5. Conditional Fama–MacBeth cross-sectional regressions
Next, we carry out Fama–MacBeth cross-sectional regressions over sub-samples by conditioning for (a) underlying bond- and issuer-specific characteristics such as rating, equity volatility, bond liquidity, and industry classification, and (b) overall market conditions such as time-period to capture regime effects, aggregate equity market volatility, and aggregate bond market liquidity. The objective is to discern how the interaction between equity volatility and bond liquidity is altered while explain- ing bond spreads when underlying issue and firm characteristics and/or market conditions change. However, since we do not explicitly capture the exogenous shocks to either idiosyncratic volatility or liquidity, our results are best interpreted as stylized facts, rather than any causal evidence.
5.1. High- and low- rating categories
We first examine how the impact of volatility and liquidity differs between high-rated, rated AA or A, and low-rated, BBB or below, bond issues.
Equity volatility alone explains 38.45% of the variation in spreads for low-rated bonds and 4.50% for high-rated bonds, as revealed in regression 1b of Panels A and B in Table 7. After controlling for default and term structure factor betas in regression 2b, volatility still retains the dominant explanatory power for low-rated bonds, but not so for high-rated bonds. On the other hand, liquidity variables, i.e., bond characteristics and the price-impact index, together account for 9.21% of bond spreads for low-rated bonds, comparing regressions 2b and 3c in Panel A, and 12.94% for high-rated bonds, com- paring regressions 2b and 3c in Panel B. Thus, volatility has higher significance for distressed bonds, while the impact of liquidity is stronger for high credit issues.20
Table 8 summarizes the absolute and relative contributions of volatility and liquidity effects. We see that, based on the total adjusted R2 in regression 3c, volatility accounts for 77.46% of the total explanatory power for low-rated portfolios, and only 22.32% for high-rated bonds; similar numbers for liquidity are 18.55% for low-rated issues and 64.19% for high-rated bonds. Analogous findings emerge from the shock analysis: 1r shocks to volatility and liquidity in regression 3c increase bond spreads respectively by 171 and 54 bps for low-rated bonds, and 13 and 20 bps for high-rated is- sues. In absolute terms, both volatility and liquidity shocks matter more for low-rated issues, as seen in columns 6 and 7; on a relative basis, however, columns 8 and 9 show that volatility shocks are more prominent for low-rated issues, while liquidity shocks have a greater impact on high-rated bonds.
5.2. Additional tests
We further repeat conditional analysis for sub-samples based on several variables: issue-specific attributes like equity volatility, bond liquidity and industry, and overall market conditions such as time-period, VIX, and aggregate bond market liquidity. We form two portfolios based on the annual median values of each underlying variable or, based on industry, classify bonds into Financials vs. Industrials and Utilities, and then conduct cross-sectional regressions for each sub-sample. Table 8 tabulates the results. Columns 6 and 7, Table 8, reveal that, in absolute terms, effects of both volatility and liquidity shocks are more prominent for high-volatility bonds; however columns 8 and 9 indicate that, on a relative basis, volatility shocks matter more for high-volatility issues, while liquidity shocks are more evident for low-volatility issues. In terms of their relative contribution to the overall explan- atory power, as columns 4 and 5 show, there is a similar segmentation in volatility and liquidity effects.
When we form portfolios based on bond liquidity, we find that while high-liquidity index issues experience higher absolute effects of both shocks, the relative impact of equity volatility matters more for low-liquidity bonds, while liquidity variables are more relevant for high-liquidity bonds. We also examine the relative impact of volatility and liquidity by industry classification. Financial issues pos- sess better credit ratings and higher liquidity than other issues. In contrast, Industrials and Utilities are relatively high-yield issues. Volatility is more prominent for Industrial and Utility bonds, and liquidity variables have greater impact on Financial issues.
We run the Fama–MacBeth regressions separately for 1995–1999, high-growth, and 2000–2004, low-growth, sub-periods. The low-growth period is characterized by higher absolute impact of vola- tility and liquidity shocks on spreads; while the relative effect of volatility shock is higher in the low- growth period, the liquidity shock has a stronger effect in high-growth years. We also observe that liquidity variables have higher incremental power during low-VIX regime, while volatility matters more during high-VIX periods. Similarly, while low bond market liquidity regimes experience higher absolute shock impact, volatility matters substantially more during low market liquidity periods, and liquidity is more relevant during high aggregate liquidity years.
To summarize, the conditional analysis reveals that, on an absolute basis, distressed bonds (i.e., is- sues with low ratings, high equity volatility or low bond liquidity, and Industrials and Utilities) as well as distress regimes (i.e., recessionary years, periods of high equity volatility or low bond liquidity) experience a greater impact of shocks to both volatility and liquidity on corporate bond prices. How- ever, on a relative basis, idiosyncratic volatility effects are considerably more prominent for distressed bonds and during high-distress regimes, whereas the liquidity variables have comparatively higher information content for low-distress bonds and during low-distress regimes.