Alternative Investment Performance and Returns: formula sheet

Key formulas

Category map

Alternatives = Hedge funds + Private capital + Real assets + Digital assets

Private capital = private equity and private debt. Real assets = real estate, infrastructure, natural resources.

Typical fee structure

Total fee = Management fee (% of assets) + Performance fee (% of profits above hurdle, if any)

Often called 2 and 20 for hedge funds. Details vary by fund. Fee mechanics are covered in the fees topic.

Key contrast with traditional assets

Alternatives: lower liquidity, higher fees, less transparency, appraisal pricing, more leverage

A tendency, not a law. Listed REITs and commodity futures are liquid.

Effect of smoothing on volatility

Reported standard deviation < true standard deviation

Smoothed returns understate risk. Reported correlation with other assets is also too low.

Sharpe ratio

Sharpe = (Rp − Rf) ÷ σp

If σp is understated by smoothing, the Sharpe ratio is overstated.

Unsmoothing (desmoothing) returns

R_true,t = (R_reported,t − (1 − α) × R_reported,t−1) ÷ α, with 0 < α ≤ 1

α is the weight on the current true return. A lower α means heavier smoothing. Know the idea more than the algebra.

Data bias direction

Survivorship, backfill and selection bias → reported returns typically biased upward

Past performance is typically overstated. Smoothing is different: it mainly understates risk and correlation.

Management fee

Management fee = fee rate × assets (start or end of period, as stated)

Use the asset base the question specifies. Do not assume one.

Incentive fee, no hurdle

Incentive fee = incentive rate × (profit after management fee)

Only if the question says the incentive fee is calculated net of the management fee. Otherwise use profit before it.

Hard hurdle

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

Fee only on the excess over the hurdle.

Soft hurdle

If return > hurdle: fee = rate × total profit; otherwise 0

Once cleared, the fee applies to the whole profit.

High-water mark

Fee = rate × max(0, ending value − high-water mark)

Applies when ending value exceeds the previous peak on which a fee was paid.

Net return

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

Subtract fees from the ending value, not from the return in percentage points unless the base is the same.

DPI (distributed to paid-in)

DPI = cumulative distributions ÷ cumulative paid-in capital

Realized return multiple. Ignores unrealized value. Uses paid-in capital, not committed capital.

RVPI (residual value to paid-in)

RVPI = NAV of remaining holdings ÷ cumulative paid-in capital

Unrealized multiple. Depends on the GP's valuations.

TVPI (total value to paid-in)

TVPI = (cumulative distributions + NAV) ÷ cumulative paid-in capital = DPI + RVPI

Total value per unit of paid-in capital. It does not consider timing.

Since-inception IRR

0 = Σ CFt ÷ (1 + IRR)^t, with calls negative, distributions positive and final NAV as the last inflow

Rate that sets the present value of net cash flows to zero. Timing matters, unlike the multiples.

Catch-up amount (full catch-up)

Catch-up c solves c = carry% × (preferred return + c)

For 20% carry and a 100% GP catch-up, c = 0.25 × preferred return.

Waterfall order (European)

1) return of paid-in capital, 2) preferred return, 3) GP catch-up, 4) split of the remainder (for example 80/20)

Applied to the whole fund. American waterfalls apply a similar order deal by deal, with a clawback.

Direct capitalization value

Value = NOI ÷ Cap rate

Use the NOI that matches the cap rate definition, usually next-year or stabilized NOI.

Cap rate

Cap rate = NOI ÷ Property value

Cap rate is also called going-in yield. It moves inversely to value.

Net operating income

NOI = Rental and other income − Operating expenses

Exclude interest, depreciation and income taxes.

Terminal value in DCF

Terminal value = NOI(year n+1) ÷ Terminal cap rate

Use the NOI of the year after the last forecast year.

Commodity futures total return

Total return = Spot return + Roll yield + Collateral yield

Applies to a fully collateralized long futures position.

Roll yield sign

Backwardation → positive; Contango → negative

Backwardation means the futures price is below the spot price.

Cost approach

Value = Replacement cost − Depreciation + Land value

Used mostly for new or unique properties.

Quick revision

• Alternatives are typically less liquid, less transparent and use more specialised managers than traditional assets.
• Appraisal-based valuations can smooth returns, understating volatility and correlation.
• Survivorship and backfill bias tend to overstate hedge fund index returns.
• Hedge fund fees: management fee on assets, incentive fee on profits, often subject to a hurdle and high-water mark.
• A high-water mark means incentive fees are paid only on gains above the previous peak value.
• DPI = cumulative distributions ÷ paid-in capital.
• RVPI = residual value of remaining holdings ÷ paid-in capital.
• TVPI = DPI + RVPI, the total value relative to paid-in capital.
• IRR depends on the timing of cash flows, while multiples such as TVPI ignore timing.
• DPI reflects realised returns only, so it is low early in a fund's life.
• Real assets earn returns from income and from changes in value; check the stated return source.
• Read each question for the stated fee basis, such as beginning or ending value, before calculating.

Common mistakes

• Assuming all alternative investments are illiquid. Fix: Remember that listed REITs, exchange-traded commodity products and many liquid hedge fund strategies trade or redeem frequently. Treat illiquidity as a common tendency.
• Placing private debt with hedge funds or traditional bonds. Fix: Private debt is lending to borrowers outside public markets. It belongs to private capital with private equity.
• Saying smoothing raises volatility or correlation. Fix: Smoothing removes noise. Volatility and correlation are understated, and the Sharpe ratio is overstated.
• Mixing up survivorship bias and backfill bias. Fix: Survivorship: failed funds disappear. Backfill: a new fund's earlier good history is added after it joins.
• Treating a hard and soft hurdle the same way Fix: Hard: fee only on the excess over the hurdle. Soft: fee on the full profit if the hurdle is beaten.
• Confusing hurdle rate with high-water mark Fix: Hurdle is a minimum return for a period. High-water mark is a prior peak value that must be exceeded.
• Dividing by committed capital instead of paid-in capital Fix: All three multiples use cumulative paid-in capital in the denominator. Committed capital is only the promise.
• Treating TVPI as realized performance Fix: TVPI includes unrealized NAV set by the GP. Only DPI measures cash already returned.
• Subtracting depreciation or interest when computing NOI. Fix: NOI uses operating items only. Exclude financing, depreciation and taxes.
• Treating a higher cap rate as a higher value. Fix: Value = NOI ÷ cap rate, so a higher cap rate lowers value.

Exam tips

• Classify by the underlying asset first, then by the structure used to hold it.
• Be suspicious of options with absolutes like always, never or guaranteed.
• Link each category to its signature feature and its main risk in one line, then use that to eliminate options.
• Remember that questions ask for best fit, so compare all three choices before selecting.
• Expect conceptual questions on direction: smoothing lowers risk and correlation, and raises the Sharpe ratio.
• Match the clue word in the stem to the bias name. Learn the three definitions precisely.
• When two options both sound plausible, go back to the mechanism: smoothing understates risk and correlation, while survivorship, backfill and selection bias typically overstate returns. Match the option to the cause named in the stem.
• Do not spend time on unsmoothing algebra. Know what it does, not a long calculation.