Archive for the ‘HIMIPref News’ Category

YLD.PR.B Tracking on HIMIPref™ Halted

Tuesday, December 6th, 2011

YLD.PR.B closed today with a bid of $0.05, having lost nearly all support with the redemption announcement this morning.

This is low enough relative to its stated dividends of $1.05 p.a. (suspended since July 2008) that HIMIPref™ assumes that there has been an input error and refuses to proceed.

Hence, the issue is no longer being tracked.

HIMIPref™ Yield Calculation Change

Sunday, June 26th, 2011

In the comments to the June 22 report, Assiduous Reader drap1 asked:

Hi…quick question about last prefletter. I’ve seen this other times, but here is a clear example:

With respect to TRP.PR.B and TRP.PR.C, TRP.PR.C has a higher dividend, higher reset price and higher market price (both are above $25); however, your model evaluates TRP.PR.C to perpetuity, but TRP.PR.B, to its reset date. What am I missing? Why doesn’t TRP.PR.C get evaluated to its reset date?

TRP.PR.C does resets a year later which could create a small difference depending on the yld curve, but I don’t think that’s the answer.

Good question! For a quick answer, here are the summaries of the two optionCalculationLists on the pseudoPortfolioReportBox:

Report Box
Instrument•:•TRP.PR.B (Security A51015)
PseudoPortfolioElement: Pricing Modification – Base Option ID: Undefined
Reporting: YTM (Port Method) at Bid
*****
Evaluated at bid price : 25.4000
Call 2015-07-30 YTM: 3.51 % [Restricted: 3.51 %] (Prob: 45.09 %)
Call 2020-07-30 YTM: 3.46 % [Restricted: 3.46 %] (Prob: 0.30 %)
Limit Maturity 2041-06-10 YTM: 3.47 % [Restricted: 3.47 %] (Prob: 54.61 %)
YTM (Port Method) : 3.4865 %

and

Report Box
Instrument•:•TRP.PR.C (Security A51016)
PseudoPortfolioElement: Pricing Modification – Base Option ID: Undefined
Reporting: YTM (Port Method) at Bid
*****
Evaluated at bid price : 25.9000
Call 2016-02-29 YTM: 3.65 % [Restricted: 3.65 %] (Prob: 52.02 %)
Limit Maturity 2041-06-10 YTM: 3.56 % [Restricted: 3.56 %] (Prob: 47.98 %)
YTM (Port Method) : 3.6095 %

So part of the problem is a stenographical error: I should have specified that the call on TRP.PR.B was calculated to the second reset date but, frankly, missed that when transcribing the table.

However, the interesting question is the appearance of second reset date in the TRP.PR.B table but not in the TRP.PR.C table, particularly given that the probability of exercise of this option is less than half a percent.

Possible options are added to the calculation list only if the probability of exercise, when initially calculated, is greater than the value OPTION_EXERCISE_CALCULATION_INCREMENT_PROBABILITY, which is currently set to 5%. However, subsequent normalizations did not enforce this constraint.

Additionally, as can be seen from the cashFlowDiscountingAnalysisBox, the cash flows to 2020 for TRP.PR.B extend one month further than the actual call date, as has been previously discussed on PrefBlog in the post What is the Yield of RY.PR.Y? due to the influence of the maturityNoticePeriod.

“Cliff Effects” are a bugaboo in all analysis and have been blamed, at least in part, for the Panic of 2007 (since a credit rating downgrade raised the capital requirements for all regulated holders, who therefore all had a strong prediliction to sell at the same time). By its nature, YTW is subject to cliff effects, at least insofar as it comes to reporting the duration of the YTW scenario (the amount of change in duration for relatively small changes in price is measured by the attribute pseudoConvexityWorst).

Two changes in programming have been made that should make the calculations at least little easier to explain, although cliff effects will still be present:
i) The constraint OPTION_EXERCISE_CALCULATION_INCREMENT_PROBABILITY is enforced during the normalization of option exercise probabilities
ii) maturityNoticePeriod is only accounted for when the exercise date is less than MATURITY_NOTICE_PERIOD days from the calculation date.

