L E V E L II SC H W ESER' C r it ic a l C o n c e pt s ETHICAL AND PROFESSIONAL STANDARDS I Professionalism I (A) Knowledge of the Law I (B) Independence and Objectivity I (C ) I (D) II II (A) II (B) III HI (A) HI (B) HI (C) HI (D) HI (E) IV IV (A) IV (B) IV (C) V v (A) V (B) V (C) VI VI (A) VI (B) VI (C) VII VII (A) VII (B) Misrepresentation Misconduct Integrity o f Capital Markets Material Nonpublic Information Market Manipulation Duties to Clients Loyalty, Prudence, and Care Fair Dealing Suitability Performance Presentation Preservation of Confidentiality Duties to Employers Loyalty Additional Compensation Arrangements Responsibilities o f Supervisors Investment Analysis, Recommendations, and Action Diligence and Reasonable Basis Communication with Clients and Prospective Clients Record Retention Conflicts o f Interest Disclosure o f Conflicts Priority of Transactions Referral Fees Responsibilities as a CFA Institute Member or CFA Candidate Conduct in the CFA Program Reference to CFA Institute, CFA Designation, and CFA Program QUANTITATIVE METHODS Simple Linear Regression Correlation: covXY rXY = ( s x )( s y ) t-test for r (n - d f): t = rVn —2 Estimated slope coefficient: cov xy B 'A ' 'A ' X vC, bid B , bid 'A ' /A X vC, offer \ B , offer VC ^ /bid / T-x \ B X \C ^ /offer Currency arbitrage: “Up the bid and down the ask.” Forward premium = (forward price) - (spot price) Value o f fwd currency contract prior to expiration: Vt = (FPt — FP)(contract size) \ days 1+ R A 360 Covered interest rate parity: Uncovered interest rate parity: e • Measuring independent variables with error Effects o f M isspecification Regression coefficients are biased and inconsistent, lack o f confidence in hypothesis tests o f the coefficients or in the model predictions Linear trend model: yt = b0 + b,t + £t Log-linear trend model: ln(yt ) = b0 + b,t + £t Covariance stationary: mean and variance don’t change over time To determine if a time series is covariance stationary, (1) plot data, (2) run an AR model and test correlations, and/or (3) perform Dickey Fuller test Unit root: coefficient on lagged dep vbl = Series with unit root is not covariance stationary First differencing will often eliminate the unit root Autoregressive (AR) model: specified correctly if autocorrelation o f residuals not significant Mean reverting level for A R(1): bo (1 — b j) RM SE: square root o f average squared error Random W alk T im e Series: xt = xt-i + £t Seasonality: indicated by statistically significant lagged err term Correct by adding lagged term ARCH: detected by estimating: = ao + ai^t-i + Bt Variance o f ARCH series: A E xa m days 1+ R a •0 360 / F = ^ -days 1+ R B 360 M odel M isspecification A2 Reject if |t| > critical t or p-value < a C FA® Standard error of estimate (SEE = VM SE ) Smaller SEE means better fit • Coefficient of determination (R2 = RSS / SST) % of variability of Y explained by Xs; higher R2 means better fit / , n —k —1 df 2018 fo r t h e (% a s w , = R , - K Fisher relation: R nominal = R real + E(inflation) International Fisher Relation: R nominal A —R nominal B = E(inflation.) v A' E(inflationB) Relative Purchasing Power Parity: High inflation rates leads to currency depreciation %AS(A/B) = inflation Xj - inflation,B) where: % AS(A/B) = change in spot price (A/B) Profit on FX Carry Trade = interest differential change in the spot rate of investment currency Mundell-Fleming model: Impact o f monetary and fiscal policies on interest rates & exchange rates Under high capital mobility, expansionary monetary policy/restrictive fiscal policy —>low interest rates —> currency depreciation Under low capital mobility, expansionary monetary policy/ expansionary fiscal policy —> current account deficits —» currency depreciation Dornbusch overshooting model: Restrictive monetary policy —» short-term appreciation of currency, then slow depreciation to PPP value Labor Productivity: output per worker Y/L = T(K/L)‘' Growth Accounting: growth rate in potential GDP = long-term growth rate of technology + a (long-term growth rate o f capital) + (1 - a) (long-term growth rate of labor) growth rate in potential GDP = long-term growth rate of labor force + long-term growth rate in labor productivity Classical Growth T heory • Real GDP/person reverts to subsistence level A A2 CTt+l = a0 + al£t Risk Types: Appropriate m ethod Distribution o f risk Sequential? Accommodates Correlated Variables' Simulations