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«Equity Volatility and Corporate Bond Yields JOHN Y. CAMPBELL and GLEN B. TAKSLER n ABSTRACT This paper explores the e¡ect of equity volatility on ...»

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THE JOURNAL OF FINANCE  VOL. LVIII, NO. 6  DECEMBER 2003

Equity Volatility and Corporate Bond Yields

JOHN Y. CAMPBELL and GLEN B. TAKSLER n

ABSTRACT

This paper explores the e¡ect of equity volatility on corporate bond yields. Panel data for the late 1990s show that idiosyncratic ¢rm-level volatility can explain as much cross-sectional variation in yields as can credit ratings. This

¢nding, together with the upward trend in idiosyncratic equity volatility documented by Campbell, Lettau, Malkiel, and Xu (2001), helps to explain recent increases in corporate bond yields.

DURING THE LATE 1990s, THE U.S. EQUITY and corporate bond markets behaved very di¡erently. As displayed in Figure 1, stock prices rose strongly, while at the same time, corporate bonds performed poorly. The proximate cause of the low returns on corporate bonds was a tendency for the yields on both seasoned and newly issued corporate bonds to increase relative to the yields of U.S.Treasury securities.

These increases in corporate^Treasury yield spreads are striking because they occurred at a time when stock prices were rising; the optimism of stock market investors did not seem to be shared by investors in the corporate bond market.

There are several reasons why the prices of corporate bonds might diverge from the prices of corporate equities. First, stock prices will increase if investors become more optimistic about future corporate pro¢ts. Optimistic expectations bene¢t stock prices much more than bond prices, since stockholders receive all residual pro¢ts, while corporate bondholders receive no more than the promised payments of principal and interest. This explanation does not account for the behavior of corporate bond yields in the late 1990s, however, because yield spreads on corporate bonds over Treasuries should fall, not rise, if investors become optimistic about corporate pro¢ts and thus reduce their expected probabilities of default. Second, there might be a composition e¡ect if corporate bonds are issued by di¡erent companies than those that dominate value-weighted equity indexes.

Third, an increase in the liquidity premium on corporate bonds relative to Treasury bonds might drive down corporate bond prices without any e¡ect on equity prices. Fourth, the yields on newly issued corporate bonds might vary because of changes in the special features of these bonds, for example, an increase in the value of call provisions. Such an increase would drive down the prices and drive Campbell is with the Department of Economics, Harvard University, and NBER. Taksler is n with Citigroup Global Markets. The views expressed are those of the author, not necessarily those of Citigroup Global Markets. The authors are grateful to Peter Hecht, Jeremy Stein, and an anonymous referee fo

–  –  –

Figure 1. Monthly index comparisons, 1990 to 2000.

Cumulative returns on the S&P 500 index, U.S. corporate bonds, and 5 -year U.S.Treasury notes, from the Global Financial Database. Spread of corporate over Treasury is the di¡erence between the cumulative returns on these two asset classes.

up the yields on newly issued bonds, but it would not have any e¡ect on seasoned bond prices. Finally, volatility has opposite e¡ects on stock and bond prices.

Given expected pro¢ts, volatility of ¢rm value hurts bondholders, because it increases the probability of default; it has a corresponding positive e¡ect for equityholders. Thus, volatility should drive up the yields on both new and seasoned corporate bonds.

Merton (1974) initiated the modern analysis of corporate debt by pointing out that the holders of risky corporate bonds can be thought of as owners of riskless bonds who have issued put options to the holders of the ¢rm’s equity. When volatility increases, the value of the put options increases, bene¢ting equityholders at the expense of bondholders. The volatility that is relevant for option value, and thus for corporate debt, is total ¢rm volatility, including both idiosyncratic volatility and systematic or market-wide volatility.This is important because idiosyncratic volatility can move very di¡erently from market-wide volatility. In particular, Campbell et al. (2001) point out that idiosyncratic volatility has trended upwards since the mid-1970s, while market-wide volatility has undergone temporary £uctuations but no trend increase.The ¢ndings of Campbell et al. suggest that increasing idiosyncratic volatility could have depressed corporate bond prices and supported corporate equity prices, during the past few decades and during the late 1990s in particular.