I have been toying with the second idea for quite some time and the change will save me a lot of explanations regarding yield calculation. I’ve resisted the idea because (a) as far as I can tell, it won’t make much difference and (b) a complex analytical programme is a chaotic system, meaning that small changes to some parts can cause huge differences in output under certain conditions. But now seems as good a time as any to proceed.

The effect of these changes on the YTW calculation is displayed in the following reports:

LimitMaturity

Friday, April 15th, 2011

I use the phrase because preferred shares can last forever; but taking account of this infinite length of time would require too many special cases in the software and take up too much computation time for very limited benefits – if any! I made the point a few times in the appendix to the April, 2011, PrefLetter that if you calculate more decimal places than are justified by the accuracy of your data, then you are really just wasting time fooling yourself.

So, instead of performing special calculations to account for the preferred share lasting forever, the software instead defines “forever” as “thirty years from the date of calculation”.

Thus, for example, the recommended BAM.PR.N issue is denoted with a “LimitMaturity”, since the fact that it is trading at a discount to par with no means by which an investor can force the company to redeem them means that it is prudent to assume they will last forever.

In order to analyze these shares in a manner consistent with all the other issues, the software then pretends, on the calculation date of 2011-4-8, that the issue will mature on 2041-4-8 at a price equal to its current price of 21.10. This assists in the computation of Modified Duration and PseudoConvexity.

In turn, this ensures that the calculations, and the valuations, are consistent with the calculations and valuations for those issues that really do mature (such as BNA.PR.C, for instance) and the increase in comparability is worth the slight loss of accuracy.

NEW.PR.C Added to HIMIPref™ Database

Friday, March 18th, 2011

I have added NEW.PR.C to the HIMIPref™ database, as the soon to expire warrant offering is in the money and can be expected to increase the number of shares – and hence the Average Trading Value – dramatically.

NEW.PR.C commenced trading 2009-6-26 after a prospectus dated 2009-6-16.

Issue price of 13.70, annual dividend of 0.822 paid quarterly, hence coupon of 6%.

Maturity date 2014-6-26; redeemable every June 26 at par.

Rated Pfd-2 by DBRS continuously since inception.

Monthly Retraction with a formula of 95%NAV – C – 1. Oddly, there is no maximum price! There is a Special Annual Concurrent Retraction (including a Capital Share) at NAV.

The dividend policy is:

The Class A Capital Shares provide their holders with a leveraged investment, the value of which is linked to changes in the market price of the Portfolio Shares. Holders of Class A Capital Shares will be entitled on redemption to the benefit of any capital appreciation in the market price of the Portfolio Shares. The fixed distributions on the Series 2 Preferred Shares will be funded from the dividends received on the Portfolio Shares. If necessary, any shortfall in the dividends on the Series 2 Preferred Shares will be funded by proceeds from the sale of Portfolio Shares. In the event that the Portfolio Share dividends exceed the amount of the fixed Series 2 Preferred Share dividends and all expenses of the Company, the excess amount may be paid as dividends on the Class A Capital Shares, as determined by the Board of Directors of the Company, subject to the dividend policy of the Board of Directors.

NEW.PR.C has been assigned initially to the Scraps index, but may migrate shortly to the SplitShares index.

There will be those, I know, who will be pleased to point out that this back-dated addition of an issue adds a little selection bias to the HIMIPref™ database, to which I am forced to respond: “Your mother wears army boots!”. I NEED DATA, and with the recent disappearance of SXT.PR.A and the imminent disappearance of MUH.PR.A, I need it badly. I hope that following the warrant expiry, NEW.PR.C will be liquid enough to trade, at least in small pieces.

TMX DataLinx: "Last" != "Close"

Tuesday, December 21st, 2010

Like the old man said … “If you go out and buy financial data and you assume something, you make an ASS out of U and ME both.”

Assiduous Readers will recall that on December 2 I reported a stupid quote for GWO.PR.J and indulged in a rant; I also sent a note of inquiry to the TSX:

According to information reported on TMXMoney.com for December 2, GWO.PR.J traded 2,831 shares in a range of 27.41-64 and the last of the eleven trades was at 3:33pm. The closing quote was 24.81-27.54, 4×9.

