CFA Level I · CFA Level I Exam

Hedge Funds: formula sheet

Full chapter guide

Key formulas

Hedge fund vs mutual fund: Hedge fund: private, lightly regulated, flexible, leverage and shorting, performance fees, limited liquidity. Mutual fund: public, heavily regulated, mostly long-only, daily liquidity, benchmark-relative.; Use this as a checklist to sort any statement in an exam item.
Typical fee structure: Total fee = management fee (% of assets under management) + incentive fee (% of profits); Details such as hurdle rates and high-water marks belong to the fee structures topic.
Master-feeder: Feeder funds (onshore, offshore) → one master fund → one portfolio; The portfolio is held and traded at the master level.
Fund of funds: Investor → fund of funds → several hedge funds; Gives diversification and due diligence, but adds a second layer of fees.
Management fee: Management fee = management fee % × AUM (beginning, average or ending, as stated); Charged regardless of performance. Use the AUM basis the question specifies.
Incentive fee, no hurdle: Incentive fee = incentive % × profit (if profit > 0); Profit may be measured before or after the management fee. Check the wording.
Incentive fee, hard hurdle: Incentive fee = incentive % × (profit − hurdle amount), if positive; Hurdle amount = hurdle rate × beginning value. Fee is on the excess only.
Incentive fee, soft hurdle: Incentive fee = incentive % × profit, if profit > hurdle amount; otherwise 0; Once the hurdle is cleared, the manager earns the fee on all profit.
Incentive fee with high-water mark: Incentive fee = incentive % × (NAV before incentive fee − HWM), if positive; Only gains above the previous peak NAV (after fees) are charged.
Net return to investor: Net return = (ending NAV after all fees ÷ beginning NAV) − 1; Ending NAV after all fees = gross ending value − management fee − incentive fee.
Net exposure: Net exposure = (Long positions − Short positions) ÷ Capital; Market neutral is near 0%. Short bias is negative. Dedicated long is high and positive.
Gross exposure: Gross exposure = (Long positions + Short positions) ÷ Capital; Shows total leverage. Two funds with the same net exposure can have very different gross exposure and risk.
Typical strategy ordering by market exposure: Short bias < Market neutral < Long/short < Dedicated long; A typical ordering only, not a fixed rule. Long/short net exposure can vary widely and can fall below market neutral or turn negative. A leveraged long/short fund can have more beta than a dedicated long fund.
Deal spread (cash deal): Spread = Offer price − Target price; Gross profit per share if the deal closes.
Spread return: Spread return = (Offer price − Target price) ÷ Target price; Not annualized. Annualize by scaling for time to close if the question asks.
Stock-deal hedge: Shares of acquirer shorted per target share = Exchange ratio; Long target, short acquirer in the exchange ratio to hedge price moves.
Expected value of a deal: E(payoff) = P(close) × Price if closes + (1 − P(close)) × Price if breaks; Used to find the probability implied by the current target price.
Relative value trade structure: Long underpriced security + Short overpriced related security → profit if the spread converges; Profit depends on the spread, not the market direction. This is the core idea behind all three strategies.
Convertible arbitrage position: Long convertible bond + Short issuer's common stock (hedge ratio based on delta); The convertible embeds a call option on the stock. The short stock hedges the equity exposure.
Volatility arbitrage rule: Implied volatility > expected realized volatility → sell options; implied volatility < expected realized → buy options; Usually delta-hedged so the position is not a directional bet.
Fixed-income arbitrage rule: Long cheap fixed-income security + Short rich related security or derivative, often duration-neutral; Exposure is to the spread. Leverage amplifies losses if the spread widens.
Survivorship bias effect: Index return (survivors only) > true average return of all funds; Failed funds drop out, so reported returns are overstated and risk understated.
Backfill bias effect: Added history of newly listed fund → upward bias in index; Managers tend to begin reporting after strong results.
Smoothed returns effect: Reported σ < true σ; correlation with marked-to-market assets: reported < true (generally); Caused by stale or model-based pricing of illiquid assets. The correlation effect applies mainly against assets that are marked to market.
Net return after fees: Net return = Gross return − management fee − incentive fee; Use net-of-fee returns when comparing with equities.
Sharpe ratio: (Rp − Rf) ÷ σp; Overstated when σ is understated by smoothing; weak for negatively skewed, fat-tailed returns.

