Lecture 6 capm apt
Download
1 / 11

- PowerPoint PPT Presentation


  • 1249 Views
  • Uploaded on

Lecture 6: CAPM & APT The following topics are covered: Deriving CAPM Extensions of CAPM Roll’s critique APT Assumptions for CAPM Investors are risk-averse individuals who maximize the expected utility of their wealth

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about '' - Olivia


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Lecture 6 capm apt l.jpg
Lecture 6: CAPM & APT

  • The following topics are covered:

    • Deriving CAPM

    • Extensions of CAPM

    • Roll’s critique

    • APT

L6: CAPM & APT


Assumptions for capm l.jpg
Assumptions for CAPM

  • Investors are risk-averse individuals who maximize the expected utility of their wealth

  • Investors are price takers and have homogeneous expectations about asset returns that have a joint normal distribution

    • When all individuals have homogeneous expectations, the market portfolio must be efficient

  • There exists a risk-free asset such that investors may borrow or lend unlimited amount at a risk-free rate.

  • The quantities of assets are fixed. Also all assets are marketable and perfectly divisible.

  • Asset markets are frictionless. Information is costless and simultaneously available to all investors.

  • There are no market imperfections such as taxes, regulations, or restriction on short selling.

L6: CAPM & APT


Deriving capm l.jpg
Deriving CAPM

  • If market portfolio exists, the prices of all assets must adjust until all are held by investors. There is no excess demand.

  • The equilibrium proportion of each asset in the market portfolio is

    • (6.1)

  • A portfolio consists of a% invested in risky asset I and (1-a)% in the market portfolio will have the following mean and standard deviation:

    • (6.2)

    • (6.3)

  • A portfolio consists of a% invested in risky asset I and (1-a)% in the market portfolio will have the following mean and standard deviation:

  • Find expected value and standard deviation of with respect to the percentage of the portfolio as follows.

L6: CAPM & APT


Derivation of capm l.jpg
Derivation of CAPM

  • Evaluating the two equations where a=0:

  • The slope of the risk-return trade-off:

  • Recall that the slope of the market line is:

    ;

  • Equating the above two slopes:

L6: CAPM & APT


Slide5 l.jpg

Extensions of CAPM

  • No riskless assets

  • Forming a portfolio with a% in the market portfolio and (1-a)% in the minimum-variance zero-beta portfolio.

  • The mean and standard deviation of the portfolio are:

  • The partial derivatives where a=1 are:

    • ;

    • ;

  • Taking the ratio of these partials and evaluating where a=1:

  • Further, this line must pass through the point and the intercept is . The equation of the line must be:

L6: CAPM & APT


Extensions of capm l.jpg
Extensions of CAPM

  • The existence of nonmarketable assets

    • E.g., human capital; page 162

  • The model in continuous time

    • Inter-temporal CAPM

  • The existence of heterogeneous expectations and taxes

L6: CAPM & APT


Empirical tests of capm l.jpg
Empirical tests of CAPM

  • Test form -- equation 6.36

    • the intercept should not be significantly different from zero

    • There should be one factor explaining return

    • The relationship should be linear in beta

    • Coefficient on beta is risk premium

  • Test results – page 167

  • Summary of the literature.

L6: CAPM & APT


Roll 1977 s critiques l.jpg
Roll (1977)’s Critiques

  • Roll (1977) : page 174

  • We are looking at an efficient index, rather than the market portfolio.

L6: CAPM & APT


Slide9 l.jpg
APT

  • Assuming that the rate of return on any security is a linear function of k factors:

    Where Ri and E(Ri) are the random and expected rates on the ith asset

    Bik = the sensitivity of the ith asset’s return to the kth factor

    Fk=the mean zero kth factor common to the returns of all assets

    Є=a random zero mean noise term for the ith asset

  • We create arbitrage portfolios using the above assets. I.e.,

    • No wealth

    • Having no risk and earning no return on average

L6: CAPM & APT


Slide10 l.jpg
APT

  • There exists a set of k+1 coefficients, such that,

    • (6.57)

  • If there is a riskless asset with a riskless rate of return Rf, then b0k =0 and Rf =

    • (6.58)

  • In equilibrium, all assets must fall on the arbitrage pricing line.

L6: CAPM & APT


Example l.jpg
Example

  • Page 182

  • Empirical tests

    • Gehr (1975)

    • Reinganum (1981)

    • Conner and Korajczyk (1993)

L6: CAPM & APT


ad