- and 7-year), while it has no influence on the return volatility of long-term bonds (e.g., 10-, 20-, and 30-year). In summary, when we decompose the bond volatility into the market-level volatility and the maturity-dependent volatility, we find that the macro factors significantly affect the maturity-dependent bond volatility. In particular, the real factor affects the bondreturn volatility across all maturities, while the monetary variables are related to the return volatility of short- and medium-term bonds, and have no influence on the return volatility of the long- term bonds. 4. CONCLUSION This paper investigates the impact of macro variables on the volatility of Treasury bond returns. We extract the real and monetary factors from the real activities and monetary variables, respectively. Then we examine the two factors impact on the daily volatility of the 1-, 2-5-, 7-, 10-, 20-, and 30-year U.S. Treasury bonds. We find that both real and monetary factors significantly affect the bond return volatility. In particular, the real factor affects the volatility across all maturities, while the monetary variables are significantly related to the volatility of short- and medium-term bonds. An extension is to analyze the relationship between the maturity-dependent volatility and the bond return for each maturity, which has the same spirit of idiosyncratic volatility in 17

20 predicting the stock market return. 18

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