Markowitz’s model suffers from several problems.

firstly

requires a huge number of estimates to fill the covariance matrix

applying it is computationally intensive, even if:

Only a relatively small numbers of assets are involved and / or;

The process is automated.

Markowitz Portfolio Selection Model.

method we use to identify the efficient set of portfolios

Markowitz’s model suffers from several problems.

secondly

does not provide any guideline to forecasting of the security risk premiums that are esesntial to construct the efficient frontier of risky assets

esp b/c **past returns are unreliable guides to expected future returns **

what does the single index model do?

simplifies way we describe sources of security risk allows us to use smaller, consistent sets of risk parameters and risk premiums

greatly enhance analysis of security risk premium

decompose risk into systematic and firm specific components --> helps simplify problem of estimating covariance and correlation

macroeconomic factor, m, and the result of firm-level surprises, ei, are

uncorrelated

beta, which is helpful in

estimating future systematic risk

alpha, however, we would not use it as a

alpha, however, we would not use it as a forecast for future alpha:

This is because evidence suggests that estimates from successive periods are essentially uncorrelated; and,

Instead, analysts must use security analysis to develop their expectation regarding future alpha

What does the CML graph?

CML graphs the risk premiums of efficient portfolios (i.e. portfolios composed of the market and the risk-free asset) as a function of portfolio standard deviation

What does SML graph?

SML graphs individual asset risk premiums as a function of asset risk.

expected return - beta relationship

SML valid for both efficient portfolios and individual assets

what does SML measure

SML provides benchmark for evaluation of investment performance

Provides required rate or return necessary to compensate investors for risk as well as the time value of money

Where do fairly priced assets lie?

Fairly priced assets will lie on the SML i.e. their expected returns are commensurate with their risk

When else do securities lie on the SML?

when market is in equilibrium all securities lie on the SML

SML

if stock is underpriced

it will provide an expected return in excess of the fair return stipulated on the SML

These stocks fall above the SML and have a positive alpha

SML

if stock is overpriced

Stocks providing an expected return less than the fair return are viewed as overpriced. These stocks fall below the SML and have a negative alpha.

The two key implications of the CAPM are:

The market portfolio is efficient; and,

The risk premium on a risky asset is proportional to its beta.

unlike the index model, the CAPM predicts

unlike the index model, the CAPM predicts that i will be zero for all assets.

How do we know if a stock has higher firm-specific risk?

Stock A has higher firm-specific risk because the deviations of the observations from the SCL are larger for Stock A than for Stock B. Deviations are measured by the vertical distance of each observation from the SCL

how do we know which stock has higher systematic risk?

Beta is the slope of the SCL, which is the measure of systematic risk. The SCL for Stock B is steeper; hence Stock B’s systematic risk is greater.

total variance is the sum of

the total variance is the sum of the explained variance plus the unexplained variance (the stock’s residual variance):

The R^{2}(or squared correlation coefficient) of the SCL is

The R2 (or squared correlation coefficient) of the SCL is the ratio of the explained variance of the stock’s return to total variance, and the total variance is the sum of the explained variance plus the unexplained variance (the stock’s residual variance):

Alpha is

Alpha is the intercept of the SCL with the expected return axis. Stock A has a small positive alpha whereas Stock B has a negative alpha; hence, Stock A’s alpha is larger.

correlation coefficient is

simply the square root of R2, so Stock B’s correlation with the market is higher.

Firm-specific risk is measured by

Market risk is measured by

Firm-specific risk is measured by the residual standard deviation.

Market risk is measured by beta, the slope coefficient of the regression

R^{2} measures

R^{2} measures the fraction of total variance of return explained by the market return.