Continuous Does not matter Yes Scenario analysis Discrete No Yes Decision trees Discrete Yes No Neoclassical Growth T heory • Sustainable growth rate is a function of population growth, labor’s share o f income, and the rate of technological advancement • Growth rate in labor productivity driven only by improvement in technology Assumes diminishing returns to capital g* = (1-a) G* = (1-a) + AL Endogenous Growth Theory • Investment in capital can have constant returns • | in savings rate —> permanent T in growth rate • R & D expenditures ] technological progress Classifications o f Regulations • Statutes: Laws made by legislative bodies • A dm inistrative regulations: Issued by government • Ju d icia l law : Findings o f the court Classifications o f Regulators • Can be government agencies or independent • Independent regulator can be SRO or non-SRO Self-Regulation in Financial Markets • Independent SROs are more prevalent in common-law countries than in civil-law countries Econom ic Rationale for Regulatory Intervention • Inform ationalfriction s arise in the presence o f information asymmetry • Externalities deal with provision o f public goods Regulatory Interdependencies and T heir Effects Regulatory capture theory: Regulatory body is influenced or controlled by industry being regulated Regulatory arbitrage: Exploiting regulatory differences between jurisdictions, or difference between substance and interpretation o f a regulation Tools o f Regulatory Intervention • Price mechanisms, restricting or requiring certain activities, and provision o f public goods or financing o f private projects Regulations Covering Com m erce • Company law, tax law, contract law, competition law, banking law, bankruptcy law, and dispute resolution system F in an cial m arket regulations: Seek to protect investors and to ensure stability o f financial system Securities m arket regulations: Include disclosure requirements, regulations to mitigate agency conflicts, and regulations to protect small investors P rudential supervision: Monitoring institutions to reduce system-wide risks and protect investors Anticompetitive Behaviors and Antitrust Laws • Discriminatory pricing, bundling, exclusive dealing • Mergers leading to excessive market share blocked N et regulatory burden: Costs to the regulated entities minus the private benefits o f regulation Sunset clauses: Require a cost-benefit analysis to be revisited before the regulation is renewed FINANCIAL STATEMENT ANALYSIS Accounting for Intercorporate Investments Investment in Financial Assets: 50% owned, control Acquisition method required under U.S GAAP and IFRS Goodwill not amortized, subject to annual impairment test All assets, liabilities, revenue, and expenses o f subsidiary are combined with parent, excluding intercomp, trans If firm contribution, diff = borrowing (reclassify difference from CFO to CFF after-tax) M ultinational Operations: Choice o f M ethod For self-contained sub, functional ^ presentation currency; use current rate method: • Assets/liabilities at current rate • Common stock at historical rate • Income statement at average rate • Exposure = shareholders’ equity • Dividends at rate when paid For integrated sub., functional = presentation currency, use temporal method: • Monetary assets/liabilities at current rate • Nonmonetary assets/liabilities at historical rate • Sales, SGA at average rate • CO G S, depreciation at historical rate • Exposure = monetary assets - monetary liabilities Net asset position & depr foreign currency = loss Net liab position & depr foreign currency = gain Original F/S vs All-Current • Pure BS and IS ratios unchanged • If LC depreciating (appreciating), translated mixed ratios will be larger (smaller) Hyperinflation: GAAP vs IFRS Hyperinfl = cumul infl > 100% over yrs GAAP: use temporal method IFRS: 1st, restate foreign curr st for infl 2nd, translate with current rates Net purch power gain/loss reported in income Beneish model: Used to detect earnings manipulation based on eight variables High-quality earnings are: Sustainable: Expected to recur in future Adequate: Cover company’s cost o f capital IFRS A N D U S GAAP D IFFER E N C ES Reclassification of passive investments: IFRS —Restricts reclassification into/out o f FVPL U.S GAAP —No such restriction Impairment losses on passive investments: IFRS —Reversal allowed if due to specific event U.S GAAP —No reversal o f impairment