I have four questions that arise from the closing quotation:

i) Who is the market-maker for this security?

ii) Will the TMX be investigating the circumstances that led to this ridiculous closing quote?

iii) Will the TMX be announcing the results of such an investigation?

iv) Will the TMX be implementing any sanctions against the market maker for this security?

I eventually received a reply:

A closing quote is considered to be the quote at the close of the regular trading session at 4pm. Market Maker responsibilities end at 4pm. The actual closing quote at 4pm on Dec.2 for this issue was 27.04 – 27.54.

After frothing at the mouth a bit, I sent the following eMail to my data provider, TMX DataLinx, who get a fat cheque every month for providing me with data:

As you will be aware, I have been a purchaser of your historical data for about ten years; and was a customer prior to then through my previous employer, Greydanus Boeckh & Associates Inc.

Amongst the data I purchase from you are the “last bid price” and the “last ask price”.

On December 2, 2010, you reported to me that these values were 24.81 and 27.54 for GWO.PR.J.

An inquiry to the exchange regarding this quote elicited the information that “A closing quote is considered to be the quote at the close of the regular trading session at 4pm. Market Maker responsibilities end at 4pm. The actual closing quote at 4pm on Dec.2 for this issue was 27.04 – 27.54.” as shown in the forwarded eMail, below.

(i) What is the difference between the data you have been selling me and the “closing quote”?

(ii) How may I purchase the “closing quote” from you?

Finally, after a fair number of reminders, a few telephone conversations and a conference call, I have sent the following eMail to the Product Manager at TMX DataLinx:

I write to you to request a new product be made available for data download through your “TMX DataLinx Market Data” facility.

This product would be accessed by entering the password-protected page http://marketdata.tsx.com/MOTD/ clicking “Custom Queries”, “New Query” and “Stock Prices” (or, after the first run, via “Saved Queries”).

Options for “Closing Bid” and “Closing Ask” would be added to the list of “Data Items”.

These data would provide the last quotation of the day at which one board lot of the security in question could be transacted; i.e. a snapshot of the market quotation immediately before the close of the regular trading session.

They would be distinct from the extant “Last Bid” and “Last Ask” data items currently available, since these two items represent the quotation at the end of the extended trading session. They will not necessarily reflect the market quotation at the close of the regular trading session since:
(i) Orders in the book at the close of the regular trading session may have been cancelled in the interim
(ii) Orders entered in the interim will not be included in the book unless they are at the Last Sale Price; they will be rejected by the Exchange.

It has been suggested that I could recover these data by clicking “Trades and Quotes” instead of “Custom Queries” and downloading the file for a period of time near the close. The “Closing Bid” and “Closing Ask” could then be determined through inspection of the downloaded data.

Such a solution is not practical because:
(i) Time resolution in this facility is limited to increments of one minute. There could, conceivably, be thousands of quotes for each security during this time frame and the cost of these data could be enormous
(ii) Data will only be recovered if the quote changes during the specified time. Thus, for some subset of the security list not known in advance, a prior time increment would need to be queried, which, in addition to being time consuming, would still bring with it the risk of enormous cost as specified in objection (i).

Therefore, I request that the “Closing Bid” and “Closing Ask”, which would together comprise the last quotation of the day at which an investor could execute at least one board lot on either side during the regular trading session, be made available as downloadable data under the same terms and conditions as your extant “Last Bid” and “Last Ask” data items.

I venture to suggest that most purchasers of the “Last Bid” and “Last Ask” data (including myself, until recently!) are under the impression that they are, in fact, purchasing the “Closing Bid” and “Closing Ask”. If you should find a customer who is not only aware of the difference, but prefers the “Last Bid” and “Last Ask” data, I would very much appreciate it if you could ask him to call me (416 604 4204) and explain, since I can see no possible use for these items which do not necessarily represent actionable bids and offers.

