Regression Models with Categorical Variables 121
where Spreadi=option-adjusted spread (in basis points) for the
bond issue of company i
Couponi=coupon rate for the bond of company i,
expressed without considering percentage sign
(i.e., 7.5% = 7.5)
CoverageRatioi=earnings before interest, taxes, depreciation
and amortization (EBITDA) divided by interest
expense for company i
LoggedEBITi=logarithm of earnings (earnings before inter-
est and taxes, EBIT, in millions of dollars) for
company i
The dependent variable, Spread, is not measured by the typically nomi-
nal spread but by the option-adjusted spread. This spread measure adjusts
for any embedded options in a bond.^4
Theory would suggest the following properties for the estimated coef-
ficients:
■ (^) The higher the coupon rate, the greater the issuer’s default risk and
hence the larger the spread. Therefore, a positive coefficient for the cou-
pon rate is expected.
■ (^) A coverage ratio is a measure of a company’s ability to satisfy fixed
obligations, such as interest, principal repayment, or lease payments.
There are various coverage ratios. The one used in this illustration is the
ratio of the earnings before interest, taxes, depreciation, and amortiza-
tion (EBITDA) divided by interest expense. Since the higher the cover-
age ratio the lower the default risk, an inverse relationship is expected
between the spread and the coverage ratio; that is, the estimated coef-
ficient for the coverage ratio is expected to be negative.
■ (^) There are various measures of earnings reported in financial statements.
Earnings in this illustration is defined as the trailing 12-months earnings
before interest and taxes (EBIT). Holding other factors constant, it is
expected that the larger the EBIT, the lower the default risk and there-
fore an inverse relationship (negative coefficient) is expected.
We used 100 observations at two different dates, June 6, 2005,
and November 28, 2005; thus there are 200 observations in total. This
will allow us to test if there is a difference in the spread regression for
(^4) See Chapter 18 in Frank J. Fabozzi, Bond Markets, Analysis, and Strategies, 8th ed.
(Upper Saddle River, NJ: Prentice-Hall, 2013).