$8.$ With a long put and a short put,

a$.$ The combined two positions equal a bullish$/$bearish spread.

b$.$ The combined two positions equal a synthetic long ES$.$

c$.$ The combined two positions equal a synthetic short ES$.$

$9.$ With the effective duration

a$.$ The numerator of the calculation is $45.$

b$.$ Given a $50$ bps increase, the percentage of the bond on a linear estimations is negative $2\mathrm{.}1\%$

c$.$ Given a $25$ bps decrease, the percentage of the bond on a linear estimation is negative $1\mathrm{.}05\%$

$10.$ A portfolio is $60\%$ equity and $40\%$ fixed income, to flip the asset allocation $(40\%$ equity and $60\%$ fixed income:

a$.$ We should long ES and short ZN

b$.$ We should short ES and long ZN

c$.$ Cannot be determined with this data.

$11.$ The formula to do a delta neutral hedge $($for a net long equity portfolio$)$ is

a$.$ Short the # of stock shares$/$ the put delta.

b$.$ Long the # of stock shares$/$ the put delta.

c$.$ Cannot be determined.

$12.$ A portfolio has equity and fixed income. The forecast is to have a stock increase and interest rate increase:

a$.$ We should lower the beta and raise the duration.

b$.$ We should raise the beta and lower the duration.

c$.$ We should raise the beta and decrease the duration

$13.$ If interest rates are expected to rise, the best target duration is:

a$.$ Duration of $2$

b$.$ Duration of $0$

c$.$ Duration of $-2$

$14.$ Ceteris paribus, if the vix is rising,

a$.$ We should long the call

b$.$ We should short the call

c$.$ Cannot be determined.

$15.$ If the vix is rising:

a$.$ We should long the call

b$.$ We should short the call

c$.$ Cannot be determined.