volatility of idiosyncratic risk. In particular, firms with higher leverage display a
smaller variance of their returns to capital.
This relationship between leverage and volatility of the idiosyncratic risk is some-
how counterintuitive, as firms with high leverage are generally thought to be riskier
than firms with low leverage. There appear to be two reasons for this result. The
first reason has to do with the assumption that ωit is distributed log-normally. Al-
though useful to obtain easily tractable expressions for ψ(ωtt; σ) and ξ(ωt; σ,μ), this
assumption implies that the leverage-spread schedule is extremely steep. As a result,
the only way for the model to fit the data is to assign a lower σit to a firm that
experienced an increase in its leverage.28
The second reason is the assumption of one-period debt in the BGG model, imply-
ing that the marginal and the average cost of external finance coincide in the model.
By contrast, credit spreads in our dataset, although they likely represent an accurate
measure of the marginal cost of external finance, are certainly a poor measure of the
average cost of external finance, as long-term bonds have a fixed coupon payment
and in many cases were issued before the drop in stock prices.
28As shown in Figure 3, the leverage-spread schedule shifts to the right as σ gets smaller, implying
a smaller spread for given leverage.
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