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# P-Strips & C-Strips

#### hellohi

##### Active Member
Hi @hellohi Can you take a look at the source http://www.treasurydirect.gov/instit/marketables/strips/strips.htm e.g.,

Notice that the original security, in the example, is a 20-year bond that pays coupons every six months (20*2 = 40 coupons). If we price this bond, there are exactly 40 cash flows, although the final cash flow consists of both a coupon and the principal ($20,o00). This one security is "stripped" into 41 separate securities, one for each cash flow. The first coupon, for example, in six months "becomes" (i.e., the broker issues a new security) its own six-month zero-coupon bond with face value equal to the coupon cash flow. The second coupon, due in one year, is stripped into its own one-year zero-coupon bond. In this way, in addition to the$20,000 Treasury stripped into 41 more affordable pieces, each new security is a (virtually) risk-free zero-coupon bond. These are very useful in finance. For one thing, they have no reinvestment risk. For another, they can be perfectly matched with liabilities. I hope that helps!
yes @David Harper CFA FRM
it helped and I understand the concept well
but I have one question, the new securities looks like the zero-coupon bond in way that they pay one cash flow at the end or at maturity, but I still see difference that the zero-coupon bond is discounted (price less than the par) and I dont think that the STRIPS will be discounted??
thanks
Nabil

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
HI @Nabil Great! But yes a zero-coupon security (bond) is discounted. Imagine I am the broker who strips the security previously mentioned by the New York Fed ("For example, a 20-year bond with a face value of $20,000 and a 10% interest rate could be stripped into its principal and its 40-semi-annual interest payments") and let's say the continuous interest rate is 2.0%. If I sell to you the P-STRIP, you will pay me only about$20,000*exp(-2%*20) = $13,406 because the P-STRIP is a zero-coupon bond paying you the face in 20 years. Similarly, for any of the individual 40 C-STRIPS, you want to pay only$1,000*exp(-r*T) where T = {1, ..., 40} where the face of each C-STRIP = $20,000 * 10%/2 =$1,000

I admit, if we use a zero interest rate, then there is effectively no discounting, and in the real world we are pretty close to that. So you have a point

#### hellohi

##### Active Member
HI @Nabil Great! But yes a zero-coupon security (bond) is discounted. Imagine I am the broker who strips the security previously mentioned by the New York Fed ("For example, a 20-year bond with a face value of $20,000 and a 10% interest rate could be stripped into its principal and its 40-semi-annual interest payments") and let's say the continuous interest rate is 2.0%. If I sell to you the P-STRIP, you will pay me only about$20,000*exp(-2%*20) = $13,406 because the P-STRIP is a zero-coupon bond paying you the face in 20 years. Similarly, for any of the individual 40 C-STRIPS, you want to pay only$1,000*exp(-r*T) where T = {1, ..., 40} where the face of each C-STRIP = $20,000 * 10%/2 =$1,000

I admit, if we use a zero interest rate, then there is effectively no discounting, and in the real world we are pretty close to that. So you have a point
thanks dear @David Harper CFA FRM
every thing about the STRIPS concept is clear to me now, thanks again