Alternative Investment Features, Methods, and Structures: formula sheet

Key formulas

Alpha versus beta

Return = beta return (market exposure) + alpha (manager skill)

Traditional funds are mostly beta. Many alternatives market themselves on alpha, which must be net of fees.

Leveraged return

Leveraged return = [r × (V_E + V_B) − V_B × i] ÷ V_E

V_E is own equity, V_B is borrowed funds, r is the asset return, i is the borrowing rate. Leverage magnifies gains and losses.

Typical fee structure

Total fee = management fee (% of assets) + performance fee (% of profit, often above a hurdle)

Fees reduce net returns and usually exceed those of traditional funds.

Management fee

Management fee = fee rate × fee base

The base may be committed capital, invested capital or NAV. Read which one the question gives. It is charged regardless of performance.

Carried interest without a hurdle

Carry = carry rate × profit

Profit is usually measured after the management fee if the question says so.

Hard hurdle carry

Carry = carry rate × (profit − hurdle amount)

Carry applies only to the excess over the hurdle. Hurdle amount = hurdle rate × capital.

Soft hurdle carry

If profit > hurdle amount: Carry = carry rate × total profit; otherwise 0

Once the hurdle is cleared, the GP earns carry on all profit.

Net return to LPs

LP profit = profit − management fee − carry

Compute fees in the order the question states.

Management fee

Management fee = fee rate × fee base (AUM or committed capital)

The base may be beginning, average or ending AUM. Use whichever the question states.

Incentive fee with a hard hurdle

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

Hurdle amount = hurdle rate × beginning value. Profit is usually measured after the management fee if the stem says so.

Incentive fee with a soft hurdle

Incentive fee = incentive rate × profit, if profit > hurdle amount; otherwise 0

The fee covers all profit once the hurdle is cleared. Use the same profit base as for the hard hurdle: after the management fee if the stem says so.

Incentive fee with a high-water mark

Incentive fee = incentive rate × max(0, NAV before fee − HWM)

After a fee is paid, the new HWM is the NAV after the fee. If no fee is paid, the HWM stays the same.

Net return to investors

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

Gross return less management fee less incentive fee, all in the same currency units.

Whole-fund waterfall order

1) Return of contributed capital 2) Preferred return 3) GP catch-up 4) Split of remainder (for example 80/20)

With a full catch-up and enough profit, the GP ends with carry rate × total profit.

Full catch-up amount

Catch-up x = carry rate × (preferred return + x), so x = carry rate × preferred return ÷ (1 − carry rate)

Applies when the GP receives 100% of distributions during the catch-up.

Clawback rule

Clawback = carry received − carry rate × total fund profit (if positive)

Simplified. Real terms may also use the preferred return or net-of-tax limits.

Unsmoothing (de-smoothing) returns

R*(t) = [R(t) − φ × R(t−1)] ÷ (1 − φ)

Here R*(t) is the unsmoothed return, R(t) is the reported return, and φ is the smoothing (first-order autocorrelation) parameter between 0 and 1. You need to know the idea and direction of the effect more than the algebra: unsmoothing raises standard deviation.

Effect of smoothing on risk statistics

Reported σ < true σ; reported correlation < true correlation; reported Sharpe ratio > true Sharpe ratio

These directions hold when appraisal smoothing is present. Use them to eliminate wrong options.

Sharpe ratio

Sharpe = (Rp − Rf) ÷ σp

Understated σp inflates the ratio. Compare it only after considering smoothing and non-normal returns.

Excess kurtosis and skew

Normal distribution: skewness = 0, kurtosis = 3 (excess kurtosis = 0)

Negative skew and positive excess kurtosis mean more frequent large losses than a normal model predicts.

Quick revision

• Alternatives are typically less liquid, harder to value, less regulated and more dependent on manager skill than traditional assets.
• Appraisal-based or smoothed valuations understate volatility and correlation with other assets.
• Private equity includes venture capital and buyouts; private debt lends outside public bond markets.
• Real estate, infrastructure and natural resources offer real-asset exposure; commodities are often accessed through derivatives.
• Hedge funds use flexible strategies, including leverage and short selling, and are often limited to qualified investors.
• In a limited partnership the GP manages the fund and LPs provide capital with limited liability.
• Co-investment lets an LP invest directly alongside the fund, typically with lower or no extra fees.
• A hurdle rate is the minimum return before the performance fee is earned.
• A high-water mark means a performance fee is paid only on gains above the prior peak value.
• A clawback lets LPs recover excess carried interest paid earlier if later results fall short.
• In a waterfall, return of capital and the preferred return come before the GP carry is shared.
• Due diligence covers the manager, strategy, risk controls, valuation process, fees and operations.

Common mistakes

• Assuming alternatives always have low correlation with traditional assets. Fix: Treat low correlation as a tendency. Correlations often rise in stress, and appraisal smoothing can understate them.
• Believing all alternatives are illiquid. Fix: Listed REITs, commodity futures and some liquid hedge fund strategies are more liquid. Read the structure in the stem.
• Treating private equity and hedge funds as the same thing. Fix: Private equity owns private companies for years. Hedge funds trade mostly liquid securities with flexible strategies.
• Assuming all alternatives are illiquid. Fix: Hedge fund holdings are often liquid, but investors face lockups and redemption limits. Liquidity varies by category.
• Treating co-investment as the same as fund investment. Fix: Co-investment is a separate, deal-specific stake alongside the fund, usually with lower or no fees. Fund investment is a commitment to the whole pool.
• Saying LPs manage the fund or have unlimited liability. Fix: The GP manages and has unlimited liability. LPs are passive and liable only up to their commitment.
• Applying the incentive fee to all profit when the hurdle is hard. Fix: Check the word hard or soft. Hard: fee on the excess over the hurdle only. Soft: fee on all profit once the hurdle is beaten.
• Computing the incentive fee on gross profit when the stem says it is calculated after the management fee. Fix: Always compute the management fee first. Then reduce profit by it if the stem says the incentive fee is net of the management fee.
• Saying smoothing raises reported volatility. Fix: Appraisals lag the market, so reported returns are damped. Reported standard deviation is too low.
• Confusing survivorship bias with backfill bias. Fix: Survivorship: failed funds disappear. Backfill: a fund's good early history is added after it joins the database.

Exam tips

• Words like always, guaranteed or eliminates risk usually mark a wrong option.
• Link each feature to its consequence: appraisal pricing leads to smoothed returns, lock-up leads to an illiquidity premium.
• Check whether the stem describes a listed or unlisted vehicle before choosing on liquidity.
• For leverage numbers, compute the borrowed cost first and subtract it from the gross gain.
• Net-of-fee comparisons are often the point of a fee question.
• Expect short definition and comparison items; one clue in the stem usually identifies the category.
• Learn one defining trait per category and one contrast pair, especially private equity versus hedge funds.
• Remember private capital includes both private equity and private debt.