PrefBlog

Assiduous Reader gsp of the Financial Wisdom Forum writes in and says:

as I posted on the Preferreds thread on FWF (LINK) I am having a hard time understanding which source to best trust when trying to figure out the GOC 5 year benchmark that resets are based on.

The site you link on prefblog(LINK) says the closing 5 year on Feb 20th was 0.72 while investing.com(LINK) says 0.79. The definitive source(BOC) today posted it as 0.80. I’m confused by the variance in all these quotes, especially for a closing rate.

I like to be as precise as possible when using your YTC resets spreadsheet, what’s the best source for intraday BOC 5 year quotes that I can access for free? I have no real use for real time quotes but prefer not to be out to lunch when the rate moves considerably intraday.

Using today’s quotes, we see that CBID’s site (which is the one I use) shows a “Closing Markets as of: 4:00 PM EST 23-Feb-15” yield of 0.66% for the “Canada 5 year”, while the invest.com GOC-5 yield list yield of 0.741% for February 23 for “Canada 5-Year Bond Yield Historical Data”.

That’s a big difference for a five year! So what’s a five-year bond, anyway? Is it the same one today as it was yesterday? Just what exactly is a “five year bond”?

According to the BoC Benchmark definition:

Selected benchmark bond yields are based on mid-market closing yields of selected Government of Canada bond issues that mature approximately in the indicated terms. The bond issues used are not necessarily the ones with the remaining time to maturity that is the closest to the indicated term and may differ from other sources. The selected 2-, 5-, 10-, or 30-year issues are generally changed when a building benchmark bond is adopted by financial markets as a benchmark, typically after the last auction for that bond. The selected 3-year issue is usually updated at approximately the same time as changes are made to the 2-year, and sometimes with the 5-year. The selected 7-year issue is typically updated at approximately the same time as the 5- or 10-year benchmarks are changed. The current benchmark bond issues and their effective dates, shown in brackets, are as follows.
•2 year – 2017.02.01, 1.50% (2014.11.21);
•3 year – 2017.08.01, 1.25% (2014.10.09);
•5 year – 2020.03.01, 1.50% (2015.02.20);
•7 year – 2022.06.01, 2.75% (2015.01.26);
•10 year – 2025.06.01, 2.25% (2015.01.26);
•Long – 2045.12.01, 3.50% (2014.02.21);
•RRB – 2041.12.01, 2.00% (2010.10.21);

So that’s pretty cool! The “Five Year Benchmark”, as defined by the Bank of Canada, changed last Friday, February 20;

From their page BOC Bond Auction information, we see that their Excel spreadsheet (updated to 2015-1-31) lists two prior auctions (of $3.4-billion a pop) of the 1.5% March 1, 2020, bond, on 2014-11-26 and 2014-10-08. The three prior five year auctions were for the 1.75% September 1, 2019, issue, on 2014-8-6, 2014-5-7 and 2014-4-9, each of which also had $3.4-billion size. And we also see that there was another “five year” auction February 18 for delivery February 23. So, it would seem, that they changed their official benchmark as of the day prior to delivery of the third and final auction of the issue.

We can go back to the CBID page: at the bottom, there are quotes for individual issues and we see:

Canada 1.750 2019-Sep-01 104.85 0.66
Canada 1.500 2020-Mar-01 103.72 0.74

So – while it’s not absolutely definitive, it would appear that investing.com is quoting the yield on the 1.5% of March 2020, while CBID is quoting the 1.75% of September 2019 as the “Five Year”.

Who’s right? Who’s wrong? It’s a meaningless question: virtually everything in the bond market is quoted in terms of convention, which is often highly exasperating when discussing yields.

How does the US Treasury do it? They provide a Constant Maturity Yield:

Treasury Yield Curve Rates. These rates are commonly referred to as “Constant Maturity Treasury” rates, or CMTs. Yields are interpolated by the Treasury from the daily yield curve. This curve, which relates the yield on a security to its time to maturity is based on the closing market bid yields on actively traded Treasury securities in the over-the-counter market. These market yields are calculated from composites of quotations obtained by the Federal Reserve Bank of New York. The yield values are read from the yield curve at fixed maturities, currently 1, 3 and 6 months and 1, 2, 3, 5, 7, 10, 20, and 30 years. This method provides a yield for a 10 year maturity, for example, even if no outstanding security has exactly 10 years remaining to maturity.

Treasury Yield Curve Methodology. The Treasury yield curve is estimated daily using a cubic spline model. Inputs to the model are primarily bid-side yields for on-the-run Treasury securities. See our Treasury Yield Curve Methodology page for details.

… and on the Treasury Yield Curve Methodology Page it states:

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. However, Treasury reserves the option to input additional bid yields if there is no on-the-run security available for a given maturity range that we deem necessary for deriving a good fit for the quasi-cubic hermite spline curve. For example, we are using composites of off-the-run bonds in the 20-year range reflecting market yields available in that time tranche. Previously, a rolled-down 10-year note with a remaining maturity nearest to 7 years was also used as an additional input. That input was discontinued on May 26, 2005.

