Net Bond Coupon/Yield

Question

I just wondered on how one can properly get the Net Bond Yield/Coupon given that you had some "trading" that happened.

Suppose, I have a group of bonds (say some Treasury bonds). I acquired a 100 Par value bond with a coupon rate of 2%. At the same time, I also disposed a 20 Par value bond with a coupon rate of 5% (again assuming that I have a portfolio of Treasury bonds)

I was kind of thinking on how the Net coupon would be based on this activity? I tried using the weighted average, i.e.

((Acquisition Par)(Acquisition Coupon)+(Disposal Par)(Disposal Coupon))/(Net Par)

=> ((100)(.02)+(-20)(.05))/(80) = .0125

But again using this method will lead to some weird results especially when Net Par -> 0 i.e. asymptotic

The image above is what I tried to plot on Excel whenever we have varying trades but consistent coupons. Notice that we would then have nonsensical values whenever we have similar par valued trades.

Do you guys know what method to properly get the net rates?

Answer 1

Well, there is one bond with a 100 par and one bond with a 20 par as

100 * .02 = 2

and

20 *.05 = 1 .

Also, (100 * .02) = (5 * 20 * .02) so there is no reason to count bonds in increments since the bond counts equal to the same coupon payment. So the total coupon payments are definitive and then the total par values are definitive as

120 * r = 3

120 * 0.025 = 3 .

Or do an average of both the par values and coupon payments for

60 * r = 1.5

r = 0.025 .

Remove one of the two bonds and then it's not necessary to total or to average.

Well, a reason to account yield-to-maturity is to determine overall financial result. A reason to account coupon payment, without regard to bond cost, is to meet current cash flow requirements. So with this logic and again, the total coupon payments are definitive. Also, par value is likely redemption value and relates to cash flow.