The following table depicts current market conditions $($assume annual

compounding$)$:

The $2-$year forward rates implies that $5-$year zero coupon bonds are rich

and $7-$year zero coupon bonds are relatively cheap. Thus, we build a

strategy as below:

Strategy $($Duration neutral barbell$)$: Short $5-$year zero coupon bonds

and Long $3-$ and $7-$year zero coupon bonds.

The prices of $3,5,$ and $7$ year zero coupon bonds are given as follows:

What is the return of the duration neutral barbell if we expect $3$ year

spot rate increases by $1\%$ in $1$ year? Assume that our investment

horizon is $1$ year.