ABCO is a conglomerate that has ksh$4$ billion in common stock. Its capital is invested in four subsidiaries: Entertainment $($ENT$),$ Consumer Products $($CON$),$ Pharmaceuticals $($PHA$),$ and insurance $($INS$).$ The four subsidiaries are expected to perform differently, depending on the economic environment as follows:

Investment in kshs millions Poor economy Average economy Good economy

ENT $1,20020\%-5\%-8\%$

CON $80015\%10\%-20\%$

PHA $1,400-10\%-5\%27\%$

INS $600-!0\%10\%10\%$

Assuming that the three economic outcomes $(1)$ have an equal likelihood of occurring and $(2)$ that the good economy is twice as likely to take place as the other two:

i$)$ Calculate the individual expected returns for each subsidiary

ii$)$ Calculate the implicit portfolio weights for each subsidiary and an expected return and variance for the equity in the ABCO Conglomerate

a$)$ Assume in a$)$ above that ABCO also has a pension fund, which has a net asset value of ksh $5$ billion, implying that ABCO$$s stock is worth ksh $9$ billion instead of ksh $4$ billion. The sh $5$ billion pension fund is invested in short$-$term government risk$-$free securities yielding $5\%$ per year. Recalculate parts i$)$ and ii$)$ of a$)$ to reflect this information.

b$)$ Assume that in a$),$ ABCO decides to borrow ksh $8$ billion at $5\%$ interest to triple its currentinvestment in each of its four lines of business. Assume this new investment has the same return outcomes as the old one.

$($I$)$ Answer parts i$)$ and ii$)$ of a$)$ given the new investment

$($II$)$ How does this result compare with the results from a$)?$

$($III$)$ To whom does this return belong? Why?

c$)$ Explain how ABCO would manage its portfolio prudently