Cfa Level 3 Formula.docx

LOS Description

Formula

11b

Investment income tax (accrual taxes)

11b

11b

Deferred capital gains tax (MV = cost basis) Deferred capital gains tax (MV ≠ cost basis) Wealth-based tax

11b

Realized after-tax returns

11b

Effective capital gains tax rate

11b

Future value interest factor after all taxes

11c

Accrual equivalent after-tax return

11c

Accrual equivalent tax rate

11

Future value interest factor for a taxdeferred account

11

Future value interest factor for a taxexempt account

12

Human capital at time = t

12

Objective function for allocation of risky assets

12

Tax-free gift: Relative after-tax value

12

Taxable gift: Relative after-tax value

12

Taxable gift (donor pays): Relative after-tax value

12

Charitable donation: Relative aftertax value

12f

Generation skipping future value (w/ skipping) equation

12f 12k

Generation skipping future value (no skipping) equation Effective tax rate: Credit Method

12k

Effective tax rate: Exemption Method Texemption = Tsource

12k

Effective tax rate: Deduction Method

11b

Tcredit = Max(Tresidence, Tsource) Tdeduction = Tresidence + Tsource(1 − Tresidence)

15

Endowment spending rules

17c

Covariance of two markets

17c

Gordon (constant) growth model

17c

Grinold-Kroner (expected ROE)

17c

Expected bond return

17c

ICAPM

17c

Equity Beta

17c

Correlation of stock i with the market

17c

Market Equity Risk Premium (ERP)

17h

Taylor Rule for Target interest rate

18a

Cobb-Douglas GDP growth function

18a

Solow residual

18c

H-model

18c

Gordon (constant) growth model

18f

Fed model

18f

Yardeni model

18f

Schiller P/E(10yr Moving Average)

18f

Tobin's Q

18f

Equity Q

19g

Risk (ultility) adjusted return

19g

Roy's Safety-First Ratio

Current Index price / 10-year moving average of earnings

20g

Dollar duration (DD)

-(Effective Duration) x (decimal change in interest rates) x (price)

20g

Rebalancing ratio

22a

Return of a leveraged investment

22a

Leveraged equity duration

22b

Dollar interest on a repo agreement

22e

Target dollar duration

22e

Dollar duration of a futures contract

22e

Number of contracts to adjust portfolio dollar duration

22e

Number of contracts for complete hedge

22e

Hedge ratio

22f

Duration of an interest rate swap

= Dfixed - Dfloating

22f

Duration of an interest rate option

= deltao x Du x Pu/Po u is underlying, o is option

22g

Payoff to a credit spread forward

R = R + [(B/E) × (R − c)] LI

UI

UI

DDt = DDp + DDfutures

22i %Δ price (foreign fond) for change in domestic interest rates

= - Duration x Δyield

domestic

xβ β is country beta (or yield beta) 22j

Approximate forward premium/discount

22j

Interest Rate Parity formula for setting exchange rates Breakeven yield change

22k

F = So [(1 + cd) / (1 + cr)]

Annual Hedge Fund Sharpe ratio

23b

Information ratio

23s

Total active risk total active risk =

23s

Active risk (alternative formula)

Active risk = √ω12σ12 + ω22σ22 + ω32σ32...

23s

True information ratio

27e

Value at Risk (VAR)

27e

Standard Deviation (daily, monthly)

27e

VAR and time period conversions

Sharpe ratio

Sortino ratio

Return over maximum drawdown

Optimal hedge ratio (h)

Delta

Beta

29a

Number of contracts required to adjust an equity portfolio's beta to a target level

29b

Number of contracts (unrounded)

29b

PV of cash required of long equity = [(# of contractsrounded)(Pf)(multiplier)] / (1+Rf) index futures position # of shares acquired from equity = [(# of contractsrounded)(multiplier)] / (1+d)t index futures position # of equity futures contracts to create synthetic cash

29b 29c

Number of contracts (fixed-income) 30f

Gamma

= [(Theld)(1+Rf)] / [(Pf)(multiplier)]

31 31

32f 32g 32g 32g 32g 33i

Duration of the portfolio plus a swap position Solving for a swap

Total implicit trading costs (ESTIMATED) Explicit Trading Costs (as a % of total order) Delay/Slippage Costs (as a % of total order) Realized Profit/Loss (as a % of total order) Missed Opportunity Trading Costs (as a % of total order) CPPI Strategies

34c

Return (external cash flows Beginning)

34c

Return (external cash flows - End)

34c

Money-Weighted Return

34c

Sources of portfolio return

34c

Sharpe ratio

Incremental return to the asset category level Incremental return to the benchmark level Return to the investment manager's level Micro performance attribution

Security Market Line Jensen's (ex-post) Alpha

Information ratio

(Actual transaction price - Benchmark price) x # of shares traded (Trading fees/share / BP) x 100% of order [(DP - BP) / BP] x % of order filled [(EP - DP) / BP] x % of order filled [(CP - BP) / BP] x % of order NOT filled

Treynor measure

34

M2