$3.$ Pure expectations theory: Two$-$year bonds

Which of the following is consistent with the pure expectations theory of the yield curve? Check all that apply.

A flat yield curve suggests that the market thinks interest rates in the future will be higher than they are today.

A downward$-$sloping yield curve suggests that the market thinks interest rates in the future will be lower than they are today.

An upward$-$sloping yield curve suggests that the market thinks interest rates are going to be higher in the future than they are today.

A downward$-$sloping yield curve suggests that the market thinks interest rates in the future will be higher than they are today.

Sam would like to invest a certain amount of money for two years and considers investing in a one$-$year bond that pays $5$ percent and a two$-$year bond that pays $9$ percent. Sam is considering the following investment strategies:

Strategy A: In the first year, buy a one$-$year bond that pays $5$ percent. Once that bond matures, buy another one$-$year bond that pays the forward rate.

Strategy B: In the first year, buy a two$-$year bond that pays $9$ percent annually.

If the one$-$year bond purchased in year two pays $11$ percent, Sam will choose Strategy A $.$

Which of the following describes conditions under which Sam would be indifferent between Strategy A and Strategy B$?$

The rate on the one$-$year bond purchased in year two pays $12\mathrm{.}363$ percent.

The rate on the one$-$year bond purchased in year two pays $13\mathrm{.}152$ percent.

The rate on the one$-$year bond purchased in year two pays $13\mathrm{.}678$ percent.

The rate on the one$-$year bond purchased in year two pays $14\mathrm{.}204$ percent.