Question here please! P47 Fixed Income, General Cash Flows. Can someone please explain how this works?
Example says if there’s a 2 year horizon, and half of the cash is available today, an initial portfolio with half of the monies should be constructed with a duration of 3.
Can someone please tell me why 3?
Then it says the other half that’s not available should be invested hypothetically with a duration of 1, in order to match the 2 year horizon.
Can someone please help out by explaining in the simplest terms possible? Thank you for your time and help. Much appreciated.
It’s all about dollar duration, which might be easier to illustrate with some numbers; suppose that you have $50 available today, and that you’ll get another $50 in one year. Your liability is $100, due in 2 years.
The key to understanding this portfolio is the realization that the $50 that you’ll get in one year has an effective duration of (approximately) one year: think of it as a zero-coupon bond with a 1-year maturity.
You want an effective duration of 2 years on your portfolio, or a dollar duration of 200 dollar-years (= $100 × 2 years). The payment in one year gives you 50 dollar-years (= $50 × 1 year), so you need 150 dollar-years from the money you have today. You have $50, so you need a duration of 3 years (150 dollar-years = $50 × 3 years).
In one year, you’ll have $100 (more or less), and one year left till the liability is due; you invest the entire $100 for one year.