$1-$ What is true for a semi$-$annual floating$-$rate bond with $6$ months to maturity and $1\%$ spread.

Select one or more alternatives:

A$-$ It has a value of $100.$

B$-$ It has a duration smaller than $0\mathrm{.}5.$

C$-$ It has a duration of $0\mathrm{.}5.$

D$-$ It has a value of $100+$ the present value of the remaining spread payment.

$2-$Suppose you are told that:

The price of a semi$-$annual $2-$year fixed$-$rate bond A with a $2\%$ coupon is USD$103.$

The price of a $2-$year zero$-$coupon bond B is USD$98.$

What is true for the arbitrage$-$free price of a $2-$year fixed$-$rate bond C with a $4\%$ coupon?

Select one or more alternatives:

A$-$ The price of C is USD$108.$

B$-$ The price of C is USD$106.$

C$-$ The price of C is USD$105.$

D$-$ There is not enough information in the question to determine the price of C

$3-$ You are told that the nominal yield is r$(0,2)=4\%$ and the continuously compounded inflation rate from t$=0$ to T$=2$ is $2\%$ per annum. What does this imply under perfect forsight?

Select one or more alternatives:

A$-$ If the price index is $100$ at t$=0,$ it will be $102$ at T$=2.$

B$-$ The real yield is $r_{\text{r}\text{e}\text{a}\text{l}}(0,2)=4\%$

C$-$ If the price index is $100$ at t$=0,$ it will be $100*e^{2\%}$ at T$=2.$

D$-$ The real yield is $r_{\text{r}\text{e}\text{a}\text{l}}(0,2)=2\%$