The S&P 500 is up 3% this month, down 2% next month, flat after that. A well-run convertible arbitrage desk tries to keep those swings from driving its results, because it is not betting on the market. It is betting that the option embedded in a convertible bond is priced cheaply relative to the volatility the stock actually delivers. Its monthly P&L still moves with stock volatility, credit spreads, and liquidity, because no hedge is perfect.
Relative value strategies exploit pricing discrepancies between related securities while hedging out most market risk. You are long one security, short a closely related one, and you win when the spread converges. The goal is little net market exposure. The hedge rests on a model, though, so some directional risk usually remains.
Two securities are "related" when an economic, contractual, or empirically observed link ties their prices together. Examples include a convertible and its underlying stock (via the conversion option) and an on-the-run Treasury (the most recently issued bond at a given maturity) and an off-the-run Treasury (an older...
Common mistakes
- Confusing hybrid with busted convertibles. Hybrid sits near the money and typically has high positive gamma, the arbitrageur's target. Busted has the stock far below conversion (delta near 0); the option is nearly worthless and the bond behaves mainly like straight debt, with credit and interest-rate risk.
- Treating delta hedging as static. The mistaken plan is "delta hedge once and collect coupon." A delta-neutral long convertible actually gains from an immediate move in either direction, as Example 1 shows. That is positive gamma. The problem is that a static hedge stops being delta-neutral after the move.
- Assuming the variance risk premium is risk-free. "Arbitrage" in vol arb does not mean riskless. Selling variance is short convexity: small premiums most of the time, then sharp losses when vol spikes during a sell-off. Do not equate zero beta with no risk.
Bottom line
- Relative value bets on spread convergence between securities linked by theory or empirical history. Neutrality is a hedged target, not a guarantee, and soft catalysts give no convergence date.
- Convertible arbitrage buys the convert and shorts the underlying to delta-hedge, earning cheap embedded vol (the complexity premium), coupon, short rebate, and gamma scalping. Unbundle the price as straight-debt PV plus conversion ratio times the per-share call.
- Hybrid (at-the-money) converts typically offer high positive gamma (delta near the middle of its range and changing quickly); busted and equity-sensitive converts give minimal arb opportunity.
- Positive gamma is the profit engine: a delta-neutral long convert gains on an immediate move either way, and resetting to the new delta restores neutrality.
Exam shortcut
When a strategy hedges most systematic risk to isolate a spread between related securities, and convergence rests on a theoretical or empirical norm rather than a dated event, it is relative value. Distinguish catalysts: a hard catalyst is a specific event expected to move prices (event-driven), while a soft catalyst is a valid reason for convergence with no triggering event (relative value).
The full lesson (about 10,337 words, 69 min read) adds 2 worked examples, all 8 common mistakes, a self-check, free in the app.
Learning objectives
- distinguishing
- short selling
- arbitrage-free models
- returns allocation
- multistrategy
- research
- indices
- macro overview
- macro
- managed futures
- systematic trading
- trend following
- mf dimensions
- systematic construction
- mf benefits
- mf evidence
- mf fund benefits
- event sources
- activist investing
- activism outcomes
- merger arb
- distressed securities
- event multi special
- rv overview
- convertible arb overview
- convertible arb drivers
- vol arb overview
- vol arb strategies
- fi arb
- rv multistrategy
- equity commonalities
- sources of return
- market anomalies
- anomaly strategies
- equity shorts
- three strategies
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