Chapter 13. Risk & Return in Asset Pricing Models. Portfolio Theory Managing Risk Asset Pricing Models. 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. goal.

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Chapter 13. Risk & Return in Asset Pricing Models

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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

goal • efficient or optimal portfolio • for a given risk, maximize exp. return • OR • for a given exp. return, minimize the risk

Measuring Return • R is ex post • based on past data, and is known • R is typically annualized change in asset value + income return = R = initial value

example 1 • Tbill, 1 month holding period • buy for $9488, sell for $9528 • 1 month R: 9528 - 9488 = .0042 = .42% 9488

Expected Return • measuring likely future return • based on probability distribution • random variable E(R) = SUM(Ri x Prob(Ri))

example 1 R Prob(R) 10% .2 5% .4 -5% .4 E(R) = (.2)10% + (.4)5% + (.4)(-5%) = 2%

example 2 R Prob(R) 1% .3 2% .4 3% .3 E(R) = (.3)1% + (.4)2% + (.3)(3%) = 2%

examples 1 & 2 • same expected return • but not same return structure • returns in example 1 are more variable

Risk • measure likely fluctuation in return • how much will R vary from E(R) • how likely is actual R to vary from E(R) • measured by • variance (s2) • standard deviation (s)

example 1 s2 = (.2)(10%-2%)2 + (.4)(5%-2%)2 + (.4)(-5%-2%)2 = .0039 s = 6.24%

example 2 s2 = (.3)(1%-2%)2 + (.4)(2%-2%)2 + (.3)(3%-2%)2 = .00006 s = .77%

same expected return • but example 2 has a lower risk • preferred by risk averse investors • variance works best with symmetric distributions

prob(R) prob(R) R R E(R) E(R) symmetric asymmetric

II. Managing risk • Diversification • holding a group of assets • lower risk w/out lowering E(R)

Why? • individual assets do not have same return pattern • combining assets reduces overall return variation

two types of risk • unsystematic risk • specific to a firm • can be eliminated through diversification • examples: -- Safeway and a strike -- Microsoft and antitrust cases

systematic risk • market risk • cannot be eliminated through diversification • due to factors affecting all assets -- energy prices, interest rates, inflation, business cycles

example • choose stocks from NYSE listings • go from 1 stock to 20 stocks • reduce risk by 40-50%

s unsystematic risk total risk systematic risk # assets

measuring relative risk • if some risk is diversifiable, • then sis not the best measure of risk • σ is an absolute measure of risk • need a measure just for the systematic component

Beta, b • variation in asset/portfolio return relative to return of market portfolio • mkt. portfolio = mkt. index -- S&P 500 or NYSE index % change in asset return b = % change in market return

interpreting b • if b = 0 • asset is risk free • if b = 1 • asset return = market return • if b > 1 • asset is riskier than market index • b < 1 • asset is less risky than market index

Testing the CAPM • CAPM overpredicts returns • return under CAPM > actual return • relationship between β and return? • some studies it is positive • some recent studies argue no relationship (1992 Fama & French)

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

APT • Arbitrage Pricing Theory • 1976, Ross • assume: • several factors affect E(R) • does not specify factors

implications • E(R) is a function of several factors, F each with its own b

APT vs. CAPM • APT is more general • many factors • unspecified factors • CAPM is a special case of the APT • 1 factor • factor is market risk premium

testing the APT • how many factors? • what are the factors? • 1980 Chen, Roll, and Ross • industrial production • inflation • yield curve slope • other yield spreads