losses Fair value accounting, investment in associates: IFRS —Only for venture capital, mutual funds, etc U.S GAAP —Fair value accounting allowed for all Goodwill impairment processes: IFRS - step (recoverable amount vs carrying value) U.S GAAP — steps (identify; measure amount) Acquisition method contingent asset recognition: IFRS —Contingent assets are not recognized U.S GAAP —Recognized; recorded at fair value Prior service cost: IFRS —Recognized as an expense in P&L U.S GAAP - Reported in O CI; amortized to P&L Actuarial gains/losses: IFRS —Remeasurements in O CI and not amortized U.S GAAP —OCI, amortized with corridor approach Dividend/interest income and interest expense: IFRS —Either operating or financing cash flows U.S GAAP —Must classify as operating cash flow R O E decomposed (extended D uPont equation) Tax Interest EBIT Burden Burden Margin NI EBT E B IT R O E = -x -x x E B T E B IT revenue Financial Leverage T otal Asset T urnover revenue average assets X average assets average equity Accruals Ratio (balance sheet approach) accruals ratio ^ = (N OAEn d — N OABEg ) (N OA e n d + NOABEg ) /2 Accruals Ratio (cash flow statem ent approach) accruals ratio ^ = (NI - CFO - CFI) (N OA e n d + N OABEg ) /2 CORPORATE FINANCE Capital Budgeting Expansion • Initial ouday = FCInv + WCInv • CF = (S - C - D ) ( l - T ) + D = (S - C )(l - T ) + D T • T N O C F = SaLr + NW CInv - T(Salr - B.r) Capital Budgeting Replacement • Same as expansion, except current after-tax salvage o f old assets reduces initial outlay • Incremental depreciation is A in depreciation Evaluating Projects with Unequal Lives • Least common multiple o f lives method • Equivalent annual annuity (EAA) method: annuity w/ PV equal to PV o f project cash flows Effects o f Inflation • Discount nominal (real) cash flows at nominal (real) rate; unexpected changes in inflation affect project profitability; reduces the real tax savings from depreciation; decreases value of fixed payments to bondholders; affects costs and revenues differently Capital Rationing • If positive NPV projects > available capital, choose the combination with the highest NPV Real Options • Timing, abandonment, expansion, flexibility, fundamental options Econom ic and Accounting Income • Econ income = AT CF + A in project’s MV • Econ dep based on A in investment’s MV • Econ income is calculated before interest expense (cost o f capital is reflected in discount rate) • Accounting income = revenues - expenses • Acc dep’n based on original investment cost • Interest (financing costs) deducted before calculating accounting income Valuation Models • Economic profit = NO PAT - $WACC • Market Value Added = t= i (1 + W A C C ) r • Residual income: = NI —equity charge; discounted at required return on equity • Claims valuation separates CFs based on equity claims (discounted at cost o f equity) and debt holders (discounted at cost o f debt) M M Prop I (No Taxes): capital structure irrelevant (no taxes, transaction, or bankruptcy costs) VV L= VVU M M Prop II (No Taxes): increased use o f cheaper debt increases cost o f equity, no change in WACC r e = < b + f O b - r d) M M Proposition I (With Taxes): tax shield adds value, value is maximized at 100% debt VL = Vu + ( t x d ) M M Proposition II (With Taxes): tax shield adds value, WACC is minimized at 100% debt re = *0 + ^ b - r d) ( ! - T c ) E Investor Preference Theories • M M ’s dividend irrelevance theory: In a no-tax/ no-fee world, dividend policy is irrelevant because investors can create a homemade dividend • Dividend preference theory says investors prefer the certainty o f current cash to future capital gains • Tax aversion theory: Investors are tax averse to dividends; prefer companies buy back shares Effective Tax Rate on Dividends D ouble taxation or split rate systems: eff rate = corp rate + (1 - corp rate)(indiv rate) Im putation system: effective tax rate is the shareholder’s individual tax rate Signaling Effects o f Dividend Changes In itiation : ambiguous signal Increase: positive signal D ecrease: negative signal unless management sees many profitable investment opportunities Price change when stock goes ex-dividend: A r = ° ( - T° ) (1_ t cg) Target Payout Ratio Adjustment Model If company earnings are expected to increase and the current payout ratio is below the target payout ratio, an investor can estimate future dividends through the following formula: expected dividend = \ target expected adjustment increase X payout x factor ratio / in EPS / \ previous dividend + Dividend Coverage Ratios dividend coverage ratio = net income / dividends FCFE coverage ratio = FCFE / (dividends + share repurchases) Share Repurchases • Share repurchase is equivalent to cash dividend, assuming equal tax treatment • Unexpected share repurchase is good news • Rationale for: (1) potential tax advantages, (2) share price support/signaling, (3) added flexibility, (4) offsetting dilution from employee stock options, and (5) increasing financial leverage Dividend Policy Approaches • Residual dividend: dividends based on earnings less funds retained to finance capital budget • Longer-term residual dividend: forecast capital budget, smooth dividend payout • Dividend stability: dividend growth aligned with sustainable growth rate • Target payout ratio: long-term payout ratio target Stakeholder impact analysis (SIA): Forces firm to identify the most critical groups Ethical Decision Making Friedman Doctrine: Only responsibility is to increase profits “within the rules o f the game ” Utilitarianism: Produce the highest good for the largest number o f people Kantian ethics: People are more than just an economic input and deserve dignity and respect Rights theories: Even if an action is legal, it may violate fundamental rights and be unethical Justice theories: Focus on a just distribution o f economic output (e.g., “veil o f ignorance”) Corporate Governance Objectives • Mitigate conflicts o f interest between (1) managers and shareholders, and (2) directors and shareholders • Ensure assets used to benefit investors and stakeholders Merger Types: horizontal, vertical, conglomerate Merger Motivations: achieve synergies, more rapid growth, increased market power, gain access to unique capabilities, diversify, personal benefits for managers, tax benefits, unlock hidden value, achieving international goals, and bootstrapping earnings Pre-Offer Defense Mechanisms: poison pills and puts, reincorporate in a state w/ restrictive takeover laws, staggered board elections, restricted voting rights, supermajority voting, fair price amendments, and golden parachutes Post-Offer Defense Mechanisms: litigation, greenmail, share repurch, leveraged recap, the “crown jewel,” “Pac-Man,” and “just say no” defenses, and white knight/white squire The Herfindahl-Hirschman Index (H H I): market power = sum o f squared market shares for all industry firms In a moderately-concentrated industry (HHI 1,000 to 1,800), a merger is likely to be challenged if H H I increases 100 points (or increases 50 points for H H I >1,800) n HHI = ^ ( M S i X l 0 ) i= l Methods to Determine Target Value D C F m ethod: target proforma FCF discounted at adjusted WACC C om parable company analysis-, target value from relative valuation metrics on similar firms + takeover premium C om parable transaction analysis: target value from takeover transaction; takeover premium included M erger Valuations C om binedfirm : Y a t = Va + V t + S — C Takeover prem ium (to target): GainT = TP = PT — VT Synergies (to acquirer): GainA = S — TP = S — (PT — VT ) M erger Risk & Reward Cash offer: acquirer assumes risk & receives reward Stock offer: some o f risks & rewards shift to target If higher confidence in synergies; acquirer prefers cash & target prefers stock Forms of divestitures: equity carve-outs, spin-offs, split-offs, and liquidations EQUITY Holding period return: = r = P l ~ p0 + c f i = p1 + c f l Po x Po Required return: Minimum expected return an investor requires given an asset’s characteristics Internal rate of return (IRR): Equates discounted cash flows to the current price Equity risk premium: required return = risk-free rate + ((3 x ERP) Gordon growth model equity risk premium: = 1-yr forecasted dividend yield on market index + consensus long-term earnings growth rate - long-term government bond yield Ibbotson-Chen equity risk premium [1 + i] x [1 + rEg] x [1 + PEg] - + Y — RF Models of required equity return: • CAPM: r = RF + (equity risk premium x 0.) • M ultifiactor m odel: required return = RF + (risk premium) j + + (risk premium) n • Fam a-French: r.j = RF + 10 mkt,j , x (R —RF)' x mkt + ^ S M B j X ^ "small _ P y g) + ^ H M L j X ~~ Pastor-Stam baugh m odel: Adds a liquidity factor to the Fama-French model • M acroeconom ic multifiactor models: Uses factors associated with economic variables • Build-up m