Default Risk in Equity Returns

Source: Vassalou, M. & Xing, Y. (2004). Journal of Finance 59(2), 831–868.

TL;DR

First study to use Merton's (1974) option-pricing model to compute firm-level **default likelihood

indicators (DLI)** from equity data and ask whether default risk is priced. It finds default risk is

systematic and priced, and that the size and book-to-market (BM) effects are largely *default

effects* that exist only within the high-default-risk segments of the market. The Fama-French SMB

and HML factors contain some default-related information, but that is not the main reason the FF model

explains the cross-section. Sample: 1971:1–1999:12.

Predictor: Merton-model default likelihood (DLI), interacted with size and BM.

Direction: Within high-default-risk stocks, high default risk → higher returns; small > big and

value > growth. Outside the high-default segments, the size and BM premia essentially vanish.

Shape: Highly conditional / non-monotonic — the premia are concentrated, not pervasive. Default

risk decreases monotonically with size and increases monotonically with BM.

Treat firm equity as a call option on firm assets (Black-Scholes/Merton). Back out asset value and

asset volatility iteratively (KMV/Crosbie 1999 procedure) using monthly equity data and book debt.

Compute the DLI, a nonlinear function of the firm's default probability (the probability that

asset value falls below the default point at the one-year horizon). Risk-free rate = 1-year T-bill.

Aggregate measure P(D) = simple average of firm DLIs; it varies with the business cycle (rises in

recessions). Sort stocks on DLI and double-sort within size / BM groups; run cross-sectional tests.

Size effect exists only in the highest-DLI quintile, where the small-minus-big return gap is on

the order of ~45% per annum; small stocks there are the smallest of the small with the highest BM.

BM effect exists only in the two highest-DLI quintiles: ~30% p.a. in the top quintile,

falling to 12.7% p.a. in the second-highest; no BM effect elsewhere.

High-default firms earn higher returns only if also small and high-BM; otherwise high default

risk alone does not earn higher returns.

Default risk is found to be systematic, hence priced. DLI carries information distinct from the

aggregate BAA–AAA default spread (consistent with Elton et al. 2001).

Note the contrast with Campbell-Hilscher-Szilagyi (2008), who find the most distressed stocks

earn low returns — the sign of the distress-return relation is sensitive to the failure measure and

sample, and remains debated (the "distress puzzle").

A rational default-risk premium: investors demand compensation for systematic bankruptcy risk that

rises in recessions.

The size/value link suggests SMB and HML partly capture distress exposure, though the authors argue

SMB/HML also contain priced information unrelated to default.

Default measure is model-dependent (Merton/KMV assumptions, iterative asset-volatility estimation).

Result conflicts with later distress-puzzle findings (opposite sign of the distress-return relation).

Effects are concentrated in tiny, illiquid, high-BM small caps where trading costs and shorting

frictions are severe; debt data limits the sample to post-1971.

Vassalou, M. & Xing, Y. (2004) — Default Risk in Equity Returns — Journal of Finance

Campbell, J., Hilscher, J. & Szilagyi, J. (2008) — In Search of Distress Risk — Journal of Finance

Merton, R. (1974) — On the Pricing of Corporate Debt — Journal of Finance

Provenance: verified/generated from the paper's full text.