Multi-Factor asset pricing And more on the homework.

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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  e is a random error term

For Beta  R j = a + bR M + 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 Surprise in factors: F 1, F 2, …, F k R i = E(R i ) +  i1 F 1 +  i2 F 2 + … +  iK F k +  i The unexpected systematic return is explained by surprise in “factors.”

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 (  ) 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.  About 30 well-chosen ones.  Statman JFQA Sept 87

Diversification for an Equally Weighted Portfolio Number of Securities Systematic risk Total risk  2 P Unsystematic risk

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

Diversification, minimum variance  E(R)  A B MV

Diversification with a risk-free asset  E(R) A= risk-free asset B MV

Capital Market Line Expected return of portfolio Standard deviation of portfolio’s return. Risk-free rate (R f ) M... Capital market line. X Y.. Indifference curve preferred

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.

Security Market Line Expected return on security (%) Beta of security RmRm RfRf 1 M. 0.8 S. Security market line (SML) S is overvalued. Its price falls T is undervalued. Its price rises. T.

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?

Answer  Portfolio beta is.4*.8+.6*1.5 = 1.22.  Work it out this way:  DevP =.4 DevA +.6 Dev B  E[DevP*DevM] =.4 E[DevA*DevM] +.6*E[DevB*DevM].  Divide by E[DevP squared].