Alternative Investments — Master Formula Sheet

1. Multiple on Invested Capital (MOIC)

$\text{MOIC}=\frac{\text{Realized Value}+\text{Unrealized Value}}{\text{Total Amount Invested}}$

where:

• Realized value = cash distributions received from exited investments
• Unrealized value = estimated fair value of remaining portfolio
• Total amount invested = total capital deployed (not committed)

MOIC does not account for the time value of money.

2. Internal Rate of Return (IRR)

${\sum }_{t=0}^T\frac{C{F}_t}{(1+IRR{)}^t}=0$

where:

• $C{F}_t$ = cash flow at time $t$ (negative for capital calls, positive for distributions)
• $T$ = total number of periods
• $IRR$ = the rate that makes NPV of all cash flows equal to zero

IRR accounts for both the magnitude and timing of cash flows.

3. Management Fee

$\text{Management Fee}=\text{Fee Rate}\times \text{AUM (or Committed Capital)}$

where:

• Fee rate = annual percentage, typically 1.5%—2.0%
• AUM = assets under management (or committed capital during investment period)

During investment period: Fee base is often committed capital After investment period: Fee base is often invested capital or NAV

4. Performance Fee — Hard Hurdle

$\text{Performance Fee}=\text{Fee Rate}\times (\text{Return}-\text{Hurdle Rate})\times \text{Capital}$

where:

• Fee rate = performance fee percentage (typically 20%)
• Return = actual fund return
• Hurdle rate = minimum return threshold (typically 6%—8%)
• Only applied when $\text{Return}>\text{Hurdle Rate}$
• GP earns fee only on the excess return above the hurdle

5. Performance Fee — Soft Hurdle

$\text{Performance Fee}=\text{Fee Rate}\times \text{Total Return}\times \text{Capital}$

where:

• Fee rate = performance fee percentage (typically 20%)
• Total return = full return of the fund
• Only applied when $\text{Return}>\text{Hurdle Rate}$
• If hurdle is met, GP earns fee on the entire return (not just excess)

6. Net Return

$\text{Net Return}=\text{Gross Return}-\text{Management Fee}-\text{Performance Fee}$

where:

• Gross return = total return on investments before fees
• Net return = return actually received by LPs

7. Commodity Futures Pricing

$F_0\approx S_0\times (1+r{)}^T+\text{Storage Costs}-\text{Convenience Yield}$

where:

• $F_0$ = futures price at time 0
• $S_0$ = spot price at time 0
• $r$ = risk-free rate
• $T$ = time to expiration (in years)
• Storage costs = cost of physically storing the commodity
• Convenience yield = benefit from holding the physical commodity (e.g., avoiding supply disruptions)

8. Contango and Backwardation

Condition	Relationship	Implication
Contango	$F_0>S_0$	Storage costs exceed convenience yield; negative roll yield
Backwardation	$F_0<S_0$	Convenience yield exceeds storage costs; positive roll yield

• Roll yield in contango: negative (selling low, buying high when rolling contracts)
• Roll yield in backwardation: positive (selling high, buying low when rolling contracts)

9. Capitalization Rate (Real Estate)

$\text{Cap Rate}=\frac{\text{NOI}}{\text{Property Value}}$

where:

• NOI = Net Operating Income = Rental income $-$ Operating expenses (excluding financing costs and depreciation)
• Property value = current market value or purchase price

Rearranged to find value:

$\text{Property Value}=\frac{\text{NOI}}{\text{Cap Rate}}$

A lower cap rate implies higher property value (and vice versa). Cap rate is analogous to an earnings yield for real estate.

Related Pages

• Performance Measurement
• Real Assets
• Private Capital
• Alternative Investment Overview