15-01-2014, 12:34 PM
Security Analysis and Portfolio Management
Capital Asset Pricing Model
Stock prices are determined by supply and demand
At equilibrium prices demand equals supply
CAPM is a set of predictions about the expected return of risky assets at the equilibrium
Key simplifying assumptions are to ensure that individuals are as alike as possible, only with different risk appetite
Key assumptions
A number of investors and one investor’s wealth is miniscule compared to the total of all
All investors have a common horizon
Investments can only be done in publicly traded risky assets and borrowing and lending at risk free rate
All investors are mean-variance optimizers
Homogeneous expectations or beliefs
Implications (CAPM)
All investors will hold a portfolio of risky assets in proportions that duplicate the assets in the market portfolio (M), which includes all traded assets
Lending and borrowing will cancel out
Value of aggregate risky portfolio will be the entire economic wealth M
All risky assets will form M, by re-adjustment of prices
Inputs for Markowitz model
Total number of estimates required for Markowitz model is:
n estimates of expected returns
n estimates of variances
(n2-n)/2 estimates of co-variances
If we consider 5000 stocks, it will require more than 12.5 million estimates, which is a formidable task
Single index model
The macro factor affecting security returns is measured by return on a broad index
Rate of return for a security then can be broken down into macro and micro components
Holding period excess returns over risk-free
(ri-rf) = ∞i + βi(rm-rf) + ei
where ∞i is security return if market excess return is 0, βi is the security’s sensitivity to market movements and ei is unexpected variation
Fama French model
A modification of multi factor model
Rit = ∞i+βimRmt+βiSMBSMBt+βiHMLHMLt+eit
SMB = return of small stock portfolio in excess of return of portfolio of big stocks
HML = return of portfolio of stocks with high ratios of book values to market values in excess of portfolio of stocks with low ratios