On December 30, in all innocence, I posted the following entry in the Volume Highlights table:

BNS.PR.X | FixedReset | 26,000 | YTW SCENARIO Maturity Type : Call Maturity Date : 2014-04-25 Maturity Price : 25.00 Evaluated at bid price : 25.63 Bid-YTW : 1.44 % |

Now Assiduous Reader SM writes in and says:

in yesterday’s volume highlights on prefblog, BNS.PR.X is listed as having a 1.44% YTW at $25.63. My use of Shakespeare’s YTC spreadsheet (14/01/06 settlement) tells me the YTW is exactly 2.00%. What gives?

The “Calculators” section of the Right Hand Navigation Panel has links to Shakespeare’s Spreadsheet and a souped-up version that accounts for dividend changes for FixedResets. Some may also be interested in my instruction manual for ytc.xls and a lengthy post discussing compounding frequency.

SM’s figure of 2.00% is derived from the following inputs:

- Current Price = 25.63
- Call Price = 25.00
- Settlement Date = 2014-1-6
- Call Date = 2014-4-25
- Quarterly Dividend = 1.5625/4
- Cycle = 1
- Pay Date = 25
- Include first Dividend = 1
- First Dividend Value = Blank

SM poses a complicated question – there are no less than three-and-a-half different things going on:

- Settlement Date
- Compounding Convention
- Cash Flow Amounts
- Cash Flow Timing

People who compulsively count up items in lists will notice that four lines are required to itemize the three-and-a-half things. The discrepancy arises because “Cash Flow Timing” is a superset of “Settlement Date”. Take some meds, guys.

__Settlement Date__

This is a more complex question than one might think. Is it really all that great to use the settlement date for yield calculations? After all, if Joe Average is going to buy security X, he’s got to fund the purchase (either with cash or margin) on the trade date – in fact, this has to be done before the trade is executed, never mind settled.

And when valuing the security, it it really all that kosher to use settlement date yields? This will include settlement date accrued interest (where applicable), which hasn’t been earned yet; additionally, financial reporting will show only the accrued interest as of the reporting date, i.e., Trade Date.

On the other hand, market prices are always quoted assuming the normal settlement convention, so if you’re going to use TD yields, you also need to use TD-specific prices. Trading bonds for non-standard settlement is – or at least was, in the old days – an intricate process that required the salesman to get the price from his trader, and then perform a lot of calculations based on the coupon, the yield and the day-count before quoting a price. This required time and swearing, but nowadays there’s probably an app for that.

It will also be noted that the Canadian Yield Calculation Conventions specify use of settlement date.

However, I use TD calculation instead and justify my decision with the argument that your mother wears army boots.

Using TD instead of VD in the Yield Calculator results in a reduction of the calculated yield to 1.88% from 2.00%.

__Compounding Convention__

Fixed Income Yield Calculations use periodic return rather than Annualized Return (IRR); that is, the yield is calculated per payment period and this yield is multiplied by the number of periods per year to express it as an annual rate (annual rate = y*4), rather than compounding it (annual rate = (1+y)^4 – 1).

In the case under discussion: HIMIPref™ calculates bond-equivalent yields. To convert quarterly compounded annual rates, y, to bond-equivalent semi-annual rates, r:

r = 2 * [(1 + y/4)^2 – 1]

so if the quarterly-compounded rate is y = 2.00%, then the bond-equivalent semi-annual rate is 2 * [1.005^2 – 1] = 2.005%. It is, obviously, a very minor difference at these yields, but can become much larger at higher levels.

__Cash Flow Amounts__

The YTC calculator calculates (in cell S4) that the final dividend, paid on April 25, will be 0.390625 – that is to say, one quarter of the annual rate, which appears at first glance to be obvious. But is it really all that obvious?

HIMIPref™ shows the prior dividend as being paid 2013-10-31 (which is wrong – the pay date was actually October 29, but a few days difference in pay date doesn’t usually matter), and therefore assumes that the next dividend will be paid on January 31. Then, when HIMIPref calculates in one part of the programme that the issue will be called on April 25, the part of the programme that calculates expected cash flows and yields says to itself, “Aha! It’s being called before the full dividend is due! Six days early, in fact!” So it takes six days’ dividend off the final payment and evaluates the last dividend as $0.36 (rounded to two decimal places in the report I’m looking at, but internal precision is higher). So right away, there’s a few pennies difference and each penny makes a difference of about 13bp in calculated yield, according to ytc.xls.

