{"id":2399,"date":"2008-07-16T21:28:29","date_gmt":"2008-07-17T01:28:29","guid":{"rendered":"http:\/\/www.prefblog.com\/?p=2399"},"modified":"2008-07-16T21:28:29","modified_gmt":"2008-07-17T01:28:29","slug":"perpetualdiscounts-playing-with-numbers","status":"publish","type":"post","link":"https:\/\/prefblog.com\/?p=2399","title":{"rendered":"PerpetualDiscounts: Playing with Numbers"},"content":{"rendered":"

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?<\/a> – might be traded away by investors unwilling to time the markets.<\/p>\n

OK, so let’s consider the following data:<\/p>\n

\n\n\n\n\n\n\n
Fixed Income Investments<\/td>\n<\/tr>\n
Asset<\/td>\nYield<\/td>\nDuration<\/td>\n<\/tr>\n
Perpetual
Discount
Preferreds<\/td>\n		9.28%<\/a>
(Interest
Equivalent)<\/td>\n		13.05<\/td>\n<\/tr>\n
iShares
CDN Bond
Index
(XBB)<\/td>\n		4.32%
-MER 0.25%<\/td>\n		6.4<\/td>\n<\/tr>\n
iShares
CDN Short
Bond Index
(XSB)<\/td>\n		3.96%
-MER 0.25%<\/td>\n		2.8<\/td>\n<\/tr>\n<\/table>\n<\/div>\n

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.<\/p>\n

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.<\/p>\n

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)<\/p>\n

Old Portfolio Weighted Duration = New Portfolio Weighted Duration
\n6.4 = 2.8 (1-P) + 13.05 P
\n6.4 = 2.8 – 2.8P + 13.05 P
\nAnd therefore
\n3.6 = 10.5P
\nAnd therefore
\nP = 0.34.<\/p>\n

Check!
\n6.4 = 2.8 * (1 – 0.34) + 13.05 * 0.34
\n6.4 = 2.8 * 0.66 + 13.05 * 0.34
\n6.4 = 1.8 + 4.4
\nClose enough!<\/p>\n

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.<\/p>\n

OK, so what’s that done to his yield?<\/p>\n

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

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

NY = 5.60% – 0.34*1.50%
\n= 5.09%<\/p>\n

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.<\/p>\n","protected":false},"excerpt":{"rendered":"

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 …<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[28],"tags":[],"class_list":["post-2399","post","type-post","status-publish","format-standard","hentry","category-spreads-to-bonds"],"_links":{"self":[{"href":"https:\/\/prefblog.com\/index.php?rest_route=\/wp\/v2\/posts\/2399","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/prefblog.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/prefblog.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/prefblog.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/prefblog.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2399"}],"version-history":[{"count":0,"href":"https:\/\/prefblog.com\/index.php?rest_route=\/wp\/v2\/posts\/2399\/revisions"}],"wp:attachment":[{"href":"https:\/\/prefblog.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2399"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/prefblog.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2399"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/prefblog.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2399"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}