The following are known about the $10$th decile of a market:

$$ Realized return in excess of the riskless rate: $16\%$

$$ CAPM$-$estimated return in excess of the riskless rate: $11\%$

$$ Beta: $1\mathrm{.}5$

$$ Risk$-$free rate: $6\%$

a$.$ Compute the size premium according to the methodology employed by Ibbotson Associates.

b$.$ Compute the general equity risk premium for the market as a whole.

c$.$ Compute the equity risk premium for the $10$th decile, according to CAPM.

d$.$ Compute the CAPM$-$estimated return for the $10$th decile.

e$.$ Given the risk$-$free rate of $6\%$ and the general equity risk premium for the market as computed in question $9,$ what should beta for the $10$th decile be for CAPM to be accurate?