Jiayu LUOz3219847

THE SINGLE INDEX MODEL – DUE IN WEEK 8

Session 9A.

The single index model (SIM) equation is defined as:

where: is the return on the stock observed in period (instead of predicted at the beginning of period)

is the return on a market index observed in period

is the return on the risk-free asset in the same period

and are the stock’s alpha and beta

is the residual return of stock in period

The characteristic line is defined as:

where: is the return on the stock predicted at the beginning of period (instead of observed in the period)

is the return on a market index predicted in the period

is the return on the risk-free asset in the same period

and are the stock’s alpha and beta

While the SIM equation is used for estimating alpha and beta, as well as for explaining the source of the residual return observed in a period, the characteristic line is used to report the linear relationship between stock excess return and the market index excess return and for computing the excess return predicted, rather than observed, by the model.

B.CBA NAB All Ords

Coefficients of SIMAlpha -0.0010 0.0012 -t-stat of alpha -(0.63) (0.62) -Beta 0.60 1.21 -t-stat of beta (4.10) (6.48) -

Other StatisticsR2 0.42 0.65 -

Residual variance, 0.00005

20.00008

5-

Excess return variance, 0.00009

00.00023

90.00010

6Historical average excess return on All - - 0.27%

Jiayu LUOz3219847

Ords

C.

D.Firm specific risk refers to the risk that is the result of a deviation of the actual observed return from the expected return of an investment of a particular firm as a direct result from firm-specific (not market related) news such as a better than expected earnings announcement. Given its large residual variance (larger than both NAB and CBA), BHP has the largest firm-specific risk. The variance of residual return is appropriate because the residual return captures the difference between the actual return and that predicted by the single index model.

E.Market risk refers to the risk as a result of a deviation of actual return from that expected as a direct result of the arrival of unexpected (or unforeseen) macro-economic news such as a higher than expected inflation figure. BHP has the largest beta, and hence, the largest market risk. Beta is a measure of the relative sensitivity of stock returns to market movements, and therefore it is the appropriate measure.

F.Given its large R2, NAB has its return variability explained the most by the market index. R2 is an appropriate measure because it reflects the proportion of variation in the dependent variable (excess return of stock) being explained by the variation in the independent variable (excess return of the market index).

G.NAB had an average return in excess of that predicted by the CAPM, given by its positive alpha. However, since the t-statistic of alpha is less than two, alpha is insignificantly different from zero, which implies that the stock is correctly priced under CAPM.

H.The variance of CBA (0.0009) can be broken down into:

1) systematic risk = = =

2) firm-specific risk = =

J.

Jiayu LUOz3219847

The input requirements are 1) the stock alpha, 2) the stock beta and 3) a forecast on the excess market index return over the forthcoming period. The stock alpha and beta are estimated by running an OLS regression on the single index model using a set of historical data. The three inputs are then applied to the characteristic line to obtain the expected return as follows: