An IO strip receives only the interest portion of mortgage payments. When rates are high, prepayments tend to be slower, so the IO can behave more like a security with more predictable cash flows. When rates fall, prepayments speed up and the IO loses valuable future interest payments, so its price can fall sharply. IOs often have negative duration because they tend to lose value when rates fall and gain value when rates rise. The false statement is that at high yields, the IO price increases dramatically due to higher coupons; the IO does not benefit from higher coupons in that way, since its value is driven mainly by the expected life of the interest stream, not by a growing coupon rate.