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].