Capital Structure Arbitrage Across Debt and Equity

A company's equity and its debt are claims on the exact same set of assets, just with different priority — equity holders get whatever is left after debt is paid. That shared foundation means the stock price and the bond's credit spread should move together in a predictable way: bad news that hurts the stock should also widen the credit spread, and vice versa. When the two markets temporarily disagree about how bad the news really is, capital structure arbitrage is the trade that bets on them converging.

The Merton-model bridge

Merton's insight: if a firm's assets are worth more than its debt at maturity, equity holders keep the residual and pay the debt off — equity behaves like a call option on the firm's assets, struck at the debt's face value. If assets are worth less, the firm defaults, equity is worthless, and debt holders take what's left — debt holders are effectively short a put option on the firm's assets. This means a firm's implied credit spread can be derived from its equity value, equity volatility, leverage, and debt maturity, using option-pricing machinery, exactly the mechanism behind Default Correlation and the Asset Threshold Model's asset-value framing, applied here to a single firm instead of a portfolio.

Worked example: spotting a dislocation

A company's equity has fallen 25 percent over two weeks on disappointing earnings, and equity implied volatility has risen from 30 percent to 45 percent — both signs the market sees more risk in the firm's assets. A Merton-style model, fed the new equity price and volatility along with the firm's known debt level and maturity, implies the firm's 5-year credit spread should now be trading around 320 basis points, up from a prior 180.

But the bond market, slower to react and thinner in liquidity (see The Corporate Bond Market and How It Trades), has only widened the actual traded spread to 230 basis points. The arbitrageur sees a 90-basis-point gap between the model-implied spread (320) and the market spread (230) and puts on the trade: buy protection via CDS (betting the spread widens further, converging toward the model-implied level) while simultaneously buying the stock or an equivalent equity hedge, because if the credit view is right and things really are worse, the delta-hedged equity position offsets losses if the stock falls further, and if instead the market is right and the credit spread actually tightens back toward the market level, the CDS protection can be unwound at a gain relative to entry — the position is structured to profit from convergence in either direction, not from a directional bet on the stock or the bond alone.

Worked example: sizing the equity hedge

The trade buys $10 million notional of 5-year CDS protection at 230 basis points. To hedge the equity leg, the model's Merton framework gives a "credit delta" — how much the CDS spread moves per 1 percent move in the stock price — of roughly 4 basis points of spread per 1 percent stock move at current levels. To be roughly market-neutral to small equity moves, the desk shorts (or, if betting the same direction as credit deterioration, goes long puts on) a stock position sized so that a 1 percent equity move changes the equity leg's P&L by approximately the same dollar amount as a 4-basis-point CDS spread move on $10 million notional — roughly $10{,}000{,}000 \times 0.0004 \times 4 \approx 16{,}000$ of CDS P&L per 1 percent stock move, which the equity leg is sized to offset, leaving the position exposed mainly to the relative mispricing between the two markets rather than to the stock's direction outright.

Where you meet it in practice

Capital structure arbitrage desks at credit hedge funds run Merton-style or reduced-form models across hundreds of names continuously, screening for exactly this kind of equity-credit gap. It is also the conceptual backbone behind why equity analysts and credit analysts covering the same company should, in principle, arrive at consistent views — and why, when they don't, it is often the first sign one side of the market hasn't caught up yet.