ethod: r = RF + equity risk premium + size premium + specific-company premium Blume adjustment: adjusted beta = (2/3 x raw beta) + (1/3 x 1.0) WACC = weighted average cost of capital MV.equity MVdebt rd (l - T ) + ^ ^ d e b t+ equity M V debt+ equity Discount cash flows to firm at WACC, and cash flows to equity at the required return on equity Discounted Cash Flow (D C F) Methods Use dividend discount models (DDM ) when: • Firm has dividend history • Dividend policy is related to earnings • Minority shareholder perspective Use free cash flow (FCF) models when: • Firm lacks stable dividend policy • Dividend policy not related to earnings Justified P /E • FCF is related to profitability • Controlling shareholder perspective Use residual income (RI) when: • Firm lacks dividend history • Expected FCF is negative leading P/E = r“ g trailing P/E = ^ - b) ( + g) r-g Gordon Growth Model (GGM ) Assumes perpetual dividend growth rate: + PVGO -Stage Growth Model Step 1: Calculate high-growth period dividends Step 2: Use G G M for terminal value at end of high-growth period Step 3: Discount interim dividends and terminal value to time zero to find stock value H-M odel V0 = D o x ( l + gL)] | [Dq x H x ( g s r ~gL Price o f a T-period zero-coupon bond: Do _ r - g Present Value o f Growth Opportunities r FIXED INCOME Justified dividend yield: V „ = -^ r-g Most appropriate for mature, stable firms Limitations are: • Very sensitive to estimates o f r and g • Difficult with non-dividend stocks • Difficult with unpredictable growth patterns (use multi-stage model) V0 = Earlier, higher payments J, DLOM Restrictions on selling stock J DLOM A greater pool o f buyers J, DLOM Greater risk and value uncertainty | DLOM -b gL ) r ~gL Sustainable Growth Rate: b x ROE Solving for Required Return For Gordon (or stable growth) model: Di r= ^ + g Ao Free Cash Flow to Firm (FC FF) Assuming depreciation is the only N CC: FCFF = NI + Dep + [Int x (1 —tax rate)] - FCInv - WCInv FCFF = [EBIT x (1 —tax rate)] + Dep —FCInv - WCInv FCFF = [EBITDA x (1 —tax rate)] + (Dep x tax rate) —FCInv - WCInv FCFF = CFO + [Int x (1 —tax rate)] —FCInv Tee Cash Flow to Equity (FC FE) FC FE = FCFF — [Int x (1 —tax rate)] + Net borrowing FC FE = NI + Dep - FCInv - W CInv + Net borrowing FC FE = NI - [(1 - DR) x (FCInv - Dep)] - [(1 - DR) x WCInv] ( Used to forecast.) Single-Stage F C F F /F C F E Models FCFF • For FCFF valuation: V0 = - -— W ACC- g FCFF • For FCFE valuation: V0 = r~g 2-Stage F C F F /F C F E Models Step 1: Calculate FCF in high-growth period Step 2: Use single-stage FCF model for terminal value at end o f high-growth period Step 3: Discount interim FCF and terminal value to time zero to find stock value; use WACC for FCFF, r for FCFE Price to Earnings (P /E ) Ratio Problems with P/E: • If earnings < 0, P/E meaningless • Volatile, transitory portion o f earnings makes interpretation difficult • Management discretion over accounting choices affects reported earnings !+ g Py = y(! + S t ) Normalization Methods • Historical average EPS • Average ROE Forward price o f zero-coupon bond: Price to Book (P /B ) Ratio Advantages: • BV almost always > • BV more stable than EPS • Measures NAV o f financial institutions Disadvantages: • Size differences cause misleading comparisons • Influenced by accounting choices • BV ^ M V due to inflation/technology j ustified P /B = —& r“ g Price to Sales (P/S) Ratio Advantages: • Meaningful even for distressed firms • Sales revenue not easily manipulated • Not as volatile as P/E ratios • Useful for mature, cyclical, and start-up firms Disadvantages: • High sales ^ imply high profits and cash flows • Does not capture cost structure differences • Revenue recognition practices still distort sales justified P/S = PMo x (1~ b)(1 + g) r- g D uPont Model ROE = net income sales x sales total assets x total assets equity Price to Cash Flow Ratios Advantages: Cash flow harder to manipulate than EPS More stable than P/E Mitigates earnings quality concerns, disadvantages: Difficult to estimate true CFO FC FE better but more volatile M ethod o f Comparables Firm multiple > benchmark implies overvalued Firm multiple < benchmark implies undervalued Fundamentals that affect multiple should be similar between firm and benchmark Residual Income Models • RI = Et —(r x Bt_i) = (ROE —r) x Bt_i • Single-stage RI model: V0 = B + (R O E —r ) x B r“ g • Multistage RI valuation: Vo = Bo + (PV o f interim