The investor has one personal view: She expects the second asset to outperform the first

by $3\%$ on average. However, the investor is not certain with her prediction such that the

error in her prediction has the standard normal distribution i$.$e $N(0,1).$ Compute

the Black$-$Litterman estimate of expected return for the investor. $(5$ marks$)$

b$)$ Let the model of the returns be given as

$r_t=+{}_t$

where $in{R}^N$ is the unknown true mean vector and ${}_{t}in{R}^N$ is a multivariate i$.$i$.$d process

with zero mean and constant covariance matrix. Assuming that $r_{t}N(,),$ derive the

Maximum Likelihood estimators for $$ and $.(6$ marks$)$

c$)$ Consider the following utility function $U()=\frac{{}^{}}{}$ for $01.$ Show that $U(w)$ has

declining absolute risk aversion and constant relative risk aversion $(4$ marks$)$