First of all, greetings to everyone. I’ve been reading for quite a time now about bonds, but I have some practical questions.
Let’s say that 3-month T-bill is issued today (July 7), and at auction it got price of $98 per $100. It has 91 days to maturity, and by convention it’s yield is calculated as bank discount yield, i.e. : bank discount yield = (100-98)*100*(360/91) = 0.0791 = 7.91% - this is the annual yield on that t-bill calculated with b.d.y. method
Because of the denominator (face value insted od price, and day count convention), this is not quite right, but it was used for quick calculation and now stayed like that as convention. More accurate measure of yield for our bill is bond equivalent yield (b.e.y): b.e.y. = (100-98)/98*(365/91) = 0.818 = 8.18%, annual yield that would one get if hold our bill till maturity. Bills are now traded on the secondary market, quoted on b.d.y. basis. Let’s assume that the next day (July 8), for some market reasons (demand and supply), price of our bod rise to 99$. Now the yield that the market will show is: (100-99)/100*(360/90) = 0.04 = 4%. (Don’t bother for drastic changes, it’s just for pedagogical purposes).
b.e.y. = (100-99)/99*(365/90) = 4.09%
As we can see, there is no more exactly 3 months T-bill outstanding, but nonetheless yields on 3 months T-bills are reported every day. Let’s find them on FRED: DGS3MO 2017-06-28 1.02 2017-06-29 1.04 2017-06-30 1.03 2017-07-03 1.06 2017-07-04 NA 2017-07-05 1.05 But these yields are Constant Maturity Treasury yields. On treasury.gov I found next explanation: ‘The Treasury’s yield curve is derived using a quasi-cubic hermite spline function. Our inputs are the Close of Business (COB) bid yields for the on-the-run securities. Because the on-the-run securities typically trade close to par, those securities are designated as the knot points in the quasi-cubic hermite spline algorithm and the resulting yield curve is considered a par curve.’ Interpolation is necessary because usually there are no on-the run t-bills with the same maturity, and let’s put aside cubic spline interpolation method.
What I’m interested is what yields will be the knot point for interpolation of 3-month T-bills? It is stated that they are COB bid yields for on-the-run securities. One on the run security is our 3-month t-bill thas now (July 8) has 4% b.d.y., and other let be 6-month t-bill that on July 8 has 150 days to maturity, etc. What yield is used in interpolation, reported b.d.y. or b.e.y?
I’ve been reading a lot, but it’s hard to grasp it when you don’t have first hand experience. So what I have managed to grasp so far is above. Every day, on the run securities of different maturities will have different prices on the secondary market, and their yield wil be used for interpolation. For T-notes and T-bonds is it YTM, and for T-bills b.e.y? Thank you.