Alternative Investments formula sheet.

Where $r$ = fund return for the period, $r_h$ = hurdle rate, $p$ = performance fee rate; management fees are ignored.

With a hard hurdle the GP earns the performance fee only on the return above the hurdle, never on the hurdle itself. If the fund does not beat the hurdle, the GP's share is zero.

Exam tip Example: $p = 20\%$, $r = 15\%$, $r_h = 8\%$ gives 20% of 7% = 1.4%, not 20% of 15%; charging $p$ on the whole return describes a soft hurdle that has been cleared.

Lesson: Compensation: fees, hurdles, catch-ups, clawbacks and waterfalls →All Alternative Investment Features, Methods, and Structures formulas

Where $r_{cu}$ = catch-up return the GP takes in full once the hurdle is beaten, $r$ = fund return, $r_h$ = hurdle rate, $p$ = performance fee rate.

After LPs receive the hurdle, the GP takes the next slice of return in full until it has caught up to its agreed share of total profit; above that, profits split again at $p$. Once a full catch-up is complete, the GP holds $p$ of the whole return.

Exam tip Full catch-up size is $r_{cu} = p \times r_h / (1 - p)$: with an 8% hurdle and 20% fee it is 2%, so at a 15% return the GP gets 2% + 20% of 5% = 3%, which is 20% of 15%.

Lesson: Compensation: fees, hurdles, catch-ups, clawbacks and waterfalls →All Alternative Investment Features, Methods, and Structures formulas

Where $CF_t$ = net cash flow to the investor at time $t$ (capital calls negative, distributions positive), $n$ = number of periods.

IRR is the discount rate that sets the NPV of the investor's cash flows to zero, so it captures both the size and the timing of calls and distributions. It is the standard money-weighted return for private funds.

Exam tip Enter calls as negative and distributions as positive in the calculator's CF/IRR worksheet; returning cash earlier raises IRR even when the total cash returned (and so MOIC) is unchanged.

Lesson: Measuring returns: IRR versus MOIC →All Alternative Investment Performance and Returns formulas

Where Realised value = cash already distributed, unrealised value = current value of remaining holdings, total invested capital = paid-in capital less management fees and fund expenses.

MOIC shows how many times the invested capital has been returned or is still held in value, so 1.8x means 80% more than was put in. It is simple and easy to compare, but says nothing about how long that took.

Exam tip MOIC ignores timing: two funds with the same MOIC can have very different IRRs, so if a question asks which measure reflects the holding period, the answer is IRR.

Lesson: Measuring returns: IRR versus MOIC →All Alternative Investment Performance and Returns formulas

Where $V_c$ = investor's own (cash) capital, $V_b$ = borrowed funds, $r$ = return on the total position, $r_b$ = borrowing rate.

The return on equity equals the unlevered return plus the debt-to-equity ratio times the spread between the asset return and the cost of debt. Leverage therefore magnifies gains when $r > r_b$ and magnifies losses when $r < r_b$.

Exam tip Use the second form for speed: with $r = 10\%$, $r_b = 5\%$ and $V_b/V_c = 1$, $r_L = 10\% + 1 \times 5\% = 15\%$; remember the interest is paid on the borrowed amount only.

Lesson: Leverage: magnifying gains and losses →All Alternative Investment Performance and Returns formulas

Where $P_0$ = beginning assets, $P_1$ = end-of-period assets before fees, $r_m$ = management fee rate on year-end assets, $p$ = performance fee rate.

Under a classic 2-and-20 deal the management fee is charged on assets whatever the result, and the incentive fee is charged on the gain. Here both fees are computed from the gross figures, so the incentive fee ignores the management fee already charged.

Exam tip Read the terms carefully: if the incentive fee is net of the management fee, apply $p$ to $P_1(1 - r_m) - P_0$ instead, which gives a smaller incentive fee.

Lesson: Fees, custom terms and redemption provisions →All Alternative Investment Performance and Returns formulas

Where $P_0$ = beginning capital, $P_1$ = end-of-period value before fees, $R_{GP}$ = total fees paid to the manager (management plus incentive).

