Imagine that you manage an investment fund that is long in

$$2\mathrm{.}00$ million pool of whole mortgages. You estimate that the

effective duration of those holdings is $6\mathrm{.}14$ years. You are

concerned that the central bank is going to tighten and you

want to hedge your exposure using an interest rate swap.

The swap has the follow terms:

Type: fixed for floating

Frequency: annual

Maturity: $10$ years

Fixed rate: $2\mathrm{.}19\%($annual percentage rate$)$

Floating rate: LIBOR

Notional principal: one million

Currently the yield curve is flat at $2\mathrm{.}19\%,$ and the first

floating rate payment will be based on $2\mathrm{.}19\%.$

Question:

How many swaps do you need to delta$-$hedge the interest rate exposure of the fund's mortgage holdings? $($Fractional swaps are permissible$)$