FRM Exam Part II · Hedge Fund Investment Strategies

Fixed Income and Convertible Arbitrage Strategies Explained

Updated 11 October 2026 · Fact-checked

Relative value strategies buy a cheap instrument and sell a related expensive one, aiming to earn a small spread as prices converge. Fixed-income arbitrage trades bond mispricings, convertible arbitrage is long convertible bond and short stock, and volatility arbitrage trades implied against realised volatility. Leverage magnifies small returns and liquidity risk.

Understand Relative Value Strategies: Fixed Income and Convertible Arbitrage

A relative value strategy does not bet on market direction. You find two related instruments whose prices are out of line, buy the cheap one, short the expensive one, and wait for the gap to close. The hedge removes most market risk. What remains is the spread.

Spreads are small, so funds use leverage to make them worthwhile. This is the core risk. If the spread widens instead of narrowing, losses are large and margin calls can force sales at the worst time. Returns look like selling insurance: steady small gains, then rare large losses. Payoffs are often described as short a put on liquidity or on convergence.

Fixed-income arbitrage includes on-the-run vs off-the-run Treasuries, swap spread trades, yield curve trades and mortgage basis trades. Each exploits a different spread. In the on-the-run vs off-the-run trade, the fund is long the cheaper, less liquid off-the-run bond and short the more liquid on-the-run bond, and the long leg is typically funded with repo. The profit comes from the liquidity premium narrowing. Swap spread, yield curve and mortgage basis trades target other spreads, not this one. LTCM (1998) is the classic lesson: very high leverage, positions that were all exposed to the same factor (liquidity and credit spreads), and a flight to quality when spreads widened. Historical correlations and VaR understated risk because diversification vanished in stress.

Convertible arbitrage is long a convertible bond and short the underlying stock. A convertible is a bond plus a call option on the stock. The fund buys the option cheaply, often because the convertible is priced on low implied volatility, and hedges equity risk by shorting delta shares. As the stock moves, delta changes (gamma), so the fund rebalances: sell stock as it rises, buy as it falls. This long gamma position earns from volatility. Income also comes from the bond coupon plus the short rebate: the interest earned on the short-sale proceeds, net of the stock borrow fee. The fund also pays its funding cost. Other risks: credit spread widening (can be hedged with CDS), interest rate risk (hedged with swaps or futures), stock borrow recall or short-selling bans, and illiquidity.

Volatility arbitrage trades implied volatility against expected realised volatility, usually with delta-hedged options. If implied is lower than your forecast of realised, you buy options and delta hedge, and profit from gamma. If implied is higher, you sell options and hedge, collecting theta but exposed to large moves. The difference from convertible arbitrage: convertible arbitrage is a credit and equity-linked trade with a bond and coupon, while volatility arbitrage uses pure options (or variance swaps) and focuses only on volatility.

Key formulas to remember

Convertible bond hedge (delta hedge): Shares to short = Delta × Conversion ratio × Number of bonds; Delta is the option delta per share of the embedded call, between 0 and 1. The hedge makes the position roughly neutral to small stock moves.
Conversion value: Conversion value = Conversion ratio × Stock price; Compare with the convertible's price. Premium = Convertible price − Conversion value, often divided by conversion value to give a percentage.
Delta-hedged P&L (approximate): P&L ≈ ½ × Gamma × (ΔS)² + Theta × Δt + Vega × Δσ; Long gamma gains from large moves in either direction and pays theta. Vega gain comes from implied volatility rising.
Break-even move: Daily break-even move ≈ S × σ_implied ÷ √252; This is approximately the one-day move implied by the volatility. A single day's move larger than this gives a gain for that day on a gamma-theta basis. Over a period, a delta-hedged long-gamma position profits when realised volatility exceeds the implied volatility embedded in theta. Use 252 trading days.
Leverage: Leverage = Total position value ÷ Equity capital; A spread return r on positions gives return ≈ leverage × r on equity, before funding costs. Losses are magnified the same way.
Convertible arbitrage return sources: Return = Coupon income + Short rebate − Borrow and funding cost + Gamma trading profit ± Spread changes; Use this to identify what drives profit and which risks need separate hedges.

How to solve Relative Value Strategies: Fixed Income and Convertible Arbitrage questions

Use this sequence for any question on relative value strategies.

1Identify the strategy: fixed-income arbitrage, convertible arbitrage or volatility arbitrage.
2Write down the long and short legs and the spread or mispricing the trade expects to converge.
3List the risk factors left after the hedge: gamma, vega, credit spread, interest rate, liquidity, borrow and funding.
4Do any required calculation: shares to short = delta × conversion ratio × bonds, or the gamma P&L approximation.
5Check the direction of each Greek: long convertible means long gamma and long vega, with negative theta.
6Think about leverage and liquidity: what happens if the spread widens or financing is withdrawn.
7Match the answer to the stated risk or lesson (for example LTCM: leverage, crowded trades, correlation rising in stress).

