# CTD and Conversion Factor

Just having a little confusion getting this down… So the Cheapest to Deliver bond (CTD) is the bond that produces a rate of return closest to the risk free rate from a strategy buying the bond itself while simultaneously shorting the futures. Why does this make it “cheapest” to deliver? The conversion factor (for ex, given std 6% yield on T-Bond futures) is over one when the bond’s coupon is >6%(someone correct me on this if I’m wrong), which should make the futures buyer pay MORE for the bond given its favourable return profile. However, when we calculate the futures price we DIVIDE by the conversion factor, lowering the futures price. Can someone clarify this? Have looked at CFAI/schweser, derivs really is one of the “tougher” bits.

conversion factors are set by the exchange for each bond and delivery month…as time goes by the level of underlying rates/curve may change. As the group of deliverable bonds will be of various maturities and coupons the ctd may well change over time…This is often the case…more often down to repo conditions, I have found. I didn’t pay much attention to this section, having traded quite a bit of basis in the real world. I have used; basis = cash/spot price of bond - (futures price x conversion factor for individual bond) This has been known to make money on occasions!

muffin09 Wrote: ------------------------------------------------------- > Just having a little confusion getting this > down… > > So the Cheapest to Deliver bond (CTD) is the bond > that produces a rate of return closest to the risk > free rate from a strategy buying the bond itself > while simultaneously shorting the futures. Why > does this make it “cheapest” to deliver? > > The conversion factor (for ex, given std 6% yield > on T-Bond futures) is over one when the bond’s > coupon is >6%(someone correct me on this if I’m > wrong), which should make the futures buyer pay > MORE for the bond given its favourable return > profile. However, when we calculate the futures > price we DIVIDE by the conversion factor, lowering > the futures price. Can someone clarify this? > > Have looked at CFAI/schweser, derivs really is one > of the “tougher” bits. I don’t get this either, the book first says that if the bond’s coupon is higher than the conversion yield then the conversion factor is greater than one and multiplied times the futures price so that the short gets more money for the higher coupon bond which delivered, but then in an example they divided the price of a >6% coupon bond by the 1+ factor making the price received by the short a lesser amount. Can somebody help with this?