• beta estimate difference - sources of error
• tax drag
• synthetic CDO
• effective collar
• option adjusted spread
• pure expectation & liquidity preference theory

IACPM = R_F + world market risk premium * sensitivity + foreign currency risk premium(expected appreciation - R_FΔ) sensitivity

Quantitative Methods

• mean reversion = b₀ / (1 - b₁)
• Sharpe ratio = E(R_m) - R_F / σ_m

ANOVA(Analysis of Variance)

• SST(total variation) = RSS(explained variation; regression value - mean) + SSE(unexplained variation; observed value - regression value)
• MSR(regression mean square) = RSS / k(# independent factors)
• MSE(mean squared error) = SSE / (n - k - 1)
• SEE(standard error of estimate) = √MSE
• R²(% of total variation explained by independent variable) = RSS/SST
• R_adj²(adjusts for cost of adding more independent variables) = 1 - [ (n-1)/(n-k-1) * (1-R²) ]
• F-statistic = MSR / MSE

Multiple Regression violations

• Heteroskedasticity residual variance // independent variable; results Type I errors; detected by Breusch-Pagan χ² test; corrected by White-corrected standard ε
• AutoCorrelation correlated residuals, error term tends in same direction as previous term(+); results Type I errors; detection with Durbin-Watson test; corrected by Hansen method
• Multicollinearity correlated independent variables; results Type II errors; conflicting t and F statistics; corrected by dropping correlated variable

Financial Statement Analysis

Intercorporate Investment

• Purchase method: consolidation at market value
• Pooling of interest method: recorded at book value, no goodwill

	Trading	Available for sale	Held to maturity
Balance Sheet	fair value	fair value w/ unrealized G/L in equity	amortized cost
Income Statement	dividend + unrealized G/L	dividend	interest + realized G/L only

• Equity method: lower leverage, higher profit margin
• Proportionate Consolidation: required under IFRS
• Bootstrap earnings effect - acquirer's P/E > acquiree's P/E, and doesn't decline post-merger

Pension program equations

• ΔPBO(projected benefit obligation) = service cost + interest cost + amortization(previous service cost + aRoA - eRoA - benefits paid

PBO ⇑ when life expectancy⇑, salary growth⇑, discount rate⇓

• ΔFVPA(fair value of plan assets) = aRoA + employer contribution - benefits paid
• Funded status = net asset - liability (U.S. GAAP)
• Net pension asset = funded status - unrecognized losses (IFRS)
• Net pension expense = service cost + interest cost - eRoA + amortization
• CTA_f = Asset - Liabilities - common equity - RE_f
• RE_f(final retained earning) = RE_i + N/I - dividend
• Economic pension expense = (PBO_f - PBO_i - actual RoA?) = ΔFS - employer contributions = service cost + interest cost - actuarial gain - actual RoPA

Overseas Subsidiary

• • translation(current method) results equity account adjustment
  • remeasurement(temporal method) results gain/loss in income statement
  • revenue & operating exp. translated at average rate under all-current method

	Temporal method	All-current method
Assets/Liabilities	monetary A/L - current rate nonmonetary A/L - historical rate	all current rate
Common stock	historical
Equity	mixed rate balanced by R/E	ΔR/E reflected at current rate, balanced by CTA account
Revenues/SG&A	average rate	average rate
COGS & Depreciation	historical rate
FX Gain/Loss	I/S at historical rate	current rate in equity CTA account

Earnings Quality

B/S adjustment	applicable situation	effect
Operating asset capitalization	operating leases, unconsolidated SPEs, receivable sales, corporate guarantees, long-term investments	Asset ↑ Liability ↑
Asset revaluation	marketable securities, inventory valuation change(LIFO->FIFO), depreciation method, foreign currency effect, R&D expense, PP&E&intangible asset impairment, goodwill write-off	ΔA -> ΔE
Reclassification	eliminated deferred tax A/L, deferred revenue, convertible debt to equity, long-term debt amortization	ΔL -> -ΔE

• LIFO review

Accrual ratio = (NI - CFO - CFI)/NOA

• lower accrual ratio -> higher earnings quality

Corporate Finance

• Static trade-off theory seeks an optimal capital structure with an optimal proportion of debt, to balance the costs of financial distress with the tax shield benefits from using debt

Divestitures

• Carve-outs: new subsidiary shares issued to existing common shareholders
• Spin-offs: shares not sold in public, only distributed to existing shareholders

• Contango: future value > spot price
• Backwardation: future value < spot price

Equity Investments

Discounted Dividend Model minority owner perspective

• Gordon growth model

equity risk premium = dividend rate on market index + long-term earnings growth - long-term govt. bond yield

• H-model

V₀ = D₀(1+g_L + H(g_s-g_L)) / (r-g_L)

• 2-stage model
• grow dividends at high growth period, then calculate future value using perpetual growth model, and discount back by required return

Free Cash Flow control perspective

• FCFF = CFO + Int(1-t) - FC_Inv = NI + NCC - WC_Inv + Int(1-t) - FC_Inv
• FCFE = FCFF + net borrowing - Int(1-t) = NI + NCC - WC_Inv - FC_Inv + net borrowing

NCC(noncash charges) = depreciation&amortization - gain/(loss) on asset sale + restructuring expense _ nonreversible deferred tax liability + bond discounts/(premiums) amortization

FCF // liability(accounts payable, accrued taxes & expenses)

Price Multiples

   (note that ROE-g ~ dividend / book value)

• EV(enterprise value) = MV_{common stock} + MV_debt + MV_preferred - cash&investment
• intrinsic P/E = tangible P/E + franchise P/E = 1/r + (1/r - 1/ROE) * (g / r-g)
• build-up method

required return on equity = risk-free rate + equity risk premium + size premium + specific company premium

Residual Income net income - opportunity cost of equity (amt. equity capital * cost of equity)

• EVA(economic value added) = NOPAT - (%_WACC x total capitalization)

NOPAT = EBIT(1-t)

single stage model: V₀ = B₀[1 + (ROE - r)/(r-g)]

Alternative Investments

Real Estate

• Taxes = (NOI - depreciation - interest) x tax rate
• CFAT(cash flows after tax) = NOI - principal debt service - taxex
• ERAT(equity reversion after taxes) = selling price - selling costs - mortgage balance - taxes on sale

Income property analysis

• capitalization rate = r - g
• MV = NOI / (r-g)

Private Equity

• Leveraged buyout

exit value = investment cost + earnings growth + multiple expansion + debt reduction

• carried interest estimation = (NAV_before - committed capital) * %carried interest

Fixed Income

• interest rates
• Z-spread - OAS = option cost
• embedded options

• finance Greek variables
  • delta: // spot price
  • gamma: // Δdelta
  • vega: // volatility
  • theta: // time to expiration
  • rho: // risk-free rate

• Conditional Payment Rate = 6% * t/30 * PSA
• Single Monthly Mortality = 1 - (1 - CPR)^0.083

Derivatives

• Futures FP = S₀(1+r)^T - FVD