CFA III Formulas

Aggregate MV of equity (V_t^e)

GDP_t × S_t^k × P/E_t

level of nominal GDP

share of profit in economy

PE Ratio

E(R_e) expected return on equity

V_t^e + D_t

MV of equity

Dividend Yield

Taylor Rule( r_target )

r_neutral + π_e + 0.5 ( GDP_e − GDP_trend ) + 0.5 ( π_e − π_target )

nominal Target Rate

Neutral Target Rate

Expected Inflation

Output Gap

Inflation Gap

Trade Deficits (X - M)

(S - I) + (T - G)

Cap Rates Positively Related to

Vacancy Rates

Cap Rates Inversely related to

Availability of Debt Financing

Utility

E/R - (0.005 × λ × σ²)
λ = Risk Aversion Coefficient

E/R = Expected Return

σ² = Variance (Square of Standard Deviation)

Grinold Kroner E(R_e)

(D/P − %ΔS) + %ΔE + %ΔP/E

Size Factor

A zero-dollar portfolio long in small stocks and short in large stocks

value-growth factor

A zero-dollar portfolio long in value (high book-to-market) stocks and short growth (low book-to-market) stocks

two-portfolio approach

The hedging portfolio could be constructed using various techniques such as cash flow matching, duration matching, and immunization.

Name few Risk Factors

volatility, liquidity, inflation, interest rates, duration, foreign exchange, and default risk

Strategic asset allocation

establishes a portfolio's long-term asset class exposures by integrating each element of investment policy with capital market expectations.It affords an investor the ability to control systematic risk exposures by aligning their risk and return objectives with the actual portfolio of investments.

Tactical asset allocation

involves adjustments away from the strategic mix to take advantage of short-term projections of relative asset class performance.

narrower rebalancing corridor

High asset class volatility

wider rebalancing corridor

Higher investor risk tolerance, Higher transaction costs

intertemporal consistency

Consistency over various time horizons

Cross-sectional consistency

refers to consistency across asset classes

financial stages that form the critical planning phase

1. Career development (age 35–50)

2. Peak accumulation (age 50–60)

3. Preretirement (age 60–65)

conditional VaR

The average loss in the tail of a distribution that lies beyond a VaR estimate,also known as expected tail loss and expected shortfall.

Empty voting

occurs when an investor borrows stock for the explicit purpose of exercising the voting rights attached to the stock.

In a stock loan

voting rights are transferred to the stock borrower.

Volatility of Equity σE

√M²σ²_A+ (M−1)²σ²_L−2×M×(M−1)×σ_A×σ_L×corr<sub>A,L

Multiplier = Assets / Equity</sub>

Duration of Equity Capital (D_E)

( D_A×M ) − (D_L×(M−1) × (△i / △y) )

Leverage multiplier = 1 / equity capitalization ratio

Rolling yield

coupon yield + rolldown return

Coupon Yield / Income

annual coupon / current average bond price

Rolldown return

( Expected bond price in one year / Current average bond price ) - 1

BHB Allocation Effect

( W_portfolio - W_BM ) × Return_BM

BHB Selection Effect

W_BM × [ Return_portfolio - Return_BM ]

BHB Interaction Effect

( W_portfolio - W_BM ) × [ Return_portfolio - Return_BM ]