My study was in a Mathematical modelling, we studied much about theory, equations, how to resolve equation, how to implement, but we don't understand well where these equations come from.

My question is not difficult, but not easy to be claire, I'll try to explain. It is about the famous Yield Curve built from a set of Treasury coupon Bonds. On most of book, I see that giving a convenable set of bond, determined by its maturities and coupon rate, one can calculate the yield curve from bond's prices, and reversely prices from yield curve. All of those are explained in mathematical formulas, not difficult to understand.

Things that I don't understand, from this equivalence of yield curve and bond's prices, so what exist before, to determine other? Is yield curve quoted, and people calculate bond's prices from this, or reversely?

I have in my mind 2 scenarios

  • The government when issued bonds, they determine every things, bond's coupon rate, bond price, and also the yield curve built in these set (so they quote the bond price?). Each time new bonds are issued, new prices added, yield curve change, people update these new yield curve to use as interest rate risk-free for other calculation. In this scenario, is the government who fully determine the interest rate (yield curve). Also by this scenario, i understand why it is call risk-free since everything are controlled by government, so do its liability.
  • The government issue bonds, but do not determine the price. It is then slapped into the market. Traders then buys and sells, these actions determine the bonds prices below the balance demand-offer. These prices so are determined and quoted by the market. So the yield curve equivalently has to change each time bond's prices change. This scenarios help me to see that the yield curve then mirror the economic condition of the market, since it is determined by the market. But also in this scenarios, i don't understand how it can still be called "risk-free" when it is completely random.

Can someone with experiences in the market explain me how that works, from issuer of the bond, what he does, how bonds pass to the market (which market?), how prices is determined, and in this case how use the corresponding yield curve?

If there are a reference links, books (pdf) that also help me a lot.

  • US Treasuries start trading BEFORE they're actually issued, in the so-called "When-Issued" market. This market allows investors to purchase the new issues for "forward settlement." Because these bonds haven't been issued, they have no coupon rates and are traded on a yield basis. On a daily basis, market forces drive the yields, until the auction date. On the day these securities are auctioned, the US Treasury will set the coupon rate at a multiple of 1/8 so that the securities are priced just under par (a little under 100), and these new "on-the-run" issues then begin trading on a price basis.

  • The vast majority of US Treasuries are quoted on a clean price basis (although some int'l bonds are quoted on a yield basis). Market forces (supply/demand) drive the prices of these securities in real time.

  • There is not one single Treasury spot curve. Currently, there are about 300 outstanding coupon Treasuries outstanding, some with overlapping maturities. Plus, the bonds can have local richness/cheapness. It's impossible to have a single spot (discount) curve that passes through all of them. Different dealers do build different curves, which can provide somewhat different spot rates and wildly different forward rates. I've also known traders who don't build a zero curve at all and trade government papers just fine.

  • It's also worth noting that out of these 300 outstanding Treasuries, only a subset is liquidly traded. How the other issues are "priced" may vary. Usually the on-the-runs (the most liquid) are accurately marked based on market traded prices, and other issues are simply marked as a spread to the on-the-runs.

  • The Fed is an active participant in the US Treasury market. But the Fed is not the issuer of US Treasuries. US Treasuries are issued by the Department of Treasury. In fact, the New York Fed has a trading desk that trades these papers. The Fed also maintains a SOMA portfolio, which is a huge portfolio of government securities and MBS. The transactions carried out by the New York Fed Trading Desk are part of the Fed's monetary policy implementations; e.g., the Fed purchased large quantities of securities during quantitative easing (QE) to push down yields.

  • $\begingroup$ Thanks @haginile. This is exactly this kind of knowledge that I need. How can I get similar knowledge from a book? Or this come uniquely from experiences? Anyway, this Q.S is very useful. $\endgroup$ – ctNGUYEN Dec 31 '14 at 16:14
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    $\begingroup$ @ctNGUYEN I was a rates strategist by training. I haven't found a really good book yet, but my favorite is Bruce Tuckman's "Fixed Income Securities", 2nd Edition (3rd edition is less great) There's also "Interest rate markets", written by Siddhartha Jha, a former JPMorgan strategist. The best way to learn though, is to read bank research reports. If you can find Lehman's rates strategy publications from 2002-2005, they're really really good. A lot of the old Salmon research is also amazing. $\endgroup$ – Helin Dec 31 '14 at 17:23
  • $\begingroup$ @ctNGUYEN Oh you should definitely read Antti Ilmanen's "Understanding the Yield Curve." Changed my life... $\endgroup$ – Helin Dec 31 '14 at 20:59
  • $\begingroup$ Do you mean this book: amazon.com/Overview-forward-rate-analysis-Understanding/dp/… ?? $\endgroup$ – SmallChess Jan 2 '15 at 0:09
  • $\begingroup$ @StudentT Yeah. You can find these papers on Google. There are 7 parts in total. $\endgroup$ – Helin Jan 2 '15 at 1:03

Your second version is correct. The market determines the price of these bonds, from which the curve is derived.

Your first version has a tiny speck of truth, in the sense that the central bank (e.g. the Fed), which is a 'government organisation' has been recently interfering with the bond market in order to affect the yield curve (so called 'operation twist').

They are called risk free because, although the price fluctuates, there is a promise of a fixed and deterministic cash-flows by the government to the holder. There are two residual risks here: that the sovereign will default and the cash-flows are not realised, or that future inflation will erode the real purchasing power of these distant cash-flows.

  • $\begingroup$ Thanks for the quick response, very clear. However another one comes to me. Agreed with the bond's prices are determined by the market, so Yield Curve is calculated and used commonly by some organisation (government?), or each institution has their own Yield Curve, calculated by their own algorithms? $\endgroup$ – ctNGUYEN Dec 31 '14 at 3:43
  • $\begingroup$ As #haginile points out, there is no single yield curve. Each institution will have an algorithm, which will use a number of traded fixed income instruments to produce an estimation of 'the yield curve'. $\endgroup$ – Kiwiakos Dec 31 '14 at 8:09

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