*The following has been copied from November 23, 2007*

I continue to be utterly amazed by the yield on BNA.PR.C, which had yet another rough ride today, down 0.9444% to close at 17.83 bid, yield 8.39% to maturity. 8.39%! Basically, 11.75% interest equivalent!

I confess, I thought for a fleeting moment today that it might be inventory overhang from a barely successful underwriting … but that doesn’t seem to fit the data. They started trading January 10 and hung around at the $25.00 level until early May, when they – quite reasonably – got caught up in the downdraft. Markets were strong in the first part of the year – if the dealers had been left holding the baby, surely they would have, and could have, blown it out the door at $24.00 in, say, March.

The fund has a position in this issue and I’m getting killed on it. But how can it possibly be fairly valued at 160bp over the similar-and-parri-passu BNA.PR.B? On the bright side, looking at the price chart is highly entertaining … I’ve found a new illustration for the word “parabola”.

*This ends the copy. The rest is new!*

I have thought of a perfectly appalling possibility, predicated by my bewilderment at the difference in yields between BNA.PR.B and BNA.PR.C … is it possible that the market has forgetten that they will mature?

Current Yields of BNA IssuesA bogus calculation that the market might be making |
||

BNA.PR.B | BNA.PR.C | |

Dividend | 1.2375 | 1.0875 |

Bid | 22.25 | 17.83 |

Current Yield |
5.56% | 6.10% |

It should be noted that **Current Yield** is a thoroughly bogus calculation – it ignores the amortization of the discount until maturity.

On the basis of Current Yield, the issues are much more equal …. is it at all possible that this is how they’re being traded? I’m grasping at straws here!

I should also note that while the price of the issue suffered on the first trading day, the volume was heavy. This indicates that the underwriting, in terms of getting the issue out the door, was a success, which makes the whole “overhang” theory even more unlikely.

*Prefhound* in the comments has some interesting things to say, as always. I will be responding in the comments, so stay tuned!

**Update, 2007-11-24**: Note that there is more discussion about Split-Shares in general and BNA.PR.C in particular in the post (and comments) : SplitShare & OpRet Yields.

**Update #2, 2007-11-24**: Sometimes I despair. I looked on Hank Cunningham’s blog, In Your Best Interest, and found Blackmont Capital’s Preferred Share Report, which – in the absence of any copyright notice telling me not to – I have uploaded here for wider distribution. Blackmont makes two rather surprising claims in this report:

*that BNA.PR.B is a Perp*.**False**. The prospectus (March 13, 2004 on SEDAR) clearly states:*The Company will redeem all outstanding Series 1 Preferred Shares on March 25, 2016 (the ‘‘Redemption Date’’).**that the yield on BNA.PR.C is 5.85%*.**False**. It appears that they have reported the current yield, being the annual dividend of 1.088 divided by the “last” price of $18.60. They have not accounted for the fact that the issue’s redemption price is $25.00.

The Blackmont report is riddled with errors – just looking at it very casually, I note that they list GWO.PR.E and GWO.PR.X as perpetuals.

**Update, 2008-1-23** I have received an inquiry from a Canadian Moneysaver subscriber who asks if the dividends on this issue are cumulative.

First off … let’s check my “information summary site”, PrefInfo … yes they are.

Now, I think this is a well-researched and well-proofread site that dispenses highly accurate information to the yearning masses …. but I still recommend looking at the prospectus before actually plunking any money down. The prospectus is on SEDAR, company name “BAM Split”, dated January, 2007 and we see on the front page:

Holders of the Series 3 Preferred Shares will be entitled to receive quarterly fixed cumulative preferential dividends of $0.2719 per Series 3 Preferred Share.

… and on page four of the PDF (which is also page four of the prospectus):

Holders of the Series 3 Preferred Shares will be entitled to receive quarterly fixed cumulative preferential dividends equal to $0.2719 per Series 3 Preferred Share.

…

Series 3 Preferred Share dividends will be funded from the dividends received on the BAM Shares. Based on the current dividends paid on the BAM Shares, it is expected that the Company will have approximately 1.08 times coverage on the dividends to be paid on all Preferred Shares. As such, the dividends paid on the Series 3 Preferred Shares will constitute ordinary dividends to the holders of the Series 3 Preferred Shares. If for any reason, the dividends received by the Company on the BAM Shares are insufficient to fully fund the Preferred Share dividends, the Company will sell BAM Shares or write covered call options on its BAM Shares to the extent necessary to fund any shortfall.

See ‘‘Dividend Policy’’ and ‘‘Details of Offering — Series 3 Preferred Shares —

Dividends’’.

…. so …. I think it’s fair to say: “Yes. The dividends are cumulative.”