The relevance of increasing idiosyncratic volatility is illustrated in Figure 2.

This ¢gure plots the average yield spread on A-rated corporate bonds, as reported by the credit rating agency Standard and Poor’s (S&P), from January 1965 EquityVolatility and Corporate Bond Yields 2323 Figure 2. S&PA-rated corporate bond yield spread versus idiosyncratic risk.We plot the average yield spread on S&P A-rated corporate bonds and a 6 -month backward moving average of idiosyncratic risk. Idiosyncratic risk is calculated from the monthly cross-sectional standard deviation of individual stock returns by Goyal and Santa-Clara (2003).

through December 1999. It also plots a six-month backward moving average of idiosyncratic volatility, calculated from monthly cross-sectional data on individual stock returns by Goyal and Santa-Clara (2003).The two series display a common upward trend and substantial correlation in their movements at intermediate frequencies; the correlation of the levels of the two series is about





0.7. The total volatility of a typical individual ¢rm behaves in a similar fashion.

The volatility of the market index, by contrast, has no upward trend and is much less closely related to the S&P corporate bond yield spread, with a correlation of only about 0.1.1 The purpose of this paper is to measure the causes of variation, across companies and over time, in corporate bond yield spreads. Speci¢cally, we evaluate the volatility e¡ect while controlling for three factors: composition e¡ects, the demand for the liquidity provided by Treasury bonds, and special features of corporate bonds.We ¢rst study corporate bond pricing in a large panel data set, the Fixed Income Securities Database (FISD) on corporate bond characteristics, We note that average yield spreads reported by Moody’s have a smaller upward trend and are about equally correlated with idiosyncratic volatility and market volatility. We discuss both the S&P and Moody’s data in more detail in sections I and III below.

2324 The Journal of Finance matched to the National Association of Insurance Commissioners (NAIC) database on bond transactions in the period 1995 to 1999. We present new evidence that equity volatility explains as much variation in corporate credit spreads as do credit ratings. Controlling for general factors such as the reference Treasury rate, issue size, years to maturity, and time-series dummies, we ¢nd that equity volatility and credit ratings each explain about a third of the variation in corporate bond yield spreads. This ¢nding is robust to the use of issuer ¢xed e¡ects. We also explore the longer-term time-series behavior of corporate bond yields, as summarized by S&P and Moody’s yield indexes, and ¢nd that movements in idiosyncratic volatility help to explain these movements in average yields over time.

There is a large theoretical literature on the pricing of corporate bonds. This literature distinguishes between ‘‘structural’’ and ‘‘reduced form’’ models. In structural models, a ¢rm is assumed to default when the value of its liabilities exceeds the value of its assets, in which case bondholders assume control of the company in exchange for its residual value. Black and Scholes (1973), Merton (1974), and Ingersoll (1977) are some of the classic papers in this area. More recently, Longsta¡ and Schwartz (1995) argue that the corporate yield spread should vary inversely with the benchmark Treasury yield, and they ¢nd evidence to support this prediction. Collin-Dufresne and Goldstein (2001) develop a structural model in which a ¢rm can issue new debt, thereby increasing the risk of default and lowering the recovery rate in the event of default.

A di⁄culty with the structural approach is that investment-grade corporate bonds very rarely default. Elton et al. (2001) argue on this basis that expected default can account for only a small part of the yield spread for investment-grade corporate over Treasury bonds, while state taxes (which are payable on corporate interest but not onTreasury interest) are relatively much more important. Huang and Huang (2000) reach a similar conclusion.

Reduced form models, by contrast, assume exogenous stochastic processes for the default probability and the recovery rate. These models can allow for premia to compensate investors for illiquidity and systematic credit risk. They can be ¢t econometrically to data on swap spreads and corporate bond yields (Jarrow and Turnbull (1995), Du⁄e and Singleton (1997, 1999), Du¡ee (1999), Liu, Longsta¡, and Mandell (2000)). The added £exibility of the reduced-form approach allows default risk to play a somewhat greater role in the pricing of corporate bonds.

