You estimate the following model:

$Exces{s}_{r}etur{n}_a{?}_t={}_j+{}_{j}Exces{s}_{r}etur{n}_m{?}_t+lo{n}_t,$

where Excess$\_$return$\_a_t$ is the difference between return on asset A and

the risk$-$free rate, Excess$\_$return$\_m_t$ is the difference between return on

the market portfolio and the risk$-$free rate, and $lo{n}_t$ is a random error term.

Data are for $174$ months. You estimate the model via OLS; results are

reported below.

OLS estimates using $174$ observations

Dependent variable: excess return on asset $A$

a$)$ How would you test the hypothesis that the market is in equilibrium?

Perform the test at the $5\%s.l.$ and present the logic of the test. What

issues can you see with this approach?

b$)$ Test the hypothesis that the stock is as risky as the market at the $5\%$

s$.$l$.$ Discuss the risks associated to your decision.

c$)$ Is the model statistically adequate? What type of analysis would you

perform to check whether this is the case? Discuss.

d$)$ Assume that you estimate the model over the period January $2002$ to

September $2013$ using monthly data. You want to check whether the

financial crisis in September $2008$ has impacted returns. You estimate

the model before and after the crisis, using September $2008$ as a

splitting montsh. Results are reported below:

Dates: $2002M1-2013MO9$;$T=141,RSS=205\mathrm{.}87$

Dates: $2002$M$1-2008$M$09$; $T=81,$ RSS ${?}_1=102\mathrm{.}87$

Dates: $2008$M$10-2013$M$09$; $T=60,$ RSS ${?}_2=81\mathrm{.}79$

What null hypothesis would you test, and why? Discuss the logic of the

test. Perform the test at the $5\%s.l,$ and discuss the conclusion. Can

you see any shortcoming of the testing procedure you are adopting?