Idea Transcript
C r it ic a l C o n c e pt s f o r t h e 2019
l
r ETHICAL AND PROFESSIONAL , STANDARDS I
Professionalism
I (A) Knowledge of the Law I (B) Independence and Objectivity I (C ) Misrepresentation
I (D) Misconduct
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)
Integrity o f Capital Markets Material Nonpublic Information Market Manipulation Duties to Clients Loyalty, Prudence, and Care Fair Dealing Suitability Performance Presentation Preservation o f 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 o f 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 Machine learning: Gives a computer the ability to improve its performance o f a task over time. Distributed ledger: A shared database with a consensus mechanism, ensuring identical copies. Simple Linear Regression Correlation: Ny =
covXY
(sx )( sy )
t-test for r (n —2 df): t =
r>/n —2
V l-r 2 cov xy Estimated slope coefficient:
CFA® E x a m
M SR = RSS / k. • M SE = SSE / (n - k - 1). • Test statistical significance o f regression: F = M SR / M SE with k and n - k — 1 df (1-tail).
Risk Types: Appropriate m ethod
D istribution o f risk
Sequential?
Accommodates Correlated Variables?
• Standard error o f estimate (SEE = >/MSE ). Smaller SEE means better fit. • Coefficient of determination (R 2 = RSS / SST). % o f variability o f Y explained by Xs; higher R 2 means better fit.
Simulations
Continuous
Does not matter
Yes
Scenario analysis
Discrete
No
Yes
Decision trees
Discrete
Yes
No
Regression Analysis— Problems • Heteroskedasticity. Non-constant error variance. Detect with Breusch-Pagan test. Correct with White-corrected standard errors. • Autocorrelation. Correlation among error terms. Detect with Durbin-Watson test; positive autocorrelation if D W < dl. Correct by adjusting standard errors using Hansen method. • Multicollinearity. High correlation among Xs. Detect if F-test significant, t-tests insignificant. Correct by dropping X variables. M odel M isspecification • Omitting a variable. • Variable should be transformed. • Incorrectly pooling data. • Using lagged dependent vbl. as independent vbl. • Forecasting the past. • 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. Supervised machine learning: Inputs, outputs are identified. Relationships modeled from labeled data. Unsupervised machine learning: Algorithm itself seeks to describe the structure o f unlabeled data. Linear trend model: Yt = b 0 + b jt + £t Log-linear trend model: ln(yt) = b0 + bjt + et 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. = 1. 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 AR(1):
Estimated intercept: b0 = Y —b jX Confidence interval for predicted Y-value: A
(1 - b j ) RM SE: square root o f average squared error.
Y ± t c x SE of forecast
Random W alk T im e Series:
M ultiple Regression Yi = b 0 + ( b , x X li) + (b 2 x X 2i) + (b 3 X X jiJ + Ej • Test statistical significance o f b; H0: b = 0
xt = x t-i + £t Seasonality: indicated by statistically significant lagged err. term. Correct by adding lagged term. ARCH: detected by estimating: = ao +
Reject if |t| > critical t or p-value < a . • Confidence Interval: bj ± • SST = RSS + SSE.
+ Mr
Variance o f ARCH series: A9 A A A9 CTt+l = a0 “b alet
(tcX Sb,
_____
k ECONOMICS
bid-ask spread = ask quote - bid quote Cross rates with bid-ask spreads:
Currency arbitrage: “Up the bid and down the ask.” Forward premium = (forward price) - (spot price) Value o f fwd currency contract prior to expiration: (FPt — FP) (contract size)
1+ Ra
days 360 ,
Covered interest rate parity:
1 + Ra 1 + Rb
days) 360 j
So
days [3 6 0 ,
Uncovered interest rate parity: E (% A S)wb, = R a - R , Fisher relation: R nominal = R real + E(inflation) v ' International Fisher Relation: R nominal . ..A —R nominal . IR = E(inflation.) —EfinflationJ B v A' v B' Relative Purchasing Power Parity: High inflation rates leads to currency depreciation. %AS(A/B) = inflation^ - inflation(B) where: % AS(AJB) = change in spot price (A/B) Profit on FX Carry Trade = interest differential change in the spot rate o f 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)Q Growth Accounting: growth rate in potential GDP = long-term growth rate o f technology + Oi (long-term growth rate o f capital) + (1 - a ) (long-term growth rate of labor) growth rate in potential GDP = long-term growth rate o f labor force + long-term growth rate in labor productivity
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ECONOMICS continued
•••
Classical Growth T heory • Real GDP/person reverts to subsistence level. Neoclassical Growth T heory • Sustainable growth rate is a function of population growth, labor’s share o f income, and the rate o f technological advancement. • Growth rate in labor productivity driven only by improvement in technology. • Assumes diminishing returns to capital.
