Hedge Fund Strategies: formula sheet

Key formulas

Management fee

Management fee = management fee rate × AUM (beginning, average or ending, as stated)

Charged regardless of performance. Use the AUM basis the vignette gives.

Incentive fee, no hurdle

Incentive fee = incentive rate × max(0, ending value − max(starting value, HWM) − management fee [only if the fee is calculated net of the management fee])

Only if ending value exceeds the high-water mark. If it does not, the fee is zero.

Hard hurdle

Incentive fee = incentive rate × max(0, profit − hurdle amount)

Fee only on the excess over the hurdle.

Soft hurdle

If profit > hurdle amount: incentive fee = incentive rate × profit. Otherwise 0.

Fee on the full profit once the hurdle is cleared.

High-water mark

Fee-eligible profit = ending NAV − max(beginning NAV, HWM)

If the result is negative or zero, no incentive fee is due.

Net return to investors

Net return = (ending NAV after all fees ÷ beginning NAV) − 1

Subtract both fees from the gross ending value.

Net exposure

Net exposure = Long exposure % − Short exposure % (of fund capital)

Example: 130% long and 30% short gives net 100%. Net near 0 means market neutral. Net negative means short bias.

Gross exposure

Gross exposure = Long exposure % + Short exposure %

Measures total capital at work and leverage. Gross can exceed 100% even when net is low.

Return of a market neutral position (approx.)

Spread return ≈ Return of longs − Return of shorts

Ignores short rebate, borrow costs and fees. A short loses when the shorted stock rises.

Beta-adjusted net exposure

Net beta exposure = Σ(long weight × beta) − Σ(short weight × beta)

Beta neutral is stricter than dollar neutral. Equal dollars do not mean zero market risk if betas differ.

Deal spread (dollar)

Spread = Offer price − Target market price

For a cash deal. For a stock deal, use the offer value implied by the acquirer's price times the exchange ratio.

Spread return (not annualised)

Spread return = (Offer price − Target price) ÷ Target price

This is the return if the deal closes at the offer price, ignoring costs and dividends.

Annualised spread return (simple)

Annualised ≈ Spread return × (12 ÷ months to close)

A quick approximation. Compounding gives (1 + spread return)^(12 ÷ months) − 1.

Stock-deal offer value

Offer value per target share = Exchange ratio × Acquirer share price

The arbitrageur buys one target share and shorts exchange-ratio shares of the acquirer.

Expected value with deal probability

E(P) = p × Price if deal closes + (1 − p) × Price if deal fails

Used to find the market-implied probability: p = (Current price − Fail price) ÷ (Close price − Fail price).

Convertible arbitrage hedge

Shares to short = Delta × Number of shares the bond converts into

Delta is the equity-option delta of the conversion feature. Short this many shares per bond to be delta neutral.

Volatility arbitrage signal

Implied vol < forecast realized vol → buy options and delta-hedge; implied vol > forecast realized vol → sell options and delta-hedge

The profit depends on realized volatility versus the volatility priced in at entry.

Convertible bond value

Convertible value ≈ Straight bond value + Value of call option on the stock

Conceptual decomposition. Issuer's call or investor's put features adjust the value.

Spread trade payoff idea

Profit ≈ Change in spread × Position size (per unit of spread sensitivity) − Financing cost

Gains come from convergence. Leverage magnifies both gains and losses.

Net return of a fund of funds

FoF net return = Underlying funds' net return (after their fees) − FoF management fee − FoF incentive fee

Underlying fees come out first, then the FoF fees. Use the order given in the vignette.

Incentive fee with a hurdle

Incentive fee = incentive rate × (return − hurdle) × assets, if return > hurdle

Apply only when the vignette says the fee is charged above a hurdle. Without a hurdle, apply the rate to the full return.

Weighted return of underlying funds

R = Σ (wᵢ × Rᵢ)

Use the net returns of each underlying fund and the FoF allocation weights.

Fee drag

Fee drag = gross return − net return

Use it to compare a FoF with a multi-strategy fund on the same gross return.