The following comment is byprefhoundand was originally posted on the November 23, 2007 thread, as were the first few paragraphs of this postBy the way, forgive me for blogging you to death, but I notice from the BAM Split Pref prospectuses that:

BNA.PR.C can be retracted in exchange for an non-marketable Series 1 Debenture paying slightly more as interest, but ranking above the prefs. There are some provisions limiting retraction if the debentures would be more than 5% of Net Asset Value, or if they couldn’t cover the interest and dividends. Difficult to say what this long put option is worth, but it does offset to some extent the short put on the BAM common — probably not much though with the 5% of NAV limit.

BNA.PR.B, on the other hand, can be retracted any time for $25 less 5% of Net Asset Value less $1.00 — payable in cash. When Net Asset Value is $85 this is $19.75, but if net asset value falls to $25, this is $22.75 (today’s closing!). In theory, then, BNA.PR.B investors could force retraction and perhaps even trigger windup of BAM Split if the Net Asset Value approaches $25.00. In practice, with notice lags and other issues related to the rate of decline and the need for BAM split to then sell BAM common into a falling market, this long put is unlikely to have much offsetting value against the short BAM put (but probably more value than the BNA.PR.C debenture conversion put).

Net Net, the short put on BAM common built into BNA.PR.B has less impact due to less time (9 vs 11 years) and a more effective counter put long.

Got my arbitrage trade completed today at a basis of $4.20 when fair value (before considering the embedded options) is more like $1.65. It took three days to get the trade in place (and to swap some long BNA.PR.B for .C for $4.45). I am giving the arbitrage trade six months to revert, based on it having taken five months to develop the curent basis. If I can get out then at a $2.00 basis, I make 12% after costs.

Now we are both long BNA.PR.C.

Enjoyed the discussion….

If the NAV becomes $30, then the asset coverage ratio will be 1.2:1 and, I very much suspect, the issue will be downgraded fearsomely. Should this be the case – and it would require a 70% decline in the price of BAM.A to get there – I suggest that investors will probably be very happy to receive $25 – 0.05*30 – 1 = $22.50 per share; although depending on the time to maturity when such an awful event has taken place, some might prefer to wait for the mandatory redemption at $25.00 and hope!

Good luck on the arbitrage!

How probable is it that BAM can fall 75% from its Oct 31 price at or before BNA.PR.C maturity in 2019? About 5-15%, perhaps. Here’s how:

I looked up 10 years of C$ BAM trading and 23 years of NYSE trading to reach these interesting insights:

1. BAM in C$ has already fallen 31% from its 2007 high to Nov 23 ($48 to $33, roughly). Some of this could be due to rapid C$ appreciation as most assets are US based. BAM US$ has fallen 25% from its high. Asset coverage for BNA.PR.C at Nov 23 is about 3.4X, down from 4.0 on Oct 31.

2. The Annual BAM-US$ log price trend rate is 0.138 for 1984-2006 (about 14%annual growth), while annual log stock price change (volatility) is 0.257 [These are calculated by averaging and taking the standard deviation of Ln(Price T / Price T-1) for each year]. Interestingly, this historical volatility is 2/3 the market estimate implied in at-the-money 2-year LEAPS on BAM (about 0.40), so the market expects higher volatility than the 22-year average.

3. If we call the log trend the “fundamentals” related to EPS growth etc, and the standard deviation the “noise” in both fundamentals and markets (not strictly true as P/E has probably expanded), we can estimate the probability that BAM will be at a low price when BNA.PR.C matures in 2019 as follows:

a) if future drift = 0 (pure random walk, no fundamental change or growth), then the probability that BAM Split Net Asset Value is $25 or less in 11.13 years is NORMSDIST(-1.42) = 7.7%. NORMSDIST is an Excel cumulative probability function for the normal distribution and -1.42 is the number of standard deviations to get to BAM Split Net Asset Value = $25, which equals: Ln[Asset Coverage of 1.0 / 3.4 Now] / [Annual Volality X SQRT(11.13 years)].

b) if future drift = 4% per year — stock trend price (after dividends) growing at or slightly above economic growth — then the probability that BAM Split Net Asset Value is $25 or less in 11.13 years is 2.7%.

You might not think that a 3-8% chance of breaking the pref at maturity is high, but these probabilities refer to “at maturity” in 2019. In my experience, the probability of hitting a price BEFORE maturity is about twice as high — say 5 to 15% in this case. This is not exactly negligible, and is only a problem for split share prefs — especially those based on a single company.

Maybe this is why BNA.PR.C (at least) trades like it may not mature in 2019, and (as discussed previously) the different terms of BNA.PR.B lead it to trade like $22.50 is its maturity price.

What a wild and woolly world is the Canadian Pref Share market! Thank goodness we have the reliable Mr. Hymas to straighten out Blackmont’s dimwits.

I have a problem with

.

As we discussed in SplitShare and OpRet Yields, I don’t think it’s plausible to extrapolate short term volatilities, even with a drunkard’s walk modifier. This, in turn, is related to the so-called reversion to mean of stock returns; which is not a reversion to mean at all, but an improved realization of the mean from a relatively stable probability distribution.

