Relative-value strategies are defined by what they explicitly refuse to do: take a naked directional market view. Instead they buy one instrument and sell a related one, hedging out the shared risk factor and keeping only the mispriced difference between the two. Capital-structure arbitrage trades a single issuer's bonds against its equity, exploiting the fact that the two securities are claims on the same enterprise value with different priority and different sensitivity to credit deterioration, this is precisely where E11.01's credit-spread decomposition (spread ≈ probability of default × loss given default) and priority-of-claims waterfall belong: a capital-structure arbitrageur is, in effect, trading a view on how the market is pricing that same PD/LGD relationship differently across an issuer's bonds versus its equity, and this module leans on that framework rather than re-deriving it. Fixed-income relative value trades related government or swap instruments against each other (an on-the-run bond versus an off-the-run bond of similar maturity, or a swap-spread trade) for a few basis points, run at meaningful leverage to turn a small edge into a real return: LTCM (discussed in the module) is the canonical cautionary tale of exactly this trade type. Statistical/pairs arbitrage is the equity long/short pair trade, generalized into a systematic, often high-turnover process across hundreds of pairs at once.
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How does convertible-bond arbitrage work?
Convertible-bond arbitrage is the family's clearest teaching case because it makes the hedge visible. A convertible bond is part ordinary bond, part embedded call option on the issuer's stock; its price therefore moves with the stock, but less than one-for-one, at a ratio the option's delta describes. An arbitrageur buys the convertible and shorts the underlying stock in an amount equal to delta × the bond's conversion ratio, which (for a small stock move) leaves the position's equity exposure approximately hedged away (Worked Example 7 computes this exactly: a $4.00 stock move nets to $0.00 combined P&L on the hedged position). This module takes delta as a given input, because DV1.02 builds delta, gamma, vega, and theta from the option-pricing mathematics properly; what belongs here is only the fund-level point: because the small-move directional risk is hedged away, the strategy's actual return comes from elsewhere, a credit/carry component (the bond's yield versus the cost of financing the position and borrowing the stock to short) and a volatility-trading component (as the stock moves, the option's delta itself changes, that is gamma, DV1.02's territory, forcing the arbitrageur to rebalance the hedge, and that continuous rebalancing captures a profit stream when realized volatility exceeds what was priced into the convertible at purchase). A relative-value fund's marketing materials describe this as "harvesting cheap volatility" or "capturing a credit spread"; underneath, it is always some version of buy the mispriced instrument, hedge away the risk you are not being paid to hold, and keep whatever is left.