More specifically, the current inputs are the most recently auctioned 4-, 13-, 26-, and 52-week bills, plus the most recently auctioned 2-, 3-, 5-, 7-, and 10-year notes and the most recently auctioned 30-year bond, plus the composite rate in the 20-year maturity range. The quotes for these securities are obtained at or near the 3:30 PM close each trading day. The inputs for the four bills are their bond equivalent yields.

Between August 6, 2004 and June 2, 2008, to reduce volatility in the 1-year Treasury Constant Maturity (CMT) rate, and due to the fact that there were no on-the-run issues between 6-months and 2-years, Treasury used an additional input to insure that the 1-year CMT rate was consistent with on-the-run yields on either side of it’s maturity range. Thus, Treasury interpolated between the secondary bond equivalent yield on the most recently auctioned 26-week bill and the secondary market yield on the most recently auctioned 2-year note and inputted the resulting yield as an additional knot point for the derivation of the daily Treasury Yield Curve. The result of that step was that the 1-year CMT was generally the same as the interpolated rate during that time period. As of June 3, 2008, the interpolated yield was dropped as a yield curve input and the on-the-run 52-week bill was added as an input knot point in the quasi-cubic hermite spline algorithm and resulting yield curve.

Between December 3, 2007 and November 7, 2008, due to Treasury’s discontinuance of 3-year notes, we added a composite rate in the 3-year range based on an average of off-the-run securities in that time tranche. This composite was replaced on November 10, 2008 with the on-the-run 3-year note upon its reintroduction.

Treasury does not provide the computer formulation of our quasi-cubic hermite spline yield curve derivation program. However, we have found that most researchers have been able to reasonably match our results using alternative cubic spline formulas.

Treasury reviews its yield curve derivation methodology on a regular basis and reserves the right to modify, adjust or improve the methodology at its option. If Treasury determines that the methodology needs to be changed or updated, Treasury will revise the above description to reflect such changes.

Yield curve rates are usually available at Treasury’s interest rate web sites by 6:00 PM Eastern Time each trading day, but may be delayed due to system problems or other issues. Every attempt is made to make this data available as soon as possible.

This is a much more sensible way to estimate what a reasonable person might call a “Five Year Yield”, with the reservation that I have always been deeply suspicious of the cubic spline curve fitting methodology. It is too abstract for me and there are mathematical problems at the knot points. But I can’t deny that it fits the data well.

While all of this may be considered illuminating, it still doesn’t really answer Assiduous Reader gsp-from-FWF’s problem: what number should he plug into his calculation in order to estimate a projected future dividend rate for FixedResets? Because the following definitions from the prospectus for RY.PR.J are pretty typical:

“Annual Fixed Dividend Rate” means, for any Subsequent Fixed Rate Period, the rate (expressed as a percentage rounded to the nearest one hundred–thousandth of one percent (with 0.000005% being rounded up)) equal to the Government of Canada Yield on the applicable Fixed Rate Calculation Date plus 2.74%.

“Bloomberg Screen GCAN5YR Page” means the display designated on page “GCAN5YR” on the Bloomberg Financial L.P. service (or such other page as may replace the GCAN5YR page on that service for purposes of displaying Government of Canada bond yields).

“Fixed Rate Calculation Date” means, for any Subsequent Fixed Rate Period, the 30th day prior to the first day of such Subsequent Fixed Rate Period.

“Government of Canada Yield” on any date means the yield to maturity on such date (assuming semi-annual compounding) of a Canadian dollar denominated non-callable Government of Canada bond with a term to maturity of five years as quoted as of 10:00 a.m. (Toronto time) on such date and which appears on the Bloomberg Screen GCAN5YR Page on such date; provided that, if such rate does not appear on the Bloomberg Screen GCAN5YR Page on such date, the Government of Canada Yield will mean the arithmetic average of the yields quoted to the Bank by two registered Canadian investment dealers selected by the Bank as being the annual yield to maturity on such date, compounded semi-annually, which a noncallable Government of Canada bond would carry if issued, in Canadian dollars in Canada, at 100% of its principal amount on such date with a term to maturity of five years.

And we don’t know how the GCAN5YR page is calculated (because it’s Bloomberg), although we can guess that it’s more akin to the US Treasury interpolation-on-a-fitted=curve method than it is to the Canadian pick-a-bond method because of the way the alternative calculation is stated. But that’s not a guarantee! Don’t bother calling your salesman to find out: if there’s one thing I have learnt over the course of my career, it’s that front-line staff don’t have a clue how their software works and wouldn’t understand it if they were told. They’re bankers, the sweet little dears, it’s their job to say “0.74 per cent” in a sincere voice, not to have a clue.

And, what’s more, we can’t even look up (for free) just what the GCAN5YR page might be saying at any particular point in time because fuck you, that’s why.

I don’t have Bloomberg – it’s incredibly expensive, it’s completely useless for serious work and it rots the brain – so I can’t provide any clues as to how the number might be calculated. Perhaps if some kind reader who does have access could provide a screenshot or two taken at around 4pm we can examine the matter more closely.

This entry was posted on Tuesday, February 24th, 2015 at 4:11 am and is filed under Primers, Reader Initiated Comments. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.