Prior correspondene on this issue is appended to this eMail

I don’t think I’m the only one who does not appreciate the difference between “Last” and “Close”; this is particularly important at this time of the year, when funds are required to provide a reconciliation between their normal method of reporting NAV and the new standards, as elucidated in the 2009 Financial Statements for PIC:

Net Assets per unit is the difference between the aggregate value of the assets of the Fund and the aggregate value of the liabilities excluding Preferred shares of the Fund on that date and including the valuation of securities at bid prices divided by the number of units then outstanding. For years prior to 2007, securities were valued at closing prices. The change to the use of bid prices is due to accounting standards set out by the Canadian Institute of Chartered Accountants adopted November 1, 2007 relating to Financial Instruments.

The Fund has adopted, effective November 1, 2008, Canadian Institute of Chartered Accountants (“CICA”) amendments to Handbook Section 3862, “Financial Instruments – Disclosures”. The revised disclosure requirements are intended to improve disclosures about fair value and liquidity risk. The amendments establish a three-tier hierarchy as a framework for disclosing fair value based on inputs used to value the Fund’s investments. The hierarchy of inputs is summarized below: (1) Level 1 – for unadjusted quoted prices in active markets for identical assets or liabilities

Securities are valued at fair value, which is determined by the closing bid price on the recognized stock exchange on which the securities are listed or principally traded. If no bid prices are available, the securities are valued at the closing sale price.

These rules have been discussed by Price-Waterhouse.

Naturally, it may be that I am the only investment manager in the world to have made this error. But, given the ubiquitous nature of the “Last Bid” and “Last Ask” on the web (fed to QuoteStream, for instance, which republishes it on the TSX’s own TMX Money website), I’ll bet I have lots of company.

Fortunately, this can only have a positive effect on the presumed efficiency of the HIMIPref™ simulations, which define the parameterization of the analytics; the programme sells at the presumed bid and buys at the offer; in nearly all cases the “Last” will be worse than the “Close” – the only exception will be when the Last Sale Price is the bid (ask) at the close and becomes the ask (bid) at the end of the extended session. Thus, simulations may have executed notional trades at worse prices than those actually available, or have missed opportunities; both of which will have resulted in underestimation of the value of the analytics.

For your further reading pleasure, here are some extracts from the TSX Trading Rules:

Rule 4-901 states:

Rule 4-901 General Provisions (Amended)
(1) All listed securities shall be eligible for trading during the Special Trading Session, provided that a MOC Security shall not be eligible for trading until the completion of the Closing Call in respect of that MOC Security.
(2) Except as otherwise provided, all transactions in the Special Trading Session shall be at the Last Sale Price for each security.
(3) Except as otherwise provided, the normal rules of priority and allocation and all other Exchange Requirements shall apply to the Special Trading Session.

Amended (March 29, 2004)

Rule 1-101 states:

“Last Sale Price” means:
(a) in respect of a MOC Security, the calculated closing price; and
(b) in respect of any other listed security, the last board lot sale price of the security on the Exchange in the Regular Session.
Amended (March 10, 2006)

Update, 2010-12-23: I do not believe that the extended session (whence the “last bid” and “last ask” quotes are obtained) meets the CICA definition of an active market:

[CICA Handbook] Para. 3855.A44. “A financial instrument is regarded as quoted in an active market when quoted prices are readily and regularly available from an exchange, dealer, broker, industry group, pricing service or regulatory agency, and those prices reflect actual and regularly occurring market transactions on an arm’s length basis. Fair value is defined in terms of a price agreed upon by a willing buyer and a willing seller in an arm’s length transaction. The objective of determining fair value for an instrument that is traded in an active market is to arrive at the price at which a transaction would occur at the balance sheet date in that instrument (i.e., without repackaging the instrument) in the most advantageous active market for that instrument to which the entity has immediate access. The existence of published price quotations in an active market is the best evidence of fair value, and when they exist they are used to measure the financial asset or financial liability.”

The “last” quotes do not reflect “actual and regularly occurring” (or even possible) market transactions, since any transactions in the extended session must occur at the Last Sale Price.

BCE.PR.F & PPL.PR.A Added to HIMIPref™ Database

Tuesday, December 16th, 2008

I have bowed to overwhelming popular demand and added the captioned issues to the database.

