# convexity & change in cash flows (bond price)

When reading about price change by convexity in the CFA book, they also talk about change in expected future cash flows (with callable and non-callable bonds). What cash flows are they talking about? (pag. 504 (5.2) vol. 5 and others). They don’t do any calculation about cash flow changing… i.e: 20 year 6% cupon smiannual Bond. The nominal cash flows are 3\$/semester. If Price is not 100, then the “relative” cash flow are not 3 but the absolute are still 3. Can you explain what you know about this? Thaks Carlos

Cash flow CAN change if the bond has a call option and interest rate is lower than coupon rate. In this case the issuer will call the bond by refinancing the debt by issuing new bonds with the lower interest rate. Relative cash flow in this case is probably defined as nominal cash flow/market value. If the bond was selling on par, then market value is 100. If it is not, then nominalCashFlow/MarketValue will not be 3…

I understand what you say tstte. I guess that it gets complicated to calculate the effective modiffied duration and covexity when we talk about callable bonds (near the option price). But, “… effective convexity adjustment assumes that the cash flows change when yiels change. this is the same distinction made for duration”. This is what it says in the book and confuses me because they bring it with callable and non-callable bonds! Am I doing it too complicated? Tanks anyway!

cash flow= payments of the coupon of the bond… easy peasy

Cash flow change means the price of the bond is either sold at discount or premium depending on yield. The beginning outflow of cash to buy this bond has changed.

tsttse Wrote: ------------------------------------------------------- > Cash flow change means the price of the bond is > either sold at discount or premium depending on > yield. The beginning outflow of cash to buy this > bond has changed. tsttse can you confirm this?

You are calculating an effective duration/convexity because standard issue Macauley-type duration/convexity is not giving you the real picture on the interest rate sensitivity of the bond. The reason for this most likely is that the bond has embedded options. If an option is exercised then the cash flows of the bond changes. For instance if a 10-yr bond is called at 5-yrs, the reminaing 5 yrs of coupon payments go away and the principal repayment moves up 5 yrs. The “expected” cash flows are “expected” in the probabilistic meaning of “expected”.