Sharpe ratio

Sharpe = (Rp − Rf) ÷ σp

Overstated when volatility is understated by smoothing and ignores skew and kurtosis.

Sortino ratio

Sortino = (Rp − MAR) ÷ downside deviation

Penalises only returns below the minimum acceptable return, so it suits skewed returns.

Survivorship bias effect

Reported return > true return; reported risk < true risk

Failed funds are dropped from the database.

Backfill bias effect

Reported return > true return

Earlier good history is added once a fund starts reporting.

Smoothing effect

Reported σ < true σ; reported correlation < true correlation; Sharpe overstated

Caused by stale or estimated valuations of illiquid assets, which creates positive serial correlation.

Non-normal return signs

Skewness < 0 and excess kurtosis > 0

Typical of many hedge fund strategies; mean-variance analysis then understates tail losses.

Quick revision

• Hedge funds typically charge a management fee on assets plus an incentive fee on profits.
• Check whether the incentive fee is computed before or after the management fee, and whether a hurdle or high-water mark applies.
• A high-water mark means the manager earns incentive fees only on gains above the prior peak value.
• Equity hedge strategies include long/short, market neutral and short bias, which differ in net market exposure.
• Event-driven strategies include merger arbitrage, distressed securities and activist approaches, driven by corporate events.
• Merger arbitrage typically goes long the target and may short the acquirer in a stock deal; deal failure is the main risk.
• Relative value strategies exploit pricing gaps between related securities, often using leverage.
• Macro funds take views on economic variables; managed futures funds usually follow systematic rules in futures markets.
• Funds of funds add diversification and due diligence but a second layer of fees.
• Survivorship bias and backfill bias tend to overstate reported index returns.
• Illiquid holdings can give smoothed returns that understate volatility and correlations.
• Always answer from the vignette facts, not from a general view of the strategy.

Common mistakes

• Treating a soft hurdle like a hard hurdle. Fix: Hard hurdle: fee only on the excess. Soft hurdle: fee on the whole profit once the hurdle is cleared.
• Charging an incentive fee on profit that only recovers a prior loss. Fix: Compare ending NAV with the HWM first. Fee applies only above the HWM.
• Treating market neutral as risk free Fix: Remember it removes market direction risk only. Stock selection, leverage, factor and liquidity risks remain.
• Assuming equal dollar longs and shorts means zero beta Fix: Check betas in the vignette. Compute Σ(weight × beta) on each side before calling a fund beta neutral.
• Saying merger arbitrage is market-neutral with no real risk. Fix: Remember the hedge does not cover deal failure. If the deal breaks, the target falls and the loss is large relative to the small spread.
• Shorting the target and buying the acquirer in a stock deal. Fix: The usual trade is long the target, short the acquirer. The target trades below the implied offer value, so you buy it.
• Calling relative value funds directional because they use leverage. Fix: Leverage amplifies spread moves. The bet is on the gap between securities, not on market direction.
• Mixing up convertible arbitrage with event-driven investing. Fix: Convertible arbitrage needs no corporate event. It profits from mispricing and hedged option value.
• Treating macro and managed futures as the same strategy. Fix: Ask what drives the trade. Macro uses an economic or policy thesis; trend-following managed futures follows price movement.
• Assuming all CTAs are systematic. Fix: CTAs can be systematic or discretionary. Read the vignette for who makes the final trade decision.

Exam tips

• Underline the fee order and AUM basis in the vignette. The same numbers give different answers if the order changes.
• Always test the HWM first. If NAV is at or below it, the incentive fee is zero and you can skip the rest.
• Hard versus soft hurdle is a favourite conceptual question. Say whether the fee applies to the excess or to the whole profit.
• Expect qualitative questions on why fees create incentives for risk taking, since the incentive fee resembles a call option.
• No penalty for wrong answers, so never leave a fee question blank.
• Always compute net and gross exposure from the numbers in the vignette before choosing a strategy label.
• When betas are given, test beta neutrality. Dollar neutral alone is a common trap.
• For risk questions, tie the answer to the strategy: short squeeze for short bias, leverage for market neutral, model risk for quantitative funds.