This is what the investor actually earns: the gross gain less every fee, divided by the capital at the start. Exam questions usually ask for it after you have worked out the fees under a given set of terms.

Exam tip Subtract both fees, not just the incentive fee, and divide by beginning capital $P_0$, not by the end-of-year value.

Lesson: Fees, custom terms and redemption provisions →All Alternative Investment Performance and Returns formulas

Where $P_t$ = end-of-period value before fees, $P_{HWM}$ = highest previous end-of-period value net of fees for this investor, $r_m$ = management fee rate, $p$ = incentive fee rate.

A high-water mark stops the manager from earning an incentive fee twice on the same gains: after a loss, no incentive fee is due until the investor's value, net of the management fee, rises back above the previous peak. The management fee is still charged every year.

Exam tip The mark is investor-specific and net of all fees: an investor who joins after a drawdown uses the entry value, so two investors in the same fund can pay different incentive fees.

Lesson: High-water marks, investor timing and either/or fees →All Alternative Investment Performance and Returns formulas

Where Loan balance = mortgage debt outstanding, property value = current appraised value of the property.

LTV measures how much of the property is financed with debt. A higher LTV means more leverage, more volatile equity returns and less cushion for the lender, so lenders cap it through covenants.

Exam tip LTV rises when the property value falls even with no new borrowing; to restore a cap, the maximum loan is cap times current value, and the required repayment is the current loan minus that amount.

Lesson: Real estate returns, the risk-return spectrum and leverage →All Real Estate and Infrastructure formulas

Where NOI = net operating income (rent less operating costs), Interest = interest paid on the loan, $\Delta V$ = change in property value, Equity = investor's own capital in the property.

Real estate returns combine an income part (NOI after debt service) and a capital part (the change in value). Financing with debt shrinks the equity base, so the same property result becomes a larger percentage gain or loss for the owner.

Exam tip NOI is measured before interest, so deduct interest separately; without debt, interest is zero and equity is the full property value.

Lesson: Real estate returns, the risk-return spectrum and leverage →All Real Estate and Infrastructure formulas

Where $S_0$ = spot price, $r$ = risk-free rate, $c$ = storage, transport and insurance costs, $i$ = convenience yield (continuously compounded annual rates), $T$ = years to delivery.

The forward price equals spot plus the costs of carrying the commodity less the benefit of holding it physically. It explains the curve shape: forward above spot (contango) when $r + c > i$, forward below spot (backwardation) when the convenience yield exceeds $r + c$.

Exam tip A high convenience yield, typical when inventories are scarce, pushes the curve into backwardation, where a long futures position earns a positive roll return.

Lesson: Commodity pricing: carry, convenience yield and curve shape →All Natural Resources formulas

Where AUM = assets under management, $r$ = fund return, $r_b$ = benchmark return, so $r - r_b$ is the alpha.

The manager receives either a 1% management fee or 30% of the alpha generated, whichever is larger. The design rewards outperformance of a benchmark rather than market exposure, while the 1% acts as a minimum fee.

Exam tip The 30% applies to the return in excess of the benchmark, not to the total return, and the two amounts are compared, never added together.

Lesson: Investing directly: partnerships, master-feeders, side letters and SMAs →All Hedge Funds formulas

Where $G$ = gross gain of the underlying funds, $m$ = management fees in money, $p$ = incentive fee rates; subscripts HF and FoHF mark the underlying fund and the fund-of-funds level.

A fund of hedge funds adds its own management and incentive fees on top of those charged by the underlying funds, so the investor pays two layers of fees. Work out the net gain at the hedge fund level first, then apply the FoHF fees to what is left.

Exam tip Apply the FoHF fees to the gain after the underlying funds' fees, never to the gross gain; also note each underlying fund charges incentive fees on its own gains, so losers do not offset winners.

Lesson: Investing indirectly: funds of funds and replication ETFs →All Hedge Funds formulas