The “unstable” confuses me a bit, but I think it simply means that as yields approach 6%, because the CF are calibrated on an assumption of 6% yield, the “competition” for the CTD bond becomes more crowded (i.e., the CTD and the next-CTD are nearer in price). The issue is that, as yields vary from this 6% “calibration point,” higher yields (> 6%) favor high duration bonds and lower yield (< 6% ) favor low duration bonds. As Hull says, “When bond yields are in excess of 6%, the conversion factor system tends to favor the delivery of low-coupon long-maturity bonds [i.e., high duration]. When yields are less than 6%, the system tends to favor the delivery of high-coupon short-maturity bonds [i.e., low duration]. Also, when the yield curve is upward-sloping, there is a tendency for bonds with a long time to maturity to be favored, whereas when it is downward-sloping, there is a tendency for bonds with a short time to maturity to be delivered. “
The “unstable” confuses me a bit, but I think it simply means that as yields approach 6%, because the CF are calibrated on an assumption of 6% yield, the “competition” for the CTD bond becomes more crowded (i.e., the CTD and the next-CTD are nearer in price). The issue is that, as yields vary from this 6% “calibration point,” higher yields (> 6%) favor high duration bonds and lower yield (< 6% ) favor low duration bonds. As Hull says, “When bond yields are in excess of 6%, the conversion factor system tends to favor the delivery of low-coupon long-maturity bonds [i.e., high duration]. When yields are less than 6%, the system tends to favor the delivery of high-coupon short-maturity bonds [i.e., low duration]. Also, when the yield curve is upward-sloping, there is a tendency for bonds with a long time to maturity to be favored, whereas when it is downward-sloping, there is a tendency for bonds with a short time to maturity to be delivered. “
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