So we might be tempted to conclude that oh, yes, just another HIMIPref™ error, so what, until we consider the data calculated by ytc.xls. It assumes full payment of the entire quarterly dividend on April 25, reasonably enough since that is essentially what we told it to do when we filled in Pay Date = 25. So that’s wrong, too. If we change Pay Date to 29, it does the same thing HIMIPref™ does and performs its calculations with a pro-rata dividend paid on the April 25 redemption date.

But that’s still wrong, probably, although we can’t say this conclusively until Scotia announces the next dividend.

Consider BNS.PR.S. It will be redeemed on January 26, but the final dividend has been announced as the full amount of $0.3906 payable January 29.

What’s more, the prospectus for BNS.PR.S states:

The holders of Preferred Shares Series 24 will be entitled to receive fixed non-cumulative preferential cash dividends, as and when declared by the board of directors of the Bank (the “Board of Directors”), for the initial period commencing on the Closing Date (as defined herein) and ending on and including January 25, 2014 (the “Initial Fixed Rate Period”), payable quarterly on the third last business day of January, April, July and October in each year (other than January 28, 2009), at a rate equal to $0.3906 per share. The initial dividend, if declared, will be payable April 28, 2009 and will be $0.5865 per share, based on the anticipated closing date of December 12, 2008 (the “Closing Date”). Reference is made to “Details of the Securities Being Distributed”.

That’s valuable information, that is, because it allows us to calculate the precise period over which that first dividend was earned. A little playing around results in the conclusion that the $0.5865 first dividend was equal to 137 days of interest at an annual rate of 6.25% (the figure to six decimal places is $0.586473).

137 days? That’s 19 (December) + 31 (January) + 28 (February) + 31 (March) + 28 (April). So the first dividend payment on April 28, 2009, included an accrual for every single day up to the payment date. Therefore, we may conclude that the final dividend of $0.3906 (equal to every other dividend other than the first) also includes accruals up to the payment date of January 29 … even though Scotia

intends to exercise its right to redeem all outstanding Non-cumulative Preferred Shares Series 24 of Scotiabank on January 26, 2014

This is complicated even more by the amusing happenstance that January 26 is a Sunday and Scotia couldn’t pay the redemption price on that day even if it wanted to. AND, that according to the prospectus:

for the initial period commencing on the Closing Date (as defined herein) and ending on and including January 25, 2014

and therefore by rights a new rate should be calculated for the period 2014-1-26 to the paydate of 2014-1-29. And what’s up with the day count? Will the shareholders be getting their capital back on Monday, January 27, but still earn dividends on that capital to the final dividend pay-date of January 29? Or will the actual payment for the redemption be made on January 29 as well?

__Cash Flow Timing__

The whole thing’s a minefield, and with respect to BNS.PR.X it will be noted that the redemption date is actually April 26 anyway, which is a Saturday.

__Conclusion__

The moral of the story is that precise calculation of yields using actual dates is a quagmire and it doesn’t usually matter, but these minor differences can add up to quite a few beeps when the remaining term is very short – as has happened in this case with BNS.PR.X. In such cases, one is better off double-checking all the dates and amounts and valuing the shares as packages of money market instruments with yields calculated according to money market conventions, which is a another kettle of fish.

Thanks for the extensive reply.

“Is it really all that great to use the settlement date for yield calculations?”

Absolutely!

“After all, if Joe Average is going to buy security X, he’s got to fund the purchase (either with cash or margin) on the trade date – in fact, this has to be done before the trade is executed, never mind settled.”

I’ve made countless purchases without cash being available in my account and have no margin. I simply do an instant transfer from my bank HISA on the morning of the settlement date or sell from a brokerage HISA the day prior to settlement(T+1 settlement on broker HISA). Those funds earn interest in either HISA until the settlement date so not sure why I would include days prior to this.

Thanks for the correction on call date, probably initially copied it from prefinfo. BTW your link to the prospectus got jumbled.

I had referenced the prospectus on sedar after emailing my query just to confirm the first/last dividend earn date as you detailed in a previous post. Thanks for explaining that, these details make a significant difference on such short term maturities.

Lest anyone think this was just me nitpicking, I had a sell order for this security and was afraid I was being too greedy when I saw your much lower YTW calc. I’m happy to report my order got matched at $25.66 yesterday cum-dividend, giving the buyer at best(using generous original assumptions of 14/04/25 full payment) a 1.62% YTW before commission and taxes.

Thanks JH.