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Bodie−Kane−Marcus: Essentials of Investments, Sixth Edition Back Matter © The McGraw−Hill Companies, 2007 Endpapers Commonly Used Notation b Retention or plowback ratio C Call option value CF rM Cash flow D Duration E Exchange rate E(x) rf Expected value of random variable x F Futures price e 2.718, the base for the natural logarithm, used for continuous compounding ROE Sp t The risk-free rate of interest The rate of return on the market portfolio Return on equity, incremental economic earnings per dollar reinvested in the firm Reward-to-volatility ratio of a portfolio, also called Sharpe’s measure; the excess expected return divided by the standard deviation Time The firm-specific return, also called the residual return, of security i in period t Tp Treynor’s measure for a portfolio, excess expected return divided by beta f Forward rate of interest V g Growth rate of dividends Intrinsic value of a firm, the present value of future dividends per share H Hedge ratio for an option, sometimes called the option’s delta X Exercise price of an option y Yield to maturity ␣ Rate of return beyond the value that would be forecast from the market’s return and the systematic risk of the security  Systematic or market risk of a security ei t i Inflation rate k Market capitalization rate, the required rate of return on a firm’s stock ln Natural logarithm function M The market portfolio i j Cumulative normal function, the probability that a standard normal random variable will have value less than d Correlation coefficient between returns on securities i and j Standard deviation N(d) p Probability P Put value PV Present value P/E Price-to-earnings multiple r Rate of return on a security; for fixed-income securities, r may denote the rate of interest for a particular period 2 Cov(ri , rj) Variance Covariance between returns on securities i and j Bodie−Kane−Marcus: Essentials of Investments, Sixth Edition Back Matter Endpapers © The McGraw−Hill Companies, 2007 Useful Web sites General business and finance information www.dowjones.com www.economist.com www.wsj.com www.ft.com www.businessweek.com www.euromoney.com www.forbes.com www.fortune.com The Economist The Wall Street Journal The Financial Times BusinessWeek Sources of data on individual companies and industries www.mhhe.com/edumarketinsight Available to users of this text, a source of extensive financial statement data as well as stock price histories www.bloomberg.com Stock price and company information finance.yahoo.com money.cnn.com www.hoovers.com Annual reports www.annualreports.com www.sec.gov Annual reports and other financial statements from the EDGAR database Macroeconomic data www.bea.doc.gov www.federalreserve.gov www.fms.treas.gov stats.bls.gov Bureau of Economic Analysis, Department of Commerce Board of Governors of the Federal Reserve System Links to publications of the Treasury Department Bureau of Labor Statistics Sites with links to other resources www.financewise.com www.investorlinks.com www.finpipe.com www.corpfinet.com www.ceoexpress.com www.cob.ohio-state.edu/fin/journal/jofsites.htm (site maintained by Ohio State University College of Business) Bodie−Kane−Marcus: Essentials of Investments, Sixth Edition Back Matter © The McGraw−Hill Companies, 2007 Endpapers Useful Formulas Measures of Risk Variance of returns: 2 ⫽ 兺 p(s)[r (s) ⫺ E(r)]2 Standard deviation: ⫽ 22 s Covariance between Cov(ri , rj ) ⫽ 兺 p(s)[ri (s) ⫺ E(ri)] [rj (s) ⫺ E(rj )] returns: s Cov(ri , rM) Beta of security i: i ⫽ Var(rM) Portfolio Theory Expected rate of return on a portfolio with weights wi in each security: E(rp) ⫽ Variance of portfolio rate of return: 2p ⫽ n n 兺 wi E(ri) i⫽1 n 兺 兺 wj wi Cov(ri , rj) j⫽1 i⫽1 Market Equilibrium The security market line: E(ri) ⫽ rf ⫹ i[E(rM) ⫺ rf] Fixed-Income Analysis Present value of $1: Discrete period compounding: Continuous compounding: PV ⫽ 1/(1 ⫹ r)T PV ⫽ e⫺rT Forward rate of interest for period T: Real interest rate: r⫽ fT ⫽ (1 ⫹ yT)T ⫺1 (1 ⫹ yT⫺1)T⫺1 1⫹R ⫺1 1⫹i where R is the nominal interest rate and i is the inflation rate Duration of a security: Modified duration: D⫽ T CF 兺 t ⫻ (1 ⫹ ty)t /Price t⫽1 D* ⫽ D/(1 ⫹ y) Bodie−Kane−Marcus: Essentials of Investments, Sixth Edition Back Matter © The McGraw−Hill Companies, 2007 Endpapers Equity Analysis D1 k⫺g Sustainable growth rate of dividends: g ⫽ ROE ⫻ b 1⫺b Price/earnings multiple: P/E ⫽ k ⫺ ROE ⫻ b Constant growth dividend discount model: V0 ⫽ ROE ⫽ (1 ⫺ Tax rate) £ROA ⫹ (ROA ⫺ Interest rate) Debt § Equity Derivative Assets Put-call parity: P ⫽ C ⫺ S0 ⫹ PV(X ⫹ dividends) Black-Scholes formula: Spot-futures parity: Interest rate parity: C ⫽ Se⫺␦TN(d1) ⫺ Xe⫺rT N(d2) ln (S/X) ⫹ (r ⫺ ␦ ⫹ 2/2)T d1 ⫽ 2T d2 ⫽ d1 ⫺ 2T F0 ⫽ S0(1 ⫹ r ⫺ d)T 1 ⫹ rUS T F0 ⫽ E0 q r 1 ⫹ rforeign Performance Evaluation Sharpe’s measure: Sp ⫽ Treynor’s measure: Tp ⫽ –r ⫺ –r p f p –r ⫺ –r p f Jensen’s measure, or alpha: p rp ⫺ [ –rf ⫹ p(–rM ⫺ –rf)] ␣p ⫽ – Geometric average return: rG ⫽ [(1 ⫹ r1)(1 ⫹ r2) . . . (1 ⫹ rT)]1/T ⫺ 1