Our paper undertakes a less structured econometric analysis, asking what observable variables are correlated with corporate bond yields cross-sectionally and over time. There are several other recent papers in a similar spirit. CollinDufresne et al. (2001) ¢nd that a single unobserved factor, common to all corporate bonds, drives most variation in credit spread changes. Kwan (1996) shows that changes in a ¢rm’s stock price are negatively correlated with contemporaneous and future changes in the yields of its bonds. Du¡ee (1998) shows that yield spreads vary more strongly with benchmark Treasury rates for callable bonds than for noncallable bonds. But these papers have done little to explore the e¡ect of equity volatility on the cross-sectional variation, long-term time-series EquityVolatility and Corporate Bond Yields 2325 behavior or recent movements of corporate yield spreads. Our paper attempts to ¢ll this gap in the academic literature.2 The remainder of the paper is organized as follows. Section I describes our panel data and the restrictions we impose on it. This section also examines trends in corporate bond spreads between 1995 and 1999.We ¢nd that, even after considering bonds without option-like features, credit spreads have been rising.

However, this widening is not as large as would appear from the indexes produced by the credit rating agencies.

Section II links our data with equity and accounting data to investigate the link between equity volatility and corporate yield spreads. We present evidence that rising equity volatility dramatically raises the cost of borrowing.This e¡ect is robust to a choice of a market model to de¢ne idiosyncratic volatility, the use of issuer ¢xed e¡ects, and several other speci¢cation choices. This section also shows that the e¡ect of volatility on corporate yield spreads is much stronger than would be predicted by the simple structural model of Merton (1974). Thus, our results pose another challenge to theorists; not only are corporate yield spreads higher on average than would be predicted by the Merton model, they are also more sensitive to movements in equity volatility.

Section III returns to the time-series data, using an updated version of the idiosyncratic volatility series of Campbell et al. (2001), provided to us by Goyal and Santa-Clara (2003).We show that equity volatility helps to explain the movements of corporate yield spreads over the past several decades, and particularly in the late 1990s. Section IVconcludes.

I. Data Description Our data come from the Fixed Investment Securities Database (FISD) and National Association of Insurance Commissioners (NAIC) transactions data. The FISD database (LJS Global Information Services, 2000) contains issue- and issuer-speci¢c variables such as callability, credit ratings, and sector, on all U.S.

corporate bonds maturing in 1990 or later. The NAIC database consists of all 1995 to 1999 transactions by life insurance companies, property and casualty insurance companies, and Health Maintenance Organizations (HMOs) as distributed byWarga (2000).This database is an alternative to the no longer available Warga (1998) database used by Du¡ee (1998), Blume, Lim, and MacKinlay (1998), Elton et al. (2000, 2001), Hecht (2000), and Collin-Dufresne et al. (2001).

According to the Flow of Funds accounts published by the Federal Reserve, insurance companies hold about one-third of outstanding corporate bonds. Thus, the NAIC database should be adequately representative of corporate bond transactions. Other important holders include foreign residents (15% to 20%), The ¢nancial press has been more sensitive to the relation between equity volatility and corporate bond spreads. For instance, in October 2000, the Financial Times wrote, ‘‘The increased volatility in the equity markets is another sign of the rising risks faced by companies, and bond investors are starting to re-price their investments.’’ (Cha⁄n and Van Duyne, 2000, p. 25).

2326 The Journal of Finance households (15%), pension and retirement funds (15%), mutual funds (5% to 10%), and commercial banks (5%).

We restrict our sample to ¢xed-rate U.S. dollar bonds in the industrial, ¢nancial, and utility sectors that are noncallable, nonputtable, nonsinking fund, and nonconvertible. To ensure that we consider bonds backed solely by the creditworthiness of the issuer, we exclude issues with asset-backed and credit-enhancement features. While this last restriction eliminates almost one-quarter of corporate debt issues reported in the Flow of Funds accounts, the yield spread on asset-backed bonds represents the creditworthiness of the collateral rather than the creditworthiness of the issuer. As such, we must exclude these issues.



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