RSM332 All Topics

Present Value (PV)

Value today of future cash flows discounted at rate r

Future Value (FV)

Value of a present amount compounded forward at rate r

Discount Rate

Required return used to discount future cash flows

Perpetuity

Constant cash flow forever: PV = C / r

Growing Perpetuity

Cash flow growing at rate g: PV = C1 / (r − g)

Annuity

Equal payments for fixed periods: PV = C/r × (1 − 1/(1+r)^T)

Growing Annuity

Finite payments growing at g: PV = C1/(r−g) × (1 − ((1+g)/(1+r))^T)

Stated Rate

Quoted annual interest rate before compounding

Effective Annual Rate (EAR)

True annual rate including compounding

Spot Rate

Yield on a zero-coupon bond for a specific maturity

Yield to Maturity (YTM)

Discount rate making bond price equal PV of coupons + face value

Par Bond

Coupon rate = YTM

Premium Bond

Coupon rate > YTM

Discount Bond

Coupon rate < YTM

Price–Yield Relationship

Bond price moves inversely with yield

Clean Price

Bond price without accrued interest

Dirty Price

Clean price + accrued interest

Accrued Interest

Interest earned since last coupon

Credit Spread

Corporate bond yield minus risk-free government yield

Recovery Rate

Fraction of face value recovered if issuer defaults

Macaulay Duration

Weighted average time of cash flow receipt

Modified Duration

Approximate % price change for small yield change

Duration Rule

Higher coupon lowers duration

lower yield increases duration

Zero-Coupon Duration

Duration equals time to maturity

Portfolio Duration

Weighted average duration of assets by market value

Immunization

Match PV and duration of assets to liabilities

Forward Contract

Agreement today to buy/sell at future date for fixed price

Long Forward

Obligation to buy at price F

payoff = S_T − F

Short Forward

Obligation to sell at F

payoff = F − S_T

No-Arbitrage Forward Price

F = S0 × (1 + r)^T (no dividends)

Cash-and-Carry Arbitrage

Buy spot

Reverse Cash-and-Carry

Short spot

Basis Risk

Hedge mismatch when asset or maturity differs

European Call Option

Right to buy at strike K at maturity

European Put Option

Right to sell at strike K at maturity

Call Payoff

max(0, S_T - X)

Put Payoff

max(0, X - S_T)

Intrinsic Value

Immediate exercise value of call or put

Time Value

Option value − intrinsic value

Put–Call Parity

C − P = S0 − PV(K)

Early Exercise Call

Never optimal for non-dividend stock

Early Exercise Put

Can be optimal if deep ITM and rates high

Option Delta

Change in option value per $1 move in stock

Delta Hedge

Choose shares to offset option delta to zero

Binomial Delta

(Optionup − Optiondown) / (Su − Sd)

Risk-Neutral Probability

q = (1+r − d) / (u − d)

Binomial Option Pricing

Discount expected payoff using risk-neutral probabilities

Straddle (Long)

Long call + long put at same strike

wins with large moves

Short Straddle

Short both

wins if price stays near strike

Volatility Effect

Higher volatility raises both call and put prices

Synthetic Long Stock

Long call + short put + PV(K)

Synthetic Short Stock

Short call + long put + PV(K)

Expected Return of Portfolio

Weighted average of asset expected returns

Portfolio Variance

wA²σA² + wB²σB² + 2wAwBCovAB

Correlation

Standardized covariance (−1 to 1) measuring co-movement

Diversification

Combining imperfectly correlated assets lowers risk

Minimum Variance Portfolio

Risky portfolio with lowest possible variance

Efficient Frontier

Set of portfolios with max return for a given risk

Risk-Free Asset

Asset with zero variance and known return

Capital Allocation Line (CAL)

Line joining risk-free asset and risky portfolio

Tangent Portfolio

Risky portfolio with highest Sharpe ratio

Sharpe Ratio

(E[R] − Rf) / σ

Borrowing on CAL

Extends portfolio beyond tangent by taking leverage

Levered Weights

Risky asset weight >1

CAPM Equation

E[R] = Rf + β(E[R_M] − Rf)

Beta

Sensitivity of asset to market risk

Systematic Risk

Non-diversifiable risk priced in equilibrium

Idiosyncratic Risk

Diversifiable firm-specific risk

Alpha

Observed return − CAPM expected return

SML (Security Market Line)

Required return vs beta graph

APT (Arbitrage Pricing Theory)

Expected returns driven by multiple factors

SMB Factor

Small-cap return minus big-cap return (size factor)

HML Factor

Value-stock return minus growth-stock return (value factor)

Fama–French Model

E[R] = Rf + βMKT + s·SMB + h·HML

Factor Loading

Sensitivity to factor (size or value tilt)

EMH Weak Form

Prices reflect all past price info

EMH Semi-Strong

Prices reflect all public info

EMH Strong Form

Prices reflect all public and private info

Post-Earnings Drift

Prices react slowly to earnings news (EMH violation)

Momentum

Buying recent winners

Ticker Anomaly

Returns linked to irrelevant identifiers (market inefficiency)

Dividend Discount Model

Stock value = PV of expected dividends

Gordon Growth Model

P0 = D1 / (r − g)

Sustainable Growth Rate

g = retention × ROE

Cash Cow Model

g = 0

Payout Ratio

Dividend / EPS

Retention Ratio

1 − payout ratio

NPVGO

Value from growth opportunities: Pwithgrowth − Pnogrowth

P/E Ratio

Price per share / earnings per share

Determinants of P/E

Higher growth or lower risk → higher P/E

Dividend Yield

Dividend / price

Price-to-Book Ratio

Price per share / book value per share

Price-to-Sales Ratio

Price per share / sales per share

Enterprise Value (EV)

Equity value + debt − cash

EV/EBITDA Multiple

EV divided by EBITDA