# Conversion factor and CTD Bond

I'm reading the book 'Options, Futures and Other derivatives' an having a hard time to understand Conversion factor and CTD bond.

1. Conversion factor

I understand this as a factor to adjust the price of the bond delivered to the hypothetical bond(with yield = 6% in my case)

ex. maturity = 20 years. Coupon rate = 10% with semiannual payment. Face value = $100 then in the book, after discounting future cash flow with annual rate = 6%$\sum_{i=1}^{40} \dfrac5{1.03^i} +\dfrac{100}{1.03^{40}} = $146.23 author says conversion factor is$\dfrac{$146.23}{$100}\$ = 1.4623

(If I'm wrong, please tell me. )

I wonder why we deal with only yield. I think the calculation must reflect the difference in maturities of each bonds.

1. CTD Bond.

In the book, author said 'when bond yields are in excess of 6%, the conversion factor system tends to favor the delivery of low-coupon, long-maturity bonds.'

I think, this means that under that circumstance, conversion factor increases as coupon rate decreases and maturity increases. However, I can't show that mathematically. I guess I misunderstood or there must be more variables that needs to be considered from the words 'tends to'. How can I understand that description both intuitively and mathematically.

• maybe you want to quote the formula for the conversion factor in your case (Bund?) – Ric Feb 26 '16 at 8:07