## What is the YTW of RY.PR.N? Win a PrefLetter!

I will admit that sometimes I look at the analysis generated by HIMIPref™ and blink. The assumptions and procedures and approximations used in the course of the analysis can sometimes work together in unexpected ways … so the results need to be reviewed in order to determine whether

• the programme is really doing what I wanted it to do, and
• whether I still want the programme to do what I previously wanted it to do

Such are the joys of quantitative analysis, when you can spend a month trying to figure out the analysis of one instrument on a date from ten years back!

This time, however, it’s today’s analysis of RY.PR.N: it closed today at 26.00-10, 28×1, after trading 29,390 shares in a range of 26.00-10.

And yet despite the \$26.00 price, HIMIPref™ shows the pre-tax bid-YTW scenario as being the limitMaturity – that is, the dummy maturity thirty-years hence which is used as a substite for “forever”.

First, some facts: the issue closed on December 9 and is a fixed reset with the terms 6.25%+350. The analysis assumes that 5-year Canadas will now and forever yield 1.83%, so the rate is presumed to be reset to 5.33% at the first (and all subsequent) reset dates.

HIMIPref™ calculates the yield to first call of 5.4130% and yield-to-limit of 5.2913%. I have uploaded the cash-flow reports for the five year and 30-year maturities. The YTW is the worst yield, 5.2913%, and the YTW scenario is the 30-year maturity.

There cannot be much argument about the yield calculation for the five year maturity; everything is known, so it’s all perfectly standard. However, the thirty year maturity is simply an analytical placeholder for “forever” and the maturity value is not known. As you can see from the reports, HIMIPref™ estimates a price of \$23.44 for the 30-year case.

Why \$23.44? For that we have to look at the HIMIPref™ calculation of costYield … I have uploaded the relevant cash flow analysis. Readers will note the cash flow entry dated 2014-3-26, for -1.73 (future value) discounted to -1.34 (present value). This is the estimate of what the issuer’s call option is costing the holder; the implication is that if this option didn’t exist, we’d be willing to pay \$1.34 (present value) more for the security.

The value of the option is calculated using a time-influenced distribution of possible prices centred on the current price. As shown by the Option Cash Flow Effect Analysis, it is currently assumed that there is a 53% chance of the option being exercised. Slicing the price distribution into two parts on that date, it is calculated that the average unconstrained price in exercise scenarios is 28.24; the average unconstrained price in non-exercise scenarios is 23.44. Voila! An estimated maturity price of \$23.44.

I’ve also uploaded an Excel spreadsheet where I did a little fooling around with the reports. Raw data is in cells a1:e128. I’ve converted the semi-annual yield back into annual in cells c129:c130. The cash-flows with some decimals put back in are in cells g1:g122. My check on the arithmetic is in cells i1:j122 and sum to a present value of \$26.03805; I’m assuming that the extra 3.805 cents is due to rounding differences of dates and days-in-year approximations. I used cells l1:n124 to play around with the yield-effect of different maturity values, and summarized my playing in cells l127:n130, which I will reproduce here:

 RY.PR.NEffect of Maturity Valueon Calculated Yield Maturity Value Semi-Annual Yield 25.00 5.38% 26.00 5.44% 23.44 5.290%

It’s not all that sensitive, but the rate with a 26.00 end-value is slightly in excess of the 5-year rate, implying that if we rely on a 26.00 end-value then the 5-year yield is the YTW … as would be expected.

But I claim that you cannot count on a 26.00 end-value. I claim that if the unconstrained market price is 26.00 on a call date, then the issuer will call the issue at 25.00 instead. All you can count on at the end of eternity (which is 30-years off) is that fraction of the price distribution that escaped the calls … and that has an average value of 23.44.

And hence, the YTW scenario for a 26.00 issue callable at 25.00 in five years is … the limit maturity. This doesn’t happen for normal “straight” perpetuals: if the issue had an expected cash flow stream of 6.25% for the entire 30-year period, rather than 6.25% for five years and 5.33% thereafter, the five-year call would have a lower yield and hence be the YTW scenario.

And, just for fun, let’s have a contest! Presuming an end-value of 23.44, what post-reset 5-Year Canada yield (and hence, what dividend rate on RY.PR.N) do we need to bump the yield up to the point where the 5-year call becomes the Yield-To-Worst scenario? First correct answer wins a copy of the January edition of PrefLetter.