BCE.PR.F is a FixedFloater, paying $1.10 annually (paid quarterly) until 2010-2-1, at which point the rate gets reset and it becomes exchangeable with BCE.PR.E. Exchange Dates recur every five years thereafter. For analytical purposes, it is assumed that the conversion to ratchet rate is automatic – this is a valid worst-case assumption, since BCE has the discretion to set the five-year rate to a very low value. It is callable on exchange dates at 25.00 and (when ratcheting) at 25.50 at other times. For analytical purposes this is simplified to two calls at $25.00, on 2010-2-1 and 2015-2-1. Dividends are cumulative. There is no retraction.

PPL.PR.A is a split share based on Canadian banks, paying dividends at a rate of Prime, capped at 7%, collared at 5%. It matures 2012-12-1 at $10.00. There is a special monthly retraction provision with the formula 96%(NAV – C). Dividends are cumulative and paid monthly. Current NAV is $16.08 according to the company. Income coverage, according to May’s semi-annual report is a hair over 1.0:1. Maturity is 2012-12-1; there are no embedded redemptions. Distributions to Capital Units will be halted if the NAV falls below 15.00 (asset coverage of 1.5:1).

What is the Yield on BCE.PR.Y?

Tuesday, December 16th, 2008

I was recently taken to task for a claim that the yield on BCE.PR.Y was 8.18% based on a dividend of $1.05715 and an end value of $25.00 – my correspondent stated – quite rightly – that:

the most recent monthly dividend, declared Oct 28, 2008, was $0.8333 or $1.00 per year. Also Prime has dropped to 3.5% from 4% earlier this month, (according to the BOC website), indicating a further cut in the dividend in the near future. Even at the rates and prices you quote I make the yield out to be 7.3%.

My defense is as follows:

They system estimates the average future rate of prime by looking at the past. If we stay at 3.5% prime for long enough, the estimated future rate will drop to this level, but for now it’s higher.

Additionally, the system estimates the end-value (a “limitMaturity” is treated as thirty years, remember) by determining the price at which the instrument is fairly valued; determining fairness by comparison with other floating-rate dependent issues. This was the result of some experimentation and proved to be a better predictor than assuming a constant price (as is done with fixed-rate perpetuals).

Basically, the assumption is that an Investment Grade issue will not pay 100% of prime forever. There will be shocks, of course, and every now and then such an issue will be downgraded and quite properly pay 100% of prime; but over the long term such a rate is not sustainable.

I will admit that this analytical framework was formulated when deviations were relatively small; an investment grade issue paying (25.00 / 14.25) = 175% of prime is not something that happens often enough to permit testing!

All the above is not very satisfactory, I know: but there are a lot of moving parts in the analysis of these ratchet rate issues and the framework was determined empirically. In some cases, to my chagrin, the results are not even internally consistent (e.g., I might be estimating a ratchet yield of less than 100% of prime with end values well below par).

All I can say is that the empirically derived system, while having theoretical holes in it, does have a statistical ability to rank the various issues with significantly better-than-random accuracy, which is all I ever wanted it to do.

Now lets do the cash flow analysis! I have uploaded the full HIMIPref™ output; the last part is:

2038-12-16 MATURITY 25.00 0.080242 2.01

Total Cash Flows 56.6052
Total Present Value 13.5028
Discounting Rate 8.5887 % (Annual rate compounded semi-annually)

So for starters, we see that the the discounted present value of the $25.00 maturity is only $2.01. It’s not a particularly important variable.

But compare four bonds priced at par, each one paying $12 p.a., but with differing frequencies (annual, semi-annual, quarterly, monthly). Each one is described by fixed income convention as having a yield-to-maturity of 12%. Which would you rather have? Obviously, the monthly payer, since then you get your money faster … and this is borne out when we look at the annualized internal rate of return for the four bonds: 12.00%, 12.36%, 12.55% and 12.69%, respectively. The limiting case is an infinite number of infinitesimally small payments totalling $12 and has an IRR of exp(0.12) – 1 = 12.75%.

We note from the HIMIPref™ report that the 30-year discounting factor is 0.080242 so
1 / (1 + I)^30 = 0.080242
(1 + I)^30 = 1 / 0.080242 = 12.4623
I = 8.7727%

To convert this annual value to semi-annual, bond-equivalent yield, we note:
1+I = (1+i)*(1+i)
(1+i) = 1.042942
i = 4.2942
and therefore, the bond-equivalent yield is 2*i = 8.5884%, which is slightly different from the quoted figure, but we’ll attribute that to rounding.

