a$.$ Consider the following regression model:

$E(r_{i,t}-r_f)=+{}_t+SM{B}_t+{}_{i,t}$

where $E(r_{i,t}-r_f)$ is the excess return on security $i$ at time $t,{}_t$ is market risk

premium and $SM{B}_t$ is the return premium of small firms. ${}_{i,t}$ is a regression

error term and $,$ and $$ are parameters to be estimated.

i$.$ Please discuss the restrictions that the CAPM places upon the estimated

parameters of this regression model.

ii$.$ Does the Fama French $3-$factor model place any restrictions upon the value of

$$ and $SM{B}_t,$ respectively? If yes, what are the restrictions?

b$.$ "Derivatives are financial instruments that can only scale up the risk of your

investment portfolio". Critically evaluate the above statement with examples.

$(13\frac{1}{3}\%)$