6 g** = 5 (1 - a )
G* = — - — + A L (1 - a )
Endogenous Growth T heory • Investment in capital can have constant returns. • | in savings rate —» permanent j in growth rate. • R & D expenditures j technological progress. Classifications o f Regulations • Statutes: Laws made by legislative bodies. • Administrative regulations: Issued by government. • Ju d icial law : Findings of the court. Classifications o f Regulators • Can be government agencies or independent. • Independent regulator can be SRO or non-SRO. Self-Regulation in Financial M arkets • Independent SROs are more prevalent in common-law countries than in civil-law countries. Econom ic Rationale for Regulatory Intervention • Inform ationalfrictions arise in the presence of information asymmetry. • Externalities deal with provision of public goods. Regulatory Interdependencies and T h eir 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 of public goods or financing o f private projects. Financial 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. Prudential supervision: Monitoring institutions to reduce system-wide risks and protect investors. Anticom petitive Behaviors and A ntitrust 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. IFR S Hyperinfl. = cumul. infl. > 100% over 3 yrs. GAAP: use temporal method. IFRS: 1st, restate foreign curr. st. for infl. 2 nd, translate with current rates. Net purch. power gain/loss reported in income. 最新CFA、FRM、AQF、ACCA资料欢迎添加微信286982279
Beneish model: Used to detect earnings manipulation based on eight variables. H igh-quality earnings are: 1 . Sustainable: Expected to recur in future. 2. Adequate: Cover company’s cost o f capital. IF R S A N D U .S. GAAP D IF F E R E N C E S Reclassification o f passive investments: IFRS - Restricts reclassification into/out of 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. • IFRS permits either the “partial goodwill’’ or “full goodwill” methods to value goodwill and noncontrolling interest. U.S. GAAP requires the full goodwill method. Goodwill impairment processes: IFRS - 1 step (recoverable amount vs. carrying value) U.S. GAAP - 2 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 OCI; amortized to P&L. Actuarial gains/losses: IFRS - Remeasurements in OCI 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 E B IT Burden Burden Margin NI EBT E B IT RO E = ------- x --------- x ------------x E B T E B IT revenue T otal Asset T urnover
Financial Leverage
revenue
average assets
x
average assets
average equity
Accruals Ratio (balance sheet approach) accruals ratio85 =
(N O A END - N O A BEG) (N O A e n d + N O A BEG) / 2
Accruals Ratio (cash flow statem ent approach) accruals ratk)
=
(NI - C FO - CFI) (N O A e n d + N O A BEG) / 2
Financial institutions differ from other companies due to systemic importance and regulated status. Basel III: Minimum levels o f capital and liquidity. CAMELS: Capital adequacy, Asset quality, Management, Earnings, Liquidity, and Sensitivity. . Liquidity coverage ratio =
Net stable funding ratio =
highly liquid assets
expected cash outflows available stable funding required stable funding
IN SU R A N C E C O M PA N Y K EY R A T IO S: Underwriting loss ratio claims paid + A loss reserves net premium earned continued on next page...
