Suppose that the initial value of an unlevered portfolio of Treasury securities is $$200$ million and the duration is $7.$ Suppose further that the manager can borrow $$800$ million and invest it in the identical Treasury securities so that the levered portfolio has a value of $$1$ billion. What is the duration of the levered portfolio? What is the duration of the unlevered portfolio $($i$.$e$.,$ the duration of the equity$)?$