Understanding Risk & Return in Asset Pricing Models: Portfolio Theory & Risk Management, Slides of Banking and Finance

Download Understanding Risk & Return in Asset Pricing Models: Portfolio Theory & Risk Management and more Slides Banking and Finance in PDF only on Docsity! Chapter 13. Risk & Return in Asset Pricing Models • Portfolio Theory • Managing Risk • Asset Pricing Models Docsity.com I. Portfolio Theory • how does investor decide among group of assets? • assume: investors are risk averse – additional compensation for risk – tradeoff between risk and expected return Docsity.com return = R = change in asset value + income initial value Measuring Return • R is ex post – based on past data, and is known • R is typically annualized Docsity.com example 1 • Tbill, 1 month holding period • buy for $9488, sell for $9528 • 1 month R: 9528 - 9488 9488 = .0042 = .42% Docsity.com • annualized R: (1.0042)12 - 1 = .052 = 5.2% Docsity.com Expected Return • measuring likely future return • based on probability distribution • random variable E(R) = SUM(Ri x Prob(Ri)) Docsity.com example 1 R Prob(R) 10% .2 5% .4 -5% .4 E(R) = (.2)10% + (.4)5% + (.4)(-5%) = 2% Docsity.com example 2 R Prob(R) 1% .3 2% .4 3% .3 E(R) = (.3)1% + (.4)2% + (.3)(3%) = 2% Docsity.com σ2 = SUM[(Ri - E(R))2 x Prob(Ri)] σ = SQRT(σ2) Docsity.com example 1 σ2 = (.2)(10%-2%)2 = .0039 + (.4)(5%-2%)2 + (.4)(-5%-2%)2 σ = 6.24% Docsity.com example 2 σ2 = (.3)(1%-2%)2 = .00006 + (.4)(2%-2%)2 + (.3)(3%-2%)2 σ = .77% Docsity.com II. Managing risk • Diversification – holding a group of assets – lower risk w/out lowering E(R) Docsity.com • Why? – individual assets do not have same return pattern – combining assets reduces overall return variation Docsity.com two types of risk • unsystematic risk – specific to a firm – can be eliminated through diversification – examples: -- Safeway and a strike -- Microsoft and antitrust cases Docsity.com unsystematic risk systematic risk total Y, visk # assets Docsity.com measuring relative risk • if some risk is diversifiable, – then σ is not the best measure of risk – σ is an absolute measure of risk • need a measure just for the systematic component Docsity.com Beta, β • variation in asset/portfolio return relative to return of market portfolio – mkt. portfolio = mkt. index -- S&P 500 or NYSE index β = % change in asset return % change in market return Docsity.com measuring β • estimated by regression – data on returns of assets – data on returns of market index – estimate ε+β+α= mRR Docsity.com problems • what length for return interval? – weekly? monthly? annually? • choice of market index? – NYSE, S&P 500 – survivor bias Docsity.com • # of observations (how far back?) – 5 years? – 50 years? • time period? – 1970-1980? – 1990-2000? Docsity.com implication • expected return is a function of – beta – risk free return – market return Docsity.com ]R)R(E[R)R(E fmf −β+= or ]R)R(E[R)R(E fmf −β=− fR)R(E − is the portfolio risk premium where fm R)R(E − is the market risk premium Docsity.com so if β >1, • portfolio exp. return is larger than exp. market return • riskier portfolio has larger exp. return fR)R(E − fm R)R(E − )R(E )R(E m > > Docsity.com so if β = 0, • portfolio exp. return is equal to risk free return fR)R(E − )R(E fR = 0 = Docsity.com example • Rm = 10%, Rf = 3%, β = 2.5 ]R)R(E[R)R(E fmf −β+= %]3%10[5.2%3)R(E −+= %5.17%3)R(E += %5.20)R(E = Docsity.com • CAPM tells us size of risk/return tradeoff • CAPM tells use the price of risk Docsity.com • other factors important in determining returns – January effect – firm size effect – day-of-the-week effect – ratio of book value to market value Docsity.com problems w/ testing CAPM • Roll critique (1977) – CAPM not testable • do not observe E(R), only R • do not observe true Rm • do not observe true Rf • results are sensitive to the sample period Docsity.com APT • Arbitrage Pricing Theory • 1976, Ross • assume: – several factors affect E(R) – does not specify factors Docsity.com testing the APT • how many factors? • what are the factors? • 1980 Chen, Roll, and Ross – industrial production – inflation – yield curve slope – other yield spreads Docsity.com summary • known risk/return tradeoff – how to measure risk? – how to price risk? • neither CAPM or APT are perfect or free of testing problems • both have shown value in asset pricing Docsity.com