Quickest way: Three-question shortcut

When to use it: Use for conceptual MCQs where options differ in which risk or Greek is described.

Ask: what is long and what is short? Long convertible plus short stock means long gamma, long vega, long credit risk.
Ask: what hurts it? Falling volatility, wider credit spreads, short squeezes or short-sale bans, and funding withdrawal.
Ask: what is the tail event? Liquidity crisis plus leverage forces unwinds, as with LTCM and the 2008 convertible arbitrage losses.
Eliminate any option that says the strategy is market-neutral and therefore free of risk.

Common mistakes in Relative Value Strategies: Fixed Income and Convertible Arbitrage

Treating relative value as risk-free because it is hedged.
Hedging removes market direction, so students assume nothing is left.
Fix: Remember the residual risks: spread widening, liquidity, credit, financing and model risk. Leverage makes them large.
Confusing convertible arbitrage with volatility arbitrage.
Both are long gamma and rely on delta hedging.
Fix: Convertible arbitrage holds a bond with a call and has credit and rate exposure. Volatility arbitrage uses pure options and trades implied vs realised volatility.
Getting the hedge direction wrong.
Students forget the embedded option is a call.
Fix: A convertible has positive delta, so you short stock. Short shares = delta × conversion ratio × number of bonds.
Saying the long convertible position has positive theta.
Students focus on coupon income instead of option decay.
Fix: The option component is long, so theta is negative. Coupons and short rebate offset it.
Blaming LTCM only on bad models.
Students recall the Nobel laureates and model story.
Fix: Key causes were extreme leverage, concentrated and crowded positions, illiquidity, and correlations rising in stress. Models understated tail risk.
Forgetting that gamma profits require movement, not direction.
Students assume a hedged position needs the stock to rise.
Fix: Long gamma profits from large moves either way if realised volatility exceeds what was priced.

Worked examples

Example 1

A fund buys 2,000 convertible bonds. Each converts into 25 shares. The embedded option delta is 0.60. How many shares should it short to delta hedge? If the stock then rises and delta becomes 0.70, what must it do?

Show the solution

Shares underlying the bonds = 2,000 × 25 = 50,000.
Hedge = 0.60 × 50,000 = 30,000 shares short.
New hedge = 0.70 × 50,000 = 35,000 shares short.
Extra shorting = 35,000 − 30,000 = 5,000 shares.
Selling after a rise is the long gamma pattern: sell high, buy low on falls.

Answer: Short 30,000 shares initially. After delta rises to 0.70, short another 5,000 shares to reach 35,000.

Example 2

A convertible arbitrage fund has equity of USD 100 million and positions worth USD 600 million. Positions lose 2% in a liquidity shock. Ignoring funding costs, what is the return on equity and what is the key lesson?

Show the solution

Leverage = 600 ÷ 100 = 6.
Loss on positions = 2% × USD 600 million = USD 12 million.
Return on equity = −12 ÷ 100 = −12%.
Equivalent check: 6 × (−2%) = −12%.
A small spread move becomes a large equity loss, and margin calls or redemptions may force sales into illiquid markets, deepening losses.

Answer: The return on equity is −12%. Leverage magnifies small spread moves, and forced liquidation is the main tail risk, as in LTCM.

Exam tips

Know what each Greek does for a long convertible: long gamma, long vega, negative theta, positive delta that must be hedged.
For LTCM, link the answer to leverage, crowded trades, liquidity and rising correlations rather than model error alone.
Expect scenario questions: volatility falls, credit spreads widen, short-selling ban or stock borrow recall. Say which leg or Greek is hurt.
Read the hedge instruction carefully: delta hedge removes stock risk only, not credit or rate risk.
Distinguish the three strategies by instruments used and the spread being traded.

Practice questions from Hedge Fund Investment Strategies

Relative Value Strategies: Fixed Income and Convertible Arbitrage in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

CFA Level IIRelative Value Strategies

Relative Value Strategies: Fixed Income and Convertible Arbitrage: frequently asked questions

What is convertible arbitrage in simple terms?

You buy a convertible bond and short some of the underlying stock. The short removes most stock price risk, leaving you with the bond's coupon and the value of the embedded option. You profit when the stock moves a lot or the option was cheap.

How do you hedge the delta and gamma of a convertible bond?

Delta is hedged by shorting delta × shares underlying the bond. Gamma is not removed by this. You manage it by rebalancing the short stock as delta changes, or by using options if you need to cut gamma exposure.

What is the difference between convertible arbitrage and volatility arbitrage?

Convertible arbitrage holds a bond plus option and carries credit, interest rate and borrow risk. Volatility arbitrage trades pure options or variance swaps on the gap between implied and realised volatility. Both rely on delta hedging.

What are the main lessons from LTCM for fixed-income arbitrage?

High leverage turned small spread trades into existential risk. Positions were large, crowded and illiquid. Correlations rose in the 1998 flight to quality, so diversification failed, and VaR understated the tail.