Research : Perpetual Misperceptions

There are a number of misperceptions held among otherwise sophisticated investors regarding perpetual preferred shares. Now that the October edition of Canadian Moneysaver has been published, I can release this article, which attempts to address two of them, published in their September edition.

Look for the research link!

Update, 2007-10-15: An assiduous commenter asks how much the numbers would have changed without rebalancing … so I’ve done the calculation.

Effect of Rebalancing
Index Performance
March 30 – July 31, 2007
Index With Rebalancing Without Rebalancing
PerpetualPremium -3.56% -4.54%
PerpetualDiscount -8.76% -9.14%

The difference is not as much as my correspondent suspected! Raw data (showing the returns for the period March 30-July 31) has been uploaded for reader inspection for both the PerpetualDiscount and PerpetualPremium indices.

The relatively small difference between the rebalanced and non-rebalanced indices illustrates the point that there is a very sharp point of inflection between “Premium” and “Discount” perpetuals; once that point is crossed, duration changes significantly and the price reaction to yield changes becomes much more like one group than the other, with very little “grey area” between the two camps.

Update, 2007-10-15, later: The immediately preceeding paragraph is nonsense. Sorry!

Update, 2009-1-29: Assiduous Reader PN writes in and says:

I have found your PrefBlog website to be an extremely useful source of information on preferred shares. I have recently delved back into the preferred share market after concentrating on common shares over the last 25 years.

I am continuing to debate the pros and cons of perpetual discounts vs. 5-year fixed resets. In this regard I found your “Perpetual Misconceptions” article in the September 2007 edition of the Canadian Moneysaver to be very useful. I liked Table 1 so much that I reproduced it as a Excel Spreadsheet so I could compute implied future yields for different x and y values (where the resultant return is x% and the current perpetual return is y%). In doing so I discovered a slight discrepancy in the calculation of the discount factors in your Table 1. For a 2% return you have
calculated the discount factor after year 1 as 1.00-.02= .9800 rather than 1/(1.02)=.9804 The small error is continually compounded for years 2 to 20. I was wondering why you choose not to use the generally accepted mathematical formula for discount rates?

I have attached a spreadsheet based on two sets of calculations: the first is based on the generally accepted mathematical formula and the second is based on your computations for Table 1. You can see the results are only very slightly different for the 2% and 5% rates you have chosen and would not affect any of the conclusions you have drawn in your article.

My question is a very minor point and I am sure you must have a good reason for your calculation of the discount factors. I am just wondering what was your reasoning was?

Well, PN, there’s a very simple answer to your question: I am an idiot.

I cannot, at this point, remember anything much about the preparation of this article; what may have happened is that a rough draft of the table made it into the final product without thorough checking; the checking being performed in a cursory fashion because, as you say, the errors are small and the conclusion robust. Let’s just pretend that we’re seeking a total return of 2.04% and that that figure is cited on the table title, shall we?

PN has won a complimentary issue of PrefLetter.

2 Responses to “Research : Perpetual Misperceptions”

  1. jiHymas says:

    I have received the following communication from an assiduous reader – JH

    In the article you note that Perpetual Discount Index had fallen about 9% whereas the Perpetual Premium Index had fallen about half the amount “due to greater interest rate protection”. However, I wonder if these Index returns really reflect what would have happened to investors over the period.

    Because so many Premium Prefs fell into the Discount Index during the period, this would reduce the apparent fall in the BOTH indices — a survivor bias to the premium index (prefs can fall only so far before they get kicked out of the index) and a systematic introduction into the Discount index of higher yielding prefs booted out of the Premium index (higher yields are slightly less sensitive to interest rate risk).

    I suspect the actual investment experience of someone who held the index of premium prefs at the beginning of the period to the end of the period (without changes) would have been closer to minus 10%, not the minus 4% of the premium index. Likewise, the actual investment experience of a holder of discount prefs from the beginning to the end of the period would have been more like 15-20% (without changes).

    Of course, to achieve the index returns, the investor would have had to make extensive changes during the period — at the prices and times assumed by the index methodology (which is probably nearly impossible due to spreads, lack of liquidity and timing of index change announcements).

    Anyway, rather than the 9%/4% index change cited in the article, perhaps knowing the unchanged portfolio returns over a period would more realistically project what longer term investors had experienced. I still expect the discount prefs to have done worse, but with your great data base, perhaps the actual result can be determined.

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