Multi-Factor asset pricing

1 / 25

# Multi-Factor asset pricing - PowerPoint PPT Presentation

Multi-Factor asset pricing. And more on the homework. Review item. Define beta. Answer. Rate of return on asset j is Rate of return on the market portfolio is . My project: AOL. Regression: y = a + bx + e. where a and b are constants y is to be explained x is an explanatory variable

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

## PowerPoint Slideshow about 'Multi-Factor asset pricing' - sebastien

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

### Multi-Factor asset pricing

And more on the homework

Review item
• Define beta.

Rate of return on asset j is

Rate of return on the market

portfolio is

Regression: y = a + bx + e
• where a and b are constants
• y is to be explained
• x is an explanatory variable
• e is a random error term
For Beta
• Rj = a + bRM + e
• e = idiosyncratic risk (diversifiable risk)
• b = beta
• a = alpha = sample average advantage over the market
• if statistically significant
Components of risk
• Diversifiable risk is unique, idiosyncratic, or unsystematic risk
• Market risk is systematic or portfolio risk
Diversifiable risk
• It is eliminated by buying other assets, i.e.,
• can be "diversified away."
Arbitrage pricing theory
• Side-issue: Arbitrage is interesting in options, bonds, CAPM, and this course.
• Notion: There are several factors (indexes).
• They are found by regression analysis.
• More notion: Each factor has its own beta.
• Risk unrelated to the factors can be diversified away, leaving only systematic risk.
The K-Factor Model

The unexpected systematic return is explained by

surprise in “factors.”

Surprise in factors: F1, F2, … ,Fk

Ri = E(Ri) + bi1F1 + bi2F2 + … + biKFk + ei

Arbitrage pricing theory is like CAPM, …
• Factor risk (previously market risk) remains even when the portfolio is fully diversified.
• Factor risk is undiversifiable.
• For any asset, the betas of factors measure factor risk.
• Required return is linear in the factor betas.
The market rewards the investor
• not for bearing diversifiable risk but
• only for bearing factor (or market) risk.
The market rewards the investor
• not for all the risk ( s ) of an asset
• but only for its betas.
Do low P/E firms contradict CAPM?
• Price at t = Earnings at t+1/r-g
• Price/Earnings = (1+g)/r-g
• Low growth and or high risk imply low P/E
• High risk implies high expected return.
• Therefore low P/E means, on average, high return. Doesn’t contradict CAPM.
How many assets in a diversified portfolio?
• Not many.
• Statman JFQA Sept 87
Diversification for an Equally Weighted Portfolio

Total risk s2

P

Unsystematicrisk

Systematicrisk

Number of Securities

Investors need only two funds.
• Figures 10.4, 10.5, and 10.6.

.

Y

.

X

Capital Market Line

Expected returnof portfolio

Indifference curve

Capital market line

.

preferred

.

M

.

.

Risk-freerate (Rf )

Standarddeviation ofportfolio’s return.

Argument for the security market line
• Only beta matters
• A mix of T-Bills and the market can produce any beta.
• An asset with that beta is no better or worse than the two-fund counterpart
• Hence it has the same return.

.

T

.

S

0.8

Security Market Line

Expected returnon security (%)

T is undervalued.

Its price rises

Security market line (SML)

.

.

M

Rm

Rf

S is overvalued.

Its price falls

Beta ofsecurity

1

Review item
• Asset A has a beta of .8.
• Asset B has a beta of 1.5.
• Consider a portfolio with weights .4 on asset A and .6 on asset B.
• What is the beta of the portfolio?