In this problem, we will go through the steps of manging an active portolio. We will

Whth a passive strategy, we believe that measured by $.$ Wal return, others, after accounting iole to identify assets that have an abno a stock to any actively managed por that is$,$ the abnormal return$-$specific When we want to add a st the extra return from the $,$ the other hand, we add firm$-$spe the one hand, we love to get have to take market risk. On companies.

stock for which we do not hasing ourselves to ind red through the information ratio. Asing this line of thinking, there This trade$-$off is meas $$ or small firm$-$specific risk, or both.

tion ratio has a large ang the weights in an aciding of In the follong active portfolio has the index $A,$ and the storing has the index $S.$

You are given the following information about the excess return and standard de of the market portfolio:

$E[R_M]=0\mathrm{.}09,{}_M=0\mathrm{.}12.$

You are given the following information about the existing active portfolio, which was estimated using a single$-$factor model:

${}_A=0\mathrm{.}044,{}_A=1\mathrm{.}25,{}^2(e_A)=0\mathrm{.}04$

The stock we wish to add has the parameters:

${}_S=0\mathrm{.}12,{}_S=1\mathrm{.}05,{}^2(e_S)=0\mathrm{.}2$

a$)$ Find the systematic and non$-$systematic components of the variance of Stock $S.$

Using the rules for building an active portfolio, we find that we should build a new active portfolio $N$ which consists of $\frac{5}{8}$ of A and $\frac{3}{8}$ of $S.$

b$)$ Find the $,$ and variance from the firm$-$specific risk of the new active portfolio $N.$ That means, find ${}_N,{}_N$ and ${}^2(e_N).$