$($ Fixed Income Securities $)$

Q$1$ Which of the following statements are true?

$1)$ Duration is defined only for rises in interest rates.

$2)$ Duration measures bond price changes best for small changes in interest rates.

$3)$ Duration assumes that all interest rates move by the same number of basis points.

$4)$ There is a single definition of duration.

A$)1$ and $2.$

B$)2$ and $3.$

C$)2$ and $4$

D$)2,3$ and $4.$

Q$2$ A portfolio valued at $10$million has a duration of $7\mathrm{.}5.$ All interest rise by $2$ basis points. How much does the value of the portfolio change by$?$

A$)15,000$

B$)-1,500,000$

C$)-15,000$

D$)1,500,000$

Q$3$ If a $4$ year zero has a face value of $100$ and the $4$ year discount factor is $0\mathrm{.}90,$ how much will the price of the zero change when all interest rates fall by $50$ basis points?

A$)-2\mathrm{.}00$

B$)2\mathrm{.}00$

C$)1\mathrm{.}80$

D$)-1\mathrm{.}80$