But how to calculate this ourselves? The “ratchet yield” is 4.1997% of par, which implies total payments of $1.049925. These are made monthly, so monthly payments are $0.087494, which has been shown as a rounded value of $0.09 in the HIMIPref™ report.

The normal quick-n-dirty calculation is:
i = [Annual Income + Annual Capital Gain]/[Average of Beginning and Ending Price]
Annual Income = oh hell, let’s just call it $1.05, shall we?
Annual Capital Gain = Total Capital Gain / Term = (25.00 – 13.50) / 30 = $0.38333
Average of Beginning and Ending Price = (25.00 + 13.50) / 2 = 19.25

resulting in a quick-n-dirty estimate of (1.05 + 0.3833) / 19.25 = 7.45%.

It’s a lousy estimate. Terrible. Why?

Mainly because the beginning and ending prices are so different. The calculation assumes that the capital gain is realized in a linear fashion … but in fact, if it accrues at a constant rate, nearly twice as much is accruing at the end of the period as at the beginning. Conversely, the $1.05 income is much more interesting at the beginning of the period (current yield = 1.05 / 13.50 = 7.78%) than at the end (current yield = 1.05 / 25 = 4.20%.

When the capital gain through the period is massive, simple methods become simplistic. Such is life! Fortunately, yield calculators and Excel Spreadsheets will be readily available to most people.

Related discussions may be found in the posts regarding Research: Modified Duration and Research: Yield from on-line Calculator.

Listen, take it from an old bond guy: if anybody ever tells you yield is simple, don’t listen to him!

HIMIPref™ Tracking of IQW.PR.C Halted

Monday, October 27th, 2008

It happened last month with IQW.PR.D and now IQW.PR.C has become impossible to handle in a standard manner.

Today’s closing bid for IQW.PR.C is $0.25, less than what the “accrued dividend” would be if it was still paying dividends, and the price rejected as an obvious error. I will no longer be tracking it.

I will continue to report the quarterly conversions of this issue into common.

HIMIPref™ Bug Fix: curveYield Calculation

Friday, October 24th, 2008

As noted on October 22

I’ll explain in another post, because it’s kind of funny, but basically there’s a little loop used in the process of curve approximation that calculates a yield; in the case of YLD.PR.B, quoted at 1.60 with a stated annual dividend of $1.05 (currently suspended) until maturity 2012-2-1 at $15 [dubious], the little loop ran ’round 5,709,833 times [in the run where the problem was unequivocally isolated] before the WebService timed out and blew up the whole programme.

The function at fault (yieldApproximatorTypeCalc::getSemiAnnualYieldFromTable) calculates the yield to maturity of a set of cash flows defined in a table (the input is set up in much the same way as Excel’s XIRR() function) by successive approximations to the yield using the Newton Method.

Unfortunately, this procedure can be unstable near a horizontal asymptote or a local extremum.

When calculating the curveYield for YLD.PR.B on October 21, the function did not converge; instead, it oscillated between two highly incorrect numbers.

The function has been adjusted such that:

  • After 500 iterations, a successively smaller damping factor is applied to the yield change, and
  • After 1,000 iterations, status information is written to the errorOutput.txt file after each iteration, and
  • After 1,010 iterations the process aborts and returns ANALYTICAL_DOUBLE_NO_SOLUTION

The function now converges for YLD.PR.B on October 21; other tests (prior to application of the damping factor) confirm that the ‘no solution’ result is handled properly by the rest of the programme.

It’s not often I find a crippling bug in HMIPref™ any more! That’s the only lack of convergence in this function in almost 15 years of daily data!

HIMIPref™ Tracking of IQW.PR.D Halted

Wednesday, September 17th, 2008

Well, it happened last March with AR.PR.B and now it’s happened again.

In my last update of the day everything IQW.PR.D was one penny bid and the quote was rejected as an obvious error. Ha!

The issue has been around in various incarnations since 1997-11-12, when it came on the scene as IQI.PR.A. Ave Atque Vale!