# Case 18.6 C18-06 A well-known model in finance, called the market model, assumes that the rate of…

Case 18.6

C18-06 A well-known model in finance,
called the market model, assumes that the rate of return on a share (R) is
linearly related to the monthly rate of return on the overall market Rm. The
mathematical description of the model is

R = _0
+ _1 Rm + _

where the error term _ is assumed to
satisfy the requirements of the linear regression model. For practical
purposes, Rm is taken to be the annual rate of return on some major stock
market index, such
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Case 18.6

C18-06 A well-known model in finance,
called the market model, assumes that the rate of return on a share (R) is
linearly related to the monthly rate of return on the overall market Rm. The
mathematical description of the model is

R = _0
+ _1 Rm + _

where the error term _ is assumed to
satisfy the requirements of the linear regression model. For practical
purposes, Rm is taken to be the annual rate of return on some major stock
market index, such as the Australian All-Ordinaries Index. The coefficient
_1, called the shares beta coefficient, measures how sensitive the
shares rate of return is to changes in the level of the overall market. For
example, if _1 > 1 (or _1 < 1),="" the="" shares="" rate="" of="" return="" is="" more="" (or="" less)="" sensitive="" to="" changes="" in="" the="" level="" of="" the="" overall="" market="" than="" is="" the="" average="" share.="" the="" annual="" rates="" of="" return="" for="" five="" shares="" (namely,="" gold,="" energy,="" retail,="" banks="" and="" property="" trusts)="" and="" for="" the="" overall="" market="" over="" a="" 17-year="" period="" are="" recorded.="" (columns="" 26="" store="" the="" annual="" percentage="" return="" for="" the="" five="" shares;="" column="" 7="" stores="" the="" all-ordinaries="" index.)="" for="" each="" share,="" determine="" the="" following:="">

a What is the sample regression line?

b Is there sufficient evidence to infer at
the 5% significance level that there is a linear relationship between the
return on the individual share and the return on the total market?

c Is there sufficient evidence to infer at
the 5% significance level that an individual share is less sensitive than the
average share?

d Discuss the significance of the findings.

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