To be clear, they’re saying that an I/O has an effective duration of -4 (years); Macaulay duration and modified duration cannot be negative. (Also, I/Os have negative duration only at low yields; when yields get high enough, they act like regular bonds, with positive effective duration.)
The way to think about effective duration – this is where the units of years can help – is that a bond with an effective duration of (positive) 4 years has (roughly) the same interest rate price sensitivity as a 4-year, zero-coupon bond. (It’s not exactly the same because the modified duration of a 4-year zero (which measures its interest rate sensitivity) is slightly less than 4 years: it’s 4 / (1 + YTM/2) years; it would be exactly 4 years only if its YTM were 0%, otherwise, it will be slightly less than 4 years.)
If a bond with a 4-year effective duration has the same price sensitivity to yield changes as a 4-year zero, then a bond with a −4-year effective duration has the same price sensitivity to yield changes as a 4-year zero, but in the opposite direction! That is, when interest rates increase, the price of a 4-year zero decreases; when interest rates increase, the price of an I/O with a −4-year effective duration increases, by the same percentage as the 4-year zero decreases. A 1% increase in interest rates leads to a 4% decrease in the price of a 4-year zero (approximately, ignoring convexity); a 1% increase in interest rates leads to a 4% increase in the price of an I/O with a −4-year duration (again, approximately, ignoring convexity).
(If you want to know how the price of a bond can increase when interest rates increase, that’s a good question for another thread; let’s not take this one off topic.)
To me as well.