## PerpetualDiscounts: Playing with Numbers

Given the recent skyrocketting of PerpetualDiscount yields, I’ve been thinking a bit about how the spread – which I consider quite excessive, but what do I know? – might be traded away by investors unwilling to time the markets.

OK, so let’s consider the following data:

 Fixed Income Investments Asset Yield Duration PerpetualDiscountPreferreds 9.28%(InterestEquivalent) 13.05 iSharesCDN BondIndex(XBB) 4.32%-MER 0.25% 6.4 iSharesCDN ShortBond Index(XSB) 3.96%-MER 0.25% 2.8

For PerpetualDiscounts, the Modified Duration is reported as it is on HIMIPref™, which assumes repayment of principal in 30-years. This isn’t quite accurate, but it’s close enough for horseshoes.

So let’s consider an investor who is holding XBB in a taxable account. There are going to be strange tax effects if we do it properly (since the average COUPON is far higher than the average YIELD: he will be paying tax on the coupon, which is partially a return of capital and, logically, getting some of this tax back via a projected capital loss), but we’re not going to do it properly. We’re going to do it on the back of an envelope; those wishing precision can either do it themselves, or pay me a huge amount of money to do it for them.

Anyway, this investor is holding XBB. He wants a duration-neutral switch into a portfolio comprised of XSB and PerpetualDiscount Preferreds, so he solves the equation (let P be the fraction of the new portfolio invested in Preferreds)

Old Portfolio Weighted Duration = New Portfolio Weighted Duration
6.4 = 2.8 (1-P) + 13.05 P
6.4 = 2.8 – 2.8P + 13.05 P
And therefore
3.6 = 10.5P
And therefore
P = 0.34.

Check!
6.4 = 2.8 * (1 – 0.34) + 13.05 * 0.34
6.4 = 2.8 * 0.66 + 13.05 * 0.34
6.4 = 1.8 + 4.4
Close enough!

So basically, a taxable investor holding XBB can swap 2/3 of his holdings into XSB and 1/3 into PerpetualDiscounts and remain duration neutral. Note that other risk-elements are not risk neutral! The portfolio is a barbell, and will underperform expectations if the curve steepens; there is a higher weight of corporates in the new portfolio; there is tax-effect-risk in the new portfolio; there is spread risk on the preferred (the spread can go to a million basis points and nobody will go to jail); there’s a whole list of things that could go wrong and would be listed in a prospectus. All I will say is that the duration-neutrality goes a long, long way towards making the portfolios equal, since to a first approximation the investor will have the same risk relative to parallel shifts in the yield curve, up or down.

OK, so what’s that done to his yield?

His old yield was 4.07% net of MER; his new yield, NY, after deduction of the MER on his perpetualDiscount position (MERP) is:
NY = 0.66*(3.96% – 0.25%) + 0.34*(9.28 – MERP)
= 0.66*(3.71%) + 0.34*9.28% – 0.34*MERP
= 2.44% + 3.16% – 0.34*MERP
= 5.60% – 0.34*MERP

Let’s assume he puts the money in my fund, MAPF, and that he assumes the fund will deliver the PerpetualDiscount yield less 1% fee and less 50bp expenses and no trading gains. Then

NY = 5.60% – 0.34*1.50%
= 5.09%

So … back of an envelope, an investor with a taxable position in XBB can make reasonably conservative assumptions and figure to pick up 100bp pre-tax yield without changing duration by putting 1/3 of his portfolio into perpetualDiscounts and keeping duration constant by swapping the other 2/3 to XSB. You could do your own calculation for the exchange traded funds, CPD and DPS.UN (these are not entirely perpetualDiscounts, so be careful!) or by using direct investment (zero MER!) on the preferred portfolio of your choice.

### 2 Responses to “PerpetualDiscounts: Playing with Numbers”

1. meander says:

This is a very interesting analysis.

The question that runs through my mind when considering perpetual preferred shares is how low can they go? I know that technically the answer is of course zero. Any security can go to \$0. But discounting default risk, which in the case of the big 5 banks I think one can safely do, how low can they go? We’ve got CIBC prefs trading at 40% below their face value. These things will eventually be redeemed, although I know eventually could be a very long time. This is in no way a sophisticated analysis, but –assuming solvency– doesn’t the face value have to place some kind of a floor on market price?

2. jiHymas says:

doesnâ€™t the face value have to place some kind of a floor on market price?

Not really, not directly.

The face value of a perp (by which I mean the same thing as the redemption price) will only become important if the issuer decides it should become important; and this is dependent on what is good for the issuer. Since the holder has no influence over this decision, any good effects that might come to pass from redemption should be ignored; only bad effects should be influential.

What one owns after buying a perp is, essentially, the promise that \$X will be paid annually for at least as long as the common shareholders get anything. That’s it. That promise will be traded in the market for whatever the market thinks it’s worth, after assigning some probability to the chance that the income stream is secure, and some value to the income stream itself (and a few other values, depending on the complexity of the analysis).

So when considering the value of CM.PR.J, the things that really count are:
(i) CM’s viability as a going concern for perpetuity
(ii) How much you thing a perpetual annuity for \$1.125 is worth.

The redemption value is only important insofar as it puts a cap on your winnings. If you think CM’s earnings are going to increase outrageously forever … buy the common! There’s no limit to how much those will be worth under such conditions, while your capital gain on the perp is (from its current price of about \$16) limited to 56%.

On the other hand, you would buy the perp if you wanted a more fixed-income-like investment, with the common shareholders providing you with first-loss protection.

How low can they go? Long Treasuries peaked at about 15% in 1981. So say long Canadas go to 15%, with a spread of 5% to pre-tax interest-equivalent perpetualDiscount yields. 20% PTIE corresponds to a dividend yield of about 14.25%. At dividend yield of 14.25% on CM.PR.J corresponds to a price of just under \$8.

Are you scared enough yet?

This is why I strive not to over-sell preferreds and emphasize that they should be considered PART of a DIVERSIFIED portfolio! In the case of the the “butterfly trade” (the medium duration part (“bullet”)gets split in a duration neutral manner to a long duration part and a short duration part (“barbell”)) suggested above, then (assuming the horrific rates scenario outlined above) the high duration preferred part would perform much worse than the alternative XBB; but the XSB would perform much better, leaving (in a first order analysis only!) the total barbell portfolio performing about the same as the total bullet bullet portfolio.

Why would you perform this butterfly trade? Because you feel SPREADS on preferreds will decline, without wishing to take a view on overall RATES. And, of course, because if spreads remain constant, you’re picking up about 1% yield without changing your overall exposure to interest-rates-in-general (more technically referred to a “parallel shifts”)