The term structure for zero$-$coupon bonds is currently: for a $1-$year zero the YTM is $4\%,2-$year zero it is $5\%,$ and $3-$year zero it is $6\%.$ Next year at this time you expect the term structure to be: $1-$year zero YTM will be $5\%,2-$year will be $6\%$ and $3-$year will be $7\%.$

a$)$ What do you expect the rate of return to be over the coming year on a $3-$year zero$-$coupon bond?

b$)$ Under the expectations theory, what yields to maturity does the market expect to observe on $1-$ and $2-$year zeros at the end of the year? Is the market's expectation of the return on the $3-$year bond over the coming year greater or less than yours $($show by calculating market expected return for the $3-$year zero over the coming year$)?$