## PrefLetter : Questions from a Subscriber

I have received an eMail with some questions of sufficient generality that I thought I would publish it – suitably redacted, of course!

I now understand YTW and the concept of pseudo convexity, but not the application of pseudo convexity e.g. in your current recommendations, which is more “bond like”, a negative 12.00 (###.##.##) or a positive 6.00 (###.##.#)?  Given my interest rate view, I should stay away from more bond like.

A “normal bond”, by which I mean a fixed-income instrument with no embedded options, will always have a positive convexity, which will vary (roughly speaking) as the square of the duration.

[One implication of this relationship is that one may use convexity as a measure of the “barbelledness” of a bond portfolio; for instance, an extremely barbelled portfolio comprised of 3-month treasury bills and 30-year bonds will have a greater convexity than an extremely bulletted portfolio comprised solely of 10-year bonds even though both portfolios have exactly the same weighted average duration.

Classical fixed-income mathematics states that a more convex portfolio will always outperform a less convex portfolio that has the same yield, regardless of the direction of a change in interest rates; this is because classical fixed income mathematics assumes that all changes to the yield curve will be parallel. In fact, (given equal durations, different convexities) convexity (= barbelledness) helps when the curve is flattening, hurts when it is steepening. When it is humping (by which I mean the middle is increasing in yield by more than the average of the two endpoints – what did you think I meant?) convexity helps; when de-humping (I will admit that I’ve never used this term before, although I have used “humpedness”) convexity hurts.

However, classical fixed income mathematics has led to one of the more truly dumb slogans ever used in portfolio management: the benter the better. This phrase picks up from looking at plots of duration vs. price; since (in classical fixed-income mathematics with perfectly normal bonds) the curvature of this plot works in the holder’s favour so some believe that more bending = more value.

End of rant, back to the main question.]

Convexity is of very little value in quantitative fixed income analysis, but has some use as a qualitative measure (as long as you don’t take it too seriously). Pseudo-Convexity, used in HIMIPref™, results from a mathematical calculation that seeks to accomplish the same thing while accounting for embedded options. It is a Good Thing for pseudoConvexity to be positive (all else being equal, which is never the case) because

• Pseudo-Convexity may be interpreted as a measure of how “bond-like” the instrument is; bonds have positive convexity (and pseudo-convexity, of course)
• It is good for preferred shares to be bond-like, because the only ways in which they differ from regular bonds are bad for the holder

When confronted by the choice between two instruments that differ in pseudo-convexity, you should ensure that you are being paid (higher expected total return) for the risks you are incurring by taking a lower convexity [to the extent that this lower convexity is due to embedded options, not simply lower duration. Virtually all differences in pseudoConvexity will be due to embedded options].

I understand the different types of pref share, but I am not clear as to how to think about that i.e. advantages/disadvantages of different types per se.

This is a big, big question. All I can really do is point you to the various articles I have written, specifically those referenced on the PrefLetter page introducing these types.

After that I am trying to turn your recommendations into practical action e.g. one of your current recommendations is ###.##.#; I own that, it is down 5.2% since I purchased (which is likely one of the reasons you are recommending it!), but, should I add to that position at this price?  I suppose that specific question resolves itself into the more general one of buy, sell, hold-at given purchase price ranges.  So, I know how to buy from your letter, but not how to sell.  I imagine your answer may be to buy your managed fund, which I may well consider, but couldn’t you turn your letter into a model portfolio, or is that the purpose of your fund?  Maybe I should be buying that as opposed to the newsletter!  My portfolio of prefs has actually done well over the couple of years I have held it but has started to head South over the last Qtr in response to inflation/interest.  I believe in prefs as a sensible part of a yield portfolio, but the prudent management is beginning to seem complex.  I own 14 different prefs of which 5 are positive, 9 are now negative by generally small amounts, and I’m fumbling as I am pretty sure further rate increases are ahead. ( I understand your view on interest rate forecasting!)

This is another big, big question. I will be writing an article shortly for Canadian Moneysaver regarding portfolio construction that I hope will be found somewhat helpful.

I don’t think you will ever see a “Model Portfolio”, labelled as such, coming from me. Model Portfolios are tools of the devil.

Assume, for instance, that you are following a model portfolio and have achieved 100% congruence with the recommendations. Then, for good reasons or bad, the model portfolio changes. In order to maintain congruence, the follower must therefore execute the required swap irrespective of price.

Those last three words are the dealbreaker, particularly in fixed income portfolio management. I might be very happy to sell X and buy Y if I can take out twenty cents, but consider it the worst trade ever proposed if I have to trade flat.

Even if I say on Day 1 that a take-out of twenty cents is a great trade, there’s no guarantee that on Day 2 I’ll say the same thing. The absolute prices may have changed (either due to normal fluctuations, or even – trivially – because of a dividend), which will change all the yields and option-exercise probabilities. Even if the prices have not changed, a change in the rest of the yield curve might make a big difference [for example, say the trade is from a short-term retractible into a perpetual discount. PerpetualDiscounts have dropped a lot in the past month; I want more yield pick-up today than I did three weeks ago before I’ll consider the trade.

I’m sure this all sounds evasive, and don’t be afraid to tell me so in the comments. But the simple fact is, fixed income portfolio management, when done professionally, is a complicated thing. And so, yes, I think that in many cases clients will be better off purchasing my fund. The objective of PrefLetter is to provide retail investors – who don’t want to give up control and who don’t want to pay fees – and their advisors with a short-list of buy-and-hold recommendations for each preferred share type.

When considering a sale … well, look at what you have. First, in terms of overall asset-class selection and how well it reflects what you are attempting to accomplish with the portfolio. Second, in terms of potential swaps. Say you hold X and I’m recommending Y, in the same class. Look at the yield-to-worst of the two instruments, their terms and their credits; if Y looks better at prices where you can execute, then by all means go for it! You might not be doing optimal trading, but if, say, you can come up with a good rationale for why Y is better than X (credit, interest rate protection, yield), after commission & taxes, for every trade, I suggest you’ll be doing all right.

### One Response to “PrefLetter : Questions from a Subscriber”

1. […] PrefBlog Canadian Preferred Shares – Data and Discussion « PrefLetter : Questions from a Subscriber […]