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Unformatted text preview: imply that: ZM is a risk-free asset. SD does not equal 0.
ZM has the same rate of return as the risk-free asset. Finally, in spite of relaxing the assumption that investors can borrow and lend at the risk free rate, the linear
pricing relationship between risk, as measured by the asset beta, and expected return, is not affected. 12 Cheryl Mew FINS2624 – Portfolio Management Semester 1, 2011 L ECTURE 7 – T HE SINGLE INDEX MODEL
T HE COMPONENTS OF RETURN ON STOCK
The Single Index Model (SIM) may be expressed by the following equation: ( − ) ( − ) rit = return on stock i observed in period t
rmt =return on a market index observed in period t
eit = residual return of stock i in period t
The SIM relates the excess return on a stock (rit – rf) to that of a market index (rmt – rf). A market index is
different from the market portfolio suggested by the CAPM. A market index usually consists of a limited
number of assets.
The SIM proposes that the excess return on a stock observed in a period is made up of: Stock alpha – constant component, irrespective of the performance of the market
Variable component - (
−) Residual component - eit, which is not explained by market movements. The SIM assumes that this
residual return on a stock is neither correlated with the excess return on the market index, nor the
residual return of another stock. Also assume that it has an average value of 0 over time. S TOCK ALPHA
The SIM identifies factors affecting the observed return of a stock at the end of a period. Whereas the CAPM
suggests the amount of return investors can expect at the beginning of a period.
After rearranging equation, ( ) ( )− Alpha > 0, it means asset i is considered as under priced, and lies above the SML
Alpha < 0, it means asset is considered as over priced, and lies below SML
In a perfect market where investors are assumed to have homogeneous expectations and remove
mispricing as it occurs, under CAPM, alpha = 0. S TOCK BETA
The beta of a stock is used to capture the sensitivity of market movements. If the market moves up by 1%, a
stock of beta 1.5 is expected to move up by 1.5%, during the same period, compared to 0.5% for another stock
with beta = 0.5.
This linear relationship was explored in CAPM. Since expected returns are not observable and the CAPM
requires the covarianc...
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