In other words, I am saying that your annual volatility is comprised of two components:

(i) Actual asset volatility; the actual standard deviation of the actual probability distribution, and

(ii) Measurement error; when you take a relatively small number of samples from the probability distribution, you will over-estimate the standard deviation of the “actual” probability distribution.

In other other words, I am saying that the annual volatilities will contain a lot of noise; the amount of this noise is important when you are tradng relatively short term exchange traded options, but it will decline over time.

The only way we’re ever going to know for sure whether or not BNA will default on it its prefs is by waiting for 2019 and finding out! There is no such thing as absence of risk. And while we can split hairs over model parameterizations, I think we can agree that 11.75% interest-equivalent is junk bond territory – and I do not consider that an appropriate characterization for this issue.

I should also point out, for the benefit of the more nervous readers, that default on the preferred does not necessarily mean you’ve lost all your money. If the NAV on maturity date is, for instance, $24.99, then the issue will default (by not returning the promised $25.00) but the recovery after default will be 99.96% (as the pref holders will receive the entire $24.99.

A decline to an NAV of $25 – which even the gloomy

prefhounddeems to have a low probability – means that preferred shareholders will own (effectively) an equity investment in BAM.A rather than a fixed income vehicle.Oh, one more thing!

In the interest of providing some comparative figures, prefhound, would it be possible for you to use the same methodology to estimate the probability of default of SBN.PR.A, another single line split-share; this one is based on BNS common, asset coverage of 2.4:1, termination date December 1, 2014?

OK, as to the assignment:

1. BNS has about 60% of the volatility of BAM. The short put option term is 7 years instead of 11.1 for BNA.PR.C. The probability (using annual BNS.TO std dev from 11 years) of SBN.PR.A having a maturity value under $10 is 0.5% to 2.9% on the same basis as the 2.7% and 7.7% probability calculated above for BNA pref. On the $10 SBN pref, the short put value would be about 50 cents.

2. To James’ point on mean reversion, one should assess volatility on an RMS rather than standard deviation basis. For BAM we find the 10-year annualized RMS volatility to be about 0.13 (2 data points, but some extrapolation available from 1 month, 1-year, 2-year, 3-year, 5-year and 10-year annualized volatilities). This is about half the value I previously assumed, and does reduce pref default probability calculated this way to 0 to 0.2%. HOWEVER, this analysis is subject to survivor bias — BAM has survived thus far, allowing a 10-year annualized volatility to be calculated, but we can’t be sure it will survive for the next 22 years!

So, there you have it. Depending on the assumptions about volatility, the BNA.PR.C short put option on BAM common is worth from about 0 to $3.60 per pref.

Now we have two alternative hypotheses for BNA.PR.C current price: marginal investors in the market these days think:

A) the short put option is worth $3.60, as I have hypothesized with partial conviction, or

B) the current yield is the metric of importance, as James notes above.

I personally have no idea which of these notions is closer to the truth. It certainly seems like the current marginal sellers of many prefs are just trying to get out at any price. Me, I keep nibbling away, without going overboard. Every day the “sale” gets better and better. Hopefully the short term pain will be followed by a medium term gain, but in the meantime, we are going to collect a lot of after-tax income.

And that’s all I’m going to say about BNA.PR.C (at least until I wind up my arbitrage trade).

I am sure James will be thankful…..

Aren’t models wonderful? All you need now is a whole mess of data and some computer time to run simulations to assign weights to your various models. And if it works, and if the way it works makes sense, you’ve got yourself a quant programme!

You too, eh? Fortunately, I long ago gave up the thought that I could out-think and out-double-bluff the market and I simply trade when things look favourable.

Thankful for your comments!

[…] The effect of these three miserable performances was to drag the SplitShare index total return down by approximately 1.75%. The strange behaviour of the BNA issues during the month has been discussed in another post. […]

[…] I will emphasize again that these trades were opportunistic and do not reflect any view on the market; I will also note that I considered BNA.PR.C to be ludicrously cheap, but had to sell the BAM.PR.N perpetuals to get into it in good size without overweighting my exposure to BAM (recall that BNA.PR.C is backed by BAM.A shares). […]

[…] The BAM Split preferreds are regularly referred to on this blog as they have been very volatile – especially BNA.PR.C, which was discussed in detail last November. […]

prefhoundadvises that he closed his arbitrage trade mentioned in the comments above at a massive profit on January 7.[…] Nice to see this issue finally catch a break! Asset coverage of 3.3+:1 as of January 31, according to the company. Now with a pre-tax bid-YTW of 6.62% based on a bid of 20.70 and a hardMaturity 2019-1-10 at 25.00. Compare with BNA.PR.A (4.25% to a call 2008-3-30 at 25.50) and BNA.PR.B (7.20% to hardMaturity 2016-3-25). […]

[…] And, Assiduous Readers will recall, BNA.PR.C often exhibits puzzling behavior. […]