Quick revision

Hedge funds are privately offered, flexibly mandated and less regulated than mutual funds, and they often use leverage, shorting and derivatives.
Common fee form is a management fee on assets plus an incentive fee on profits.
A hurdle rate means the incentive fee is earned only if the return exceeds it. With a hard hurdle the fee applies only to the excess over the hurdle; with a soft hurdle it applies to the full return once the hurdle is cleared.
A high-water mark means incentive fees are charged only on gains above the fund's previous peak value.
Equity hedge strategies include long/short, market neutral and short bias, plus others such as fundamental growth, fundamental value, quantitative directional and sector specialist.
Event-driven strategies include merger arbitrage, distressed securities and activist approaches.
Merger arbitrage typically buys the target and may short the acquirer in a stock deal; the risk is deal failure.
Relative value strategies exploit price gaps between related securities, such as convertible or fixed-income arbitrage.
Macro funds take top-down directional views on rates, currencies and economies; managed futures follow trading rules in futures markets.
Survivorship and backfill biases overstate reported returns.
Illiquid holdings and smoothed valuations understate reported volatility and correlation.
Hedge fund returns are often non-normal, so standard deviation alone can understate tail risk.

Common mistakes

Saying hedge funds always hedge or always have low risk. Fix: Remember many hedge funds take concentrated or leveraged risk. The name does not describe risk level.
Assuming hedge funds offer daily liquidity like mutual funds. Fix: Link hedge funds to lock-ups, notice periods and gates, which limit redemptions.
Charging the incentive fee on the full profit when the hurdle is hard. Fix: Hard hurdle: fee on profit above the hurdle only. Soft hurdle: fee on all profit once the hurdle is beaten.
Forgetting to deduct the management fee before the incentive fee. Fix: Check the stem. If the incentive fee is calculated net of the management fee, subtract the management fee from profit first.
Thinking market neutral means no risk. Fix: Neutral refers only to market exposure. Stock selection, leverage, factor and liquidity risks remain.
Treating long/short and market neutral as the same. Fix: Long/short usually keeps a positive net exposure and some beta. Market neutral targets near-zero net exposure.
Saying merger arbitrage buys the acquirer in a cash deal. Fix: In a cash deal, buy the target only. Short the acquirer only in a stock deal.
Treating merger arbitrage as risk-free. Fix: The spread is earned only if the deal closes. Deal break can cause large losses.
Saying convertible arbitrage is long stock and short the convertible bond. Fix: Remember: long the convertible (cheap option), short the stock to hedge.
Treating relative value strategies as directional bets. Fix: Ask whether profit depends on market direction. In relative value, it depends on spread convergence or volatility, with direction hedged.

Exam tips

Expect three-option items that test one core difference. Find the option that matches the other vehicle and remove it first.
Remember that fund of funds means diversification and due diligence, but a second fee layer and less transparency.
For master-feeder, think one portfolio at the master and tax or legal tailoring at the feeders.
Questions on investors often point to institutions and high-net-worth individuals who can accept limited liquidity.
Read the order of fees in the stem before you calculate. 'Net of management fees' and 'on beginning AUM' change the answer.
The trap option is usually 20% of the gross profit. Do not select it unless the stem has no hurdle, HWM or management fee deduction.
Know hard versus soft hurdle cold. The same numbers give different fees, and the exam likes to test the contrast.
After a loss year, ask whether NAV has regained the high-water mark. If not, the incentive fee is zero.