high-growth RI) + (PV o f continuing RI) Econom ic Value Addedđ ã EVA = NOPAT - $WACC; NOPAT = E B IT (1-1) Private Equity Valuation D LO C = - 1 + Control Premium Total discount = - [(1 - D L O C )(l - DLO M )] The D LO M varies with the following • An impending IPO or firm sale [ DLOM The payment o f dividends J, DLOM Sno= — i + Z O ’ k)) Forward pricing model: B F0 ’k) P()+k> p AJ Forward rate model: [1 +/j,k)]k= [ l + S(( investment horizon, with upward sloping yield curve swap spread = swap rate - treasury yield T E D spread: = (3-month L IB O R rate) —(3-month T-bill rate) Libor-OIS spread = L IB O R rate - “overnight indexed swap” rate Term Structure o f Interest Rates Traditional theories: Unbiased (pure) expectations theory Local expectations theory Liquidity preference theory Segmented markets theory Preferred habitat theory Modern term structure models: Cox-Ingersoll-Ross: dr = a (b -r)^ + a fr d z Vasicek model: dr = a(b - r)d t+ ad z Ho-Lee model: drt = Qt dt+ a d z t Managing yield curve shape risk: AP/P » - D l A x l - D sAxs - D cAxc (L = level, S = steepness, C = curvature) Yield volatility: Long-term errective convexity = -— BV0 x A y2 Effective duration: • ED (callable bond) < ED (straight bond) • ED (putable bond) < ED (straight bond) • ED (zero-coupon) « maturity o f the bond • ED fixed-rate bond < maturity o f the bond • ED o f floater « time (years) to next reset One-sided durations: Callables have lower downduration; putables have lower up-duration Value o f a capped floater = straight floater value - embedded cap value Value o f a floored floater = straight floater value + embedded floor value Minimum value o f convertible bond = greater 0/conversion value or straight value Conversion value o f convertible bond = market price o f stock x conversion ratio Market conversion price market price o f convertible bond conversion ratio FP (on an equity index) = Sq X where: 8C = continuously com pounded dividen d y ield P0 = e-*X N (-d 2) - S0e-6TN (-d 1) Forward price on a coupon-paying bond: where: FP (on a fixed income security) = continuously compounded dividend yield = (S0 - PVC) x (1 + R f )T or = SQ x (1 + R f )T — FVC market price o f convertible bond straight value Callable and putable convertible bond value = straight value o f bond + value o f call option on stock — value o f call option on bond + value o f put option on bond recovery rate = % money received upon default Loss given default (%) = 100 —recovery rate Expected loss = prob o f default x loss given default Present value o f expected loss = (risky bond value) - (risk-free bond value) Structural model o f corporate credit risk: • value o f risky debt = value o f risk-free debt —value o f put option on the companys assets ã equity ô European call on company assets Reduced form models: Impose assumptions on the output o f a structural model Credit analysis o f ABS: • ABS not default but lose value w/defaults • Modeled w/probability o f loss, loss given default, expected loss, present value o f the loss Credit Default Swap (C D S): Upon credit event, protection buyer compensated by protection seller Index CDS: Multiple borrowers, equally weighted Default: Occurrence o f a credit event Common credit events in CD S agreements: Bankruptcy, failure to pay, restructuring C D S spread: Higher for a higher probability o f default and for a higher loss given default Hazard rate = conditional probability o f default, expected losst = (hazard rate) t x (loss given default) t Upfront CD S payment (paid by protection buyer) = PV(protection leg) - PV(premium leg) « (CDS spread - CDS coupon) x duration x NP Change in value for a CD S after inception « chg in spread x duration x notional principal DERIVATIVES Forward contract price (cost-of-carry model) FP T Price o f equity forward with discrete dividends FP(on an equity security) = (SQ- P V D )x(l+ R f) ! Value o f forward on dividend-paying stock Vt (long position) = [St — PVD t — , (—h s - + c - ) Black-Scholes-M erton option valuation model C = S0e ^ N (d [) - e'rIXN (d2) RC f = continuously com pounded risk-free rate Vt (long) = [St - P V C t ] - (i + R f) ( - h S + + C + ) Lc di = ln(S/X) + ( r - + a /2)T aVT d2 = di — a^/T market price o f common stock Premium over straight value So = _ uc C — hoQ H -— = hS0 H— (1 + R f ) (1 + R f ) (—hS+ + P + ) (—hS~ + P ~ ) — hS0 + Pq — hSn0 + (1 + R f ) (l + R f) Value o f a forward on a coupon-paying