FINANCIAL STATEMENT ANALYSIS continued. •• Expense ratio underwriting expenses inch commissions net premium written Loss and loss adjustment expense ratio loss expense + loss adjustment expense net premiums earned Dividends to policyholders dividends to policyholders net premiums earned Combined ratio after dividends = combined ratio - dividends to policyholders Total investment return ratio = total investment income / invested assets Life and health insurers’ ratios total benefits paid / (net premiums written and deposits) commissions + expenses / (net premiums written + deposits)
CORPORATE FINANCE Capital Budgeting Expansion • Initial outlay = FCInv + WCInv • CF = (S - C - D ) ( l - T ) + D = (S - C )(l - T ) + D T • T N O C F = SalT + NWCInv - T(SalT - BT) Capital Budgeting Replacem ent • Same as expansion, except current after-tax salvage o f old assets reduces initial outlay. • Incremental depreciation is A in depreciation. Evaluating Projects w ith 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 O ptions • Timing, abandonment, expansion, flexibility, fundamental options. Econom ic and Accounting Incom e • Econ income = AT CF + A in projects 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 = NOPAT - $W ACC oo EP • Market Value Added = X I ----t = i (1 + W A C C ) 1
M M Prop II (No Taxes): increased use o f cheaper debt increases cost o f equity, no change in WACC. re = < b + f ( r o - r d) E 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 = r 0 + ^ ( r 0 - r d )(1 - 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 Double taxation or split rate systems: eff. rate = corp. rate + (1 - corp. rate)(indiv. rate) Imputation system: effective tax rate is the shareholder’s individual tax rate. Signaling Effects o f Dividend Changes Initiation: ambiguous signal. Increase: positive signal. Decrease: negative signal unless management sees many profitable investment opportunities. Price change when stock goes ex-dividend: AP =
d
(i - t d )
{l -
t c g
)
Target Payout Adjustm ent Model expected increase in dividends = ■ target expected b „ \ previous ^ . x payout I —K. . , , earnings r ' -q / dividend
Corporate Governance Objectives • Mitigate conflicts of 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, 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 HHI increases 100 points (or increases 50 points for HHI >1,800). n
H H I = ^ ( M S j xlOO): i=l M ethods to D eterm ine Target Value D C F method: target proforma FCF discounted at adjusted WACC. Com parable company analysis: based on relative valuation vs. similar firms + takeover premium. Com parable transaction analysis-, target value from takeover transaction; takeover premium included. M erger Valuations C om binedfirm : VAT = VA+ VT + S - C
adjustment factor
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 (SLA): Forces firm to identify the most critical groups.
Ethical D ecision M aking Friedman Doctrine: Only responsibility is to increase profits “within the rules o f the game.” • Residual income: = NI - equity charge; Utilitarianism: Produce the highest good for the discounted at required return on equity. largest number o f people. • Claims valuation separates CFs based on equity Kantian ethics: People are more than just an claims (discounted at cost o f equity) and debt economic input and deserve dignity and respect. holders (discounted at cost o f debt). Rights theories: Even if an action is legal, it may M M Prop I (No Taxes): capital structure irrelevant violate fundamental rights and be unethical. (no taxes, transaction, or bankruptcy costs). Justice theories: Focus on a just distribution of VL= VU 最新CFA、FRM、AQF、ACCA资料欢迎添加 economic output (e.g., “veil o f ignorance”). 微信zyz786468331
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 of risks & rewards shift to target. If higher confidence in synergies; acquirer prefers cash & target prefers stock. Forms o f divestitures: equity carve-outs, spin-offs, split-offs, and liquidations.
EQUITY Holding period return: P i— P o + C F , o
P i+ C F ,
-1
0
Required return: Minimum expected return an investor requires given an asset’s characteristics. Internal rate o f 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-C hen equity risk premium
[1 + i] x [1 + rEg] x [1 + PEg] - 1 + Y - RF Models o f required equity return: • CAPM\ r. = RF + (equity risk premium x (3.) • M ultifactor m odel: required return = RF + (risk premium) + (risk premium) n Fam a-French: r.j = RF + 13 mkt,j x (R mkt —RF) + ^SMB,j x ( P'small —
'big'
+ ^H HML.j M U X ^ H B M “ ^ LBM
)
continued on next page...
EQUITY continued...
