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02-04 The Capital Assets Pricing

02-04 The Capital Assets Pricing

作者: 非常暴龙兽 | 来源:发表于2019-06-09 20:09 被阅读0次

资本资产定价模型
\omega_i:portion of funds in asset i
\sum_i \mathrm{abs}(\omega_i)=1.0
\gamma_p(t)=\sum_i \omega_i \gamma_i(t)

Assume:
stock A +1%,\omega_A=75%, stock B - 2%,\omega_B=-25%
\gamma_p=1%75% + (-2%)(-25%)=1.25%

the market portfolio
Cap weighted
\omega_i=\frac{\mathrm{mktcap}_i}{ \sum_j \mathrm{mktcap}_j}

The CAPM equation:

\gamma_i(t)=\beta_i \gamma_m(t) + \alpha_i(t)
particular stock return = market + residual

CAPM says:
E(\alpha)=0

CAPM vs Active managment

passive: buy index and hold
active: pick stocks, buy underweight, sell overweight
\gamma_i(t)=\beta_i \gamma_m(t) + \alpha_i(t)
for \alpha_i(t):

  1. CAPM says \alpha is random, and E(\alpha)=0
  2. however, active managers believe they can predict \alpha

CAPM for portfolios

\gamma_p(t)=\sum_i \omega_i (\beta_i \gamma_m(t) + \alpha_i (t)
\beta_p = \sum_i \omega_i \beta_i
\gamma_p(t)=\beta_p \gamma_m (t) + \alpha_p (t) [CAPM]
= \beta_p \gamma_m (t) + \sum_i \omega_i \alpha_i (t) [Active]

Implications of CAPM

\gamma_p=\beta_p \gamma_m + \alpha_p

  • Expected value of \alpha = 0
  • Only way to beat market is choose \beta
  • Choose high \beta in up markets
  • choose low beta in down markets
  • Efficent Market Hypothesis(EMH)
    says you can't predict the market, so CAPM says you can't beat market.

Arbitrage Pricing Theory (APT, 套利定价理论)

  • Stephen Rors, 1976
    \gamma_i=\beta_i \gamma_m + \alpha_i
    CAPM = Ocean
    \beta项可以分解为finance, tech等
    \gamma_i=\beta_{iF} \gamma_F + \beta_{iT} \gamma_T + \beta_{iM} \gamma_M...+\alpha_i

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