bond: market conversion premium per share T „ (r £ - c )x T r RrXT S o X e " 6CxT x e t Market conversion premium per share = market conversion price —stock’s market price Market conversion premium ratio FP — S0 x (l + R f ) O ption value using arbitrage-free pricing portfolio Forward on equity index with continuous dividends FP (l + R f F - ' J FP Sge ^ = stock price, less PV o f dividends (l + R f )(T+t) Price o f a bond futures contract: FP = [(full price) (l+ R f)T - AI.r - FVC] full price = quoted spot price + AI Q uoted bond futures price: QFP = forward price /conversion factor (foil price) (1+Rf )T - AIT - FVC CFj Price o f a currency forward contract: Fr = S x (l + R p c )T T (! + r Bc ) Value o f a currency forward contract _ [FPt - FP] X (contract size) V t= (l + * c ) (T- r) O P T IO N STRA TEG IES: Covered call = long stock + short call Protective put = long stock + long put Bull spread: Long option with low exercise price + short option with higher exercise price Profit if underlying $| Bear spread: exercise price o f long > exc price o f short Collar = covered call + protective put Long straddle = long call + long put (w ith sam e strike) Pays off if future volatility is higher Calendar spread: Sell one option + buy another at a maturity where higher volatility is expected Long calendar spread: Short near-dated call + long long-dated call (Short calendar spread is opposite.) Breakeven volatility analysis ^annual = % A P X Currency forward price (continuous time) \ R c —R c xT PC BC) F p = S0 x e 252 trading days until maturity where %AP = absolute (breakeven price — current price) current price Swap fixed rate: C = 1-Z ALTERNATIVE INVESTMENTS Z j + Zo + Z * + Z, where: Z = 1/(1+ R J = price o f n-period zero-coupon bon d p er $ o f prin cipal Value o f interest rate swap to fixed payer: = Yj Z x (SFRjqew —SFR q j j ) x — — x notional 360 Binomial stock tree probabilities: Ttu = probability o f up move = ^ ^ U -D t t d = probability o f a down move = (1 —Ttu) Value o f property using direct capitalization: rental income if fully occupied + other income = potential gross income —vacancy and collection loss = effective gross income —operating expense = net operating income cap rate NOIf comparable sales price Put-call parity: S0 + Po = C o + PV (X) Put-call parity when the stock pays dividends: Po + S0e-*T = C + e"rIX Dynamic delta hedging # o f short call options = # shares hedged delta o f call option # o f long put options = - # shares hedged delta o f put option Change in option value A C « call delta x A S + Vi gamma x A S2 A P ps put delta x A S + Vi gamma x A S2 value = V q = NOI l stabalized NOI or V0 = cap rate cap rate Property value based on “All Risks Yield”: value = V Q= rentj /ARY Value o f a property using gross income multiplier: gross income multiplier = sales price gross income Term and reversion property valuation approach: total property value = PV o f term rent + PV reversion to ERV Layer approach: total property value = PV o f term rent + PV o f incremental rent Debt service coverage ratio: D SC R = firSt' year N Q I debt service Loan-to-value (LTV) ratio: LTV = loan amount appraisal value first year cash flow equity dividend rate = - ; equity Net asset value approach to REIT share valuation: estimated cash NO I 4- assumed cap rate = estimated value o f operating real estate + cash & accounts receivable —debt and other liabilities = net asset value ± shares outstanding = NAV/share Price-to-FFO approach to REIT share valuation: funds from operations (FFO) * shares outstanding = FFO/share x sector average P/FFO multiple = NAV/share Price-to-AFFO approach to REIT share valuation: funds from operations (FFO) —non-cash rents —recurring maintenance-type capital expenditures = AFFO 4- shares outstanding = AFFO/share x property subsector average P/AFFO multiple = NAV/share Discounted cash flow REIT share valuation: value o f a R E IT share = PV(dividends for years through n) + PV (terminal value at the end o f year n) Private Equity Sources o f value creation: reengineer firm, favorable debt financing; superior alignment o f interests between management and PE ownership Valuation issues (V C firm s relative to Buyouts): DCF not as common; equity, not debt, financing Key drivers o f equity return: Buyout: t o f multiple at exit, j in debt VC: pre-money valuation, the investment, and subsequent equity dilution Components o f perform ance (LBO ): earnings growth, | o f multiple at exit, [ in debt E xit routes (in order o f exit value, high to low): IPOs secondary mkt sales; M BO ; liquidation Perform ance M easurement: gross IR R = return from portfolio companies Net IR R = relevant for LP, net o f fees & carried interest Perform ance Statistics: • PIC = % capital utilized by GP; cumulative sum o f capital called down • Management fee: % o f PIC • Carried interest: % carried interest x (change in NAV before distribution) • NAV before distrib = prior yr NAV after distrib + cap called down - mgmt fees + op result • NAV after distributions = NAV before distributions - carried interest - distributions • DPI multiple = (cumulative distributions) / PIC = LP s realized return • RVPI multiple = (NAV after distributions) / PIC = LP’s unrealized return • TVPI mult = DPI mult + RVPI mult N PV VC & IRR methods-, calculate pre-money value, post-money value, ownership fraction, & price per share NPV methods starts with POST, IR R with expected future wealth Assessing Risk: (1) adjust discount rate for prob of failure; (2) use scenario analysis for term Commodities Contango: futures prices > spot prices Backwardation: futures prices < spot prices Term Structure o f Comm odity Futures Insurance theory: Contract buyers compensated for providing protection to commodity producers Implies backwardation is normal Hedging pressure hypothesis: Like insurance theory, but includes both long hedgers ( —> contango) and short hedgers (—>backwardation) Theory of storage: Spot and futures prices related through storage costs and convenience yield Total return on fully collateralized long futures = collateral return + price return + roll return Roll return: positive in backwardation because longdated contracts are cheaper than expiring contracts PORTFOLIO MANAGEMENT Portfolio M anagement Planning Process • Analyze risk and return objectives • Analyze constraints: liquidity, time horizon, legal and regulatory, taxes, unique circumstances • Develop IPS: client description, purpose, duties, objectives and constraints, performance review schedule, modification policy, rebalancing guidelines Arbitrage Pricing Theory E(Rp) = Rp + Piu^i) + P p ,A ) + ••• + Pp,A ) Expected return = risk free rate + E (factor sensitivity) x (factor risk premium) Value at risk (VaR) is an estimate o f the minimum loss that will occur with a given probability over a specified period, expressed as a currency amount or as percentage o f portfolio value 5% annual $VaR = (Mean annual return — 1.65 x annual standard deviation) x portfolio value Conditional VaR (CVaR) is the expected loss given that the loss exceeds the VaR Incremental VaR (IVaR) is the estimated change in VaR from a specific change in the size o f a portfolio position Marginal VaR (MVaR) is the estimate o f the change in VaR for a small change in a portfolio position and is used as an estimate o f the position’s contribution to overall VaR Variance for W A % fluid A + W D °/o fluid B ^Portfolio = W a + + W a Wb C o va b Annualized standard deviation = V250 x (daily standard deviation) % change in value vs change in YTM = -duration (AY) + V2 convexity (AY)2 fo r M acaulay duration, replace A Y by A Y/(1 + Y) Inter-temporal rate o f substitution = mt = u0 marginal utility o f consuming unit in the future marginal utility o f current consumption o f unit Real risk-free rate o f return = l-P o _ Po E(mt) -1 Default-free, inflation indexed, zero coupon: Bond price = Pn = ^- + cov(Pi, m i) v (1 + R ) 1 Nominal short term interest rate (r) = real risk-free rate (R) + expected inflation (it) Nominal long term interest rate = R + tt + where = risk prem ium fo r inflation uncertainty Break-even inflation rate (BEI) ^^non-inflation jndCXedbond yield^a^op indexedbond BEI for longer maturity bonds = expected inflation (t t ) + infl risk premium (0) Credit risky bonds required return = R + tt + + where = risk prem ium (spread) fo r credit risk Discount rate for equity = R + tt + + + k , A = equity risk prem ium = + k = risk prem ium fo r equity vs risky debt Discount rate for commercial real estate = R + TT + + + K + cj> K, = term inal value risk, p = illiquidity prem ium Multifactor model return attribution: k factor return = ^ ( / pi - ( bi) x ( \ ) i=l Active return = factor return + security selection return Active risk squared = active factor risk + active specific risk n Active specific risk = ^ ] (w pi —wbi)2