• Pastor-Stambaugh model: Adds a liquidity factor to the Fama-French model. • M acroeconom ic m ultifactor models: Uses factors associated with economic variables. • Build-up method: 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 M Vequity MV.debt ^Xdebt+equity
> a (i-T )+
^ ^ d e b t -(-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) M ethods 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. • FCF is related to profitability. • Controlling shareholder perspective. Use residual income (RI) when: • Firm lacks dividend history. • Expected FCF is negative. Gordon Growth M odel (G G M ) Assumes perpetual dividend growth rate: V0 =
r~g
Most appropriate for mature, stable firms. Limitations are: • Very sensitive to estimates of r and g. • Difficult with non-dividend stocks. • Difficult with unpredictable growth patterns (use multi-stage model). Present Value o f Growth Opportunities V0 =
+ PVGO
H -M odel
_ D 0 x(l + gL)] | [P 0 x H x ( gs —gL)]
v0=
r ~gL
r ~gL
Sustainable Growth Rate: b x ROE. Required Return From Gordon Growth Model: r = (D, / P0) + g Free Cash Flow to Firm (FC FF) Assuming depreciation is the only NCC: 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 = C FO + [Int x (1 - tax rate)] - FCInv. ;ree Cash Flow to Equity (FC FE) FCFE = FCFF - [Int x (1 - tax rate)] + Net borrowing. FCFE = NI + Dep - FCInv - WCInv + Net borrowing. FCFE = NI - [(1 - DR) x (FCInv - Dep)] - [(1 - DR) x WCInv]. ( Used to forecast.) Single-Stage FC FF/FC FE Models • For FCFF valuation: V 0 = • For FCFE valuation: V 0 =
FCFFj W ACC- g FC FE 1 r~g
2-Stage FC FF/FC FE Models Step 1: Calculate FCF in high-growth period.
Step 2: Use single-stage FCF model for terminal value at end of 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. Justified P/E leading P/E = -----r~g
trailing P/E =
!+ g
1 + / ( j.k ) ]
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 M odel 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. FCFE 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 Incom e Models • RI = Et —(r x Br-i) = (ROE —r) x Bt_i • Single-stage RI model: V0 = B 0 +
T
1 . F(i,k) = ---------------- --
justified P / B = R Q E ~ g r~g
sales
1
(l + ST )
Forward price of zero-coupon bond:
Price to Book (P/B) Ratio Advantages: • BV almost always > 0. • BV more stable than EPS. • Measures NAV of financial institutions. Disadvantages: • Size differences cause misleading comparisons. • Influenced by accounting choices. • BV ^ M V due to inflation/technology.
net income
1 1+Control Premium
Total discount = 1 - [(1 - D L O C )(l - DLOM)] The DLO M varies with the following. • An impending IPO or firm sale [ DLOM . • The payment o f dividends J, DLOM . • Earlier, higher payments { DLOM . • Restrictions on selling stock | DLOM . • A greater pool of buyers J, DLOM . Greater risk and value uncertainty | DLOM .
rT=
f-g
Normalization M ethods • Historical average EPS. • Average ROE.
RO E =
D LO C = 1 —
Price o f a T-period zero-coupon bond:
Justified dividend yield:
0
Private Equity Valuation
FIXED INCOME
( l - b ) ( l + g) r~g
Do
Econom ic Value Added® • EVA - NOPAT - $WACC; NOPAT - E B I T ( 1 - 1)
(RO E —r ) x B 0 r~g
• Multistage RI valuation: Vo = Bo + (PV of interim high-growth RI) + (PV o f continuing RI)
Forward pricing model:
p0+k) F(i.k) =
P;
J
Forward rate model: [i +y(j>k)]k = [i + S(j+k)](j+k) / (i + s.)j “Riding the yield curve”: Holding bonds with maturity > investment horizon, with upward sloping yield curve. swap spread = swap rate - treasury yield T E D spread: = (3-month LIBO R rate) —(3-month T-bill rate) Libor-OIS spread = LIBO 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)^r + a\[tdz Vasicek model: dr = a(b - r)dt + ad z Ho-Lee model: drt = 0t dt + ad z t Managing yield curve shape risk: AP/P = - D l A x l - D sA xs - D c;Axc (L = level, S = steepness, C = curvature) Yield volatility: Long-term c)