Chapter 14 The CaPm---applications and tests an longzhen
Chapter 14 The CAPM ---Applications and tests Fan Longzhen
Predictions and applications CAPM: in market equilibrium, investors are only rewarded for bearing the market risk APT: in the absence of arbitrage investors are only rewarded for bearing the factor risk Applications ---professional portfolio managers: evaluating security returns and fund performance corporate manager: capital budgeting decisions
Predictions and applications • CAPM: in market equilibrium, investors are only rewarded for bearing the market risk; • APT: in the absence of arbitrage, investors are only rewarded for bearing the factor risk; • Applications: • ---professional portfolio managers: evaluating security returns and fund performance • ---corporate manager: capital budgeting decisions
early tests of CAPM Cross-sectional test of the model Douglas(1969) Miller and Scholes ( 1972) Black, Jensen and Scholes (1972 ); Fama and Macbeth (1973) E(R)=R+B(E[Rm]-RD) R=+y1月+e,i=12,,n Yi=R-R
Early tests of CAPM • Cross-sectional test of the model: • Douglas (1969); • Miller and Scholes (1972); • Black, Jensen and Scholes (1972); • Fama and Macbeth (1973) m f f i i i i f i m f R R R R e i n E R R E R R − = + + = = + − = = ? 1 ? 0 0 1 ˆ ˆ , 1,2,..., ˆ ( ) ( [ ] ) γ γ γ γ β β
continued Douglas(1969) Adds own-variance to regression significant Linter adds(e to regression - significant Miller and Scholes(1972) Measurement error inbs Correlation between measurement error and a(e) Skewness of returns Black, Jensen, and Scholes (1972) Use portfolio to maximize dispersion of beta s isa+ RI -, B (R -R)+e Time-series test Low B stocks - positive a,'s High B stoCkS -> negative d,'s
continued • Douglas (1969) • Adds own-variance to regression significant; • Linter adds to regression significant; • Miller and Scholes (1972) • Measurement error in ‘s; • Correlation between measurement error and • Skewness of returns . • Black, Jensen, and Scholes (1972) • Time-series test • Use portfolio to maximize dispersion of beta’s • Low stocks positive • High stocks negative ˆ ( ) 2 i σ e βi ˆ ˆ ( ) 2 i σ e 0 ( ) ? = − = + − + i it f i i mt f it R R R R e α α β β ˆ s i α ˆ ' β ˆ s i α ˆ
Hypothesis testing Definition of size and power H true H false Accept correct Type I error Reject type i error correct Size=Pr(Type I error) Power=l-Pr(type II error) Tradeoff between size and power Fix size find most powerful test
Hypothesis testing • Definition of size and power • H true H false • Accept correct Type II error • Reject type I error correct • Size=Pr(Type I error); • Power=1-Pr(type II error); • Tradeoff between size and power; • Fix size, find most powerful test