From the finance theory, the Capital Asset Pricing Model postulates a relationship between the returns on a particular security and the market return. An asset's risk premium is represents the excess of its returns over the risk free rate. Assets having risk premia that fluctuate less than one-for-one with the market are called defensive assets, and those whose risk premia fluctuate more than one-for-one with the market are called aggressive assets. From a sample of 135 monthly observations from February 2002 to April 2013, the estimation of the CAPM model for GE yielded the following results: left parenthesis r subscript G E end subscript minus r subscript t b i l l end subscript right parenthesis space equals space 0.050 space plus space 1.296 space left parenthesis r subscript S & P 500 end subscript minus r subscript t b i l l end subscript right parenthesis space space space space space space space space space space space space space space space space space space space space space space space space left parenthesis 0.513 right parenthesis space space space left parenthesis 0.1003 right parenthesis space space space space space space space space space space space space space space space space space space space space space space space R squared equals 0.5565 space Where: minus space r subscript G E end subscript equals G E space r e t u r n s minus space r subscript t b i l l s end subscript equals space U S space T b i l l s space r e t u r n s minus space r subscript S & P 500 end subscript equals r e t u r n s space o n space t h e space S space & space P space 500 space i n d e x
On the basis of the above results:
a) Obtain a 95% confidence interval for both the intercept and the slope coefficents.
b) With a 5% significance level, what can you infer about the relationship between market returns and GE returns?
c) State whether GE can best be described as aggressive, neutral, or defensive security. Test your statement at a 5% significance level.
d) From the results above, what proportion of the variability of GE premium can be attributable to systematic risk? To specific risk?
Over the same 135 months period above, the CAPM estimation for XYZ security and the S&P 500 yielded a beta coefficient of 0.214, with acoefficient standard error of 0.186.
e) Form and interpret a 95% confidence interval for XYZ beta.
f) With a 5% significance, would you say that XYZ securities have no systematic risk, i.e that movements of its shares are completely unrelated to movements in the market?