Question: Real Return Bonds

[DanielCarrera]

Ok, I've read most of Bylo's excellent page on RRBs. I still have a couple of question about finding out what the current yield is:

(1) Is there a website that posts the current yield for RRBs?

(2) I believe I know how to calculate the real yield based on the index ratio or real price. Perhaps someone can confirm that I got it right:

Joe buys an RRB for $1000 with a real yield of 2% for 5 years. In 5 years it'll pay $1000 x 1.02^5 in inflation-adjusted terms.

A year later people are willing to pay $1075 for this bond, and inflation has been 3%. Therefore, the index ratio today is 1.03 and the real price is $1075/1.03 = $1043.69. This is the current price of the bond adjusted for inflation, measured in one-year-ago dollars. The real return of this RRB, if I bought it now, would be:

($1000 x 1.02^5 / $1043.69)^(1/4) - 1 = 0.836%

The exponent is 1/4 because there are 4 years left until payment.

Did I get the yield right? If so, to calculate the yield I need to find out:

* The original price of the bond.
* Either the current real price or the current index ratio.
* How many years before the bond pays.

[Bylo Selhi]

1. It's in the FAQ: RRB Offer Prices and Yields [CanadianFixedIncome.ca]. Print editions of the G&M and FP used to publish this as well, however I have no idea if they still do since I haven't read their hardcopy in years. The online edition of the G&M posts data but only for selected issues, mostly stripped coupons.

2. Calculating the real yield of an RRB is no different than calculating the nominal yield of a nominal bond. You can use any standard bond calculator. For bond price use current market price divided by the index ratio.

[IdOp]

Joe buys an RRB for $1000 with a real yield of 2% for 5 years. In 5 years it'll pay $1000 x 1.02^5 in inflation-adjusted terms.

A year later people are willing to pay $1075 for this bond, and inflation has been 3%. Therefore, the index ratio today is 1.03 and the real price is $1075/1.03 = $1043.69. This is the current price of the bond adjusted for inflation, measured in one-year-ago dollars. The real return of this RRB, if I bought it now, would be:

($1000 x 1.02^5 / $1043.69)^(1/4) - 1 = 0.836%

The exponent is 1/4 because there are 4 years left until payment.

Did I get the yield right?

This looks ok provided I am interpreting the first sentence of the quote correctly. To clarify that: in this hypothetical example (with no coupons) Joe would receive $1000 x 1.02^5 if inflation over the next five years was 0%. If it turned out to be higher, he'd receive more than that in nominal dollars. Then it looks good, as you have expressed all amounts in dollars at a common time. For an actual RRB there would normally be coupons, so you need to use a bond calculator as Bylo suggested.

You can find recent RRB yields at the BoC Bond Yield Summary (see bottom of page).

[DanielCarrera]

1. It's in the FAQ: RRB Offer Prices and Yields [CanadianFixedIncome.ca].

Any idea how often these numbers are updated and ho reliable they are? I kow nothing about Premier Financial, I've never hear of them before.

2. Calculating the real yield of an RRB is no different than calculating the nominal yield of a nominal bond. You can use any standard bond calculator. For bond price use current market price divided by the index ratio.

I'm not convinced. I'm ok with "for bond price use current market price divided by the index ratio", but the calculator you linked to requires me to know the coupon rate. I don't understand coupon rate, so all we've done is shift the question from "how do I find the yield?" to "how do I find the coupon rate?".

Finally, I always feel more comfortable when I can calculate things myself. Whether it is a mortgage schedule, a rent vs buy a house decision, present value or the yield of a bond, I don't like to trust a calculator that I didn't write myself.

[Shakespeare]

"how do I find the coupon rate?".

It's the second column....

[DanielCarrera]

This looks ok provided I am interpreting the first sentence of the quote correctly. To clarify that: in this hypothetical example (with no coupons) Joe would receive $1000 x 1.02^5 if inflation over the next five years was 0%. If it turned out to be higher, he'd receive more than that in nominal dollars.

Yes, that is exactly what I meant. For example, if inflation was a constant 3% for 5 years, then in nominal terms Joe would get $1000 x 1.02^5 x 1.03^5.

My first attempt to calculate the yield used nominal dollars and it included a bunch of inflation factors. I was not able to find a clear answe this way, so on my second try I expressed all amounts in dollars at a common time.

Then it looks good, as you have expressed all amounts in dollars at a common time. For an actual RRB there would normally be coupons, so you need to use a bond calculator as Bylo suggested.

Thanks. I wanted to master stripped bonds first because they are easier to understand.

You can find recent RRB yields at the BoC Bond Yield Summary (see bottom of page).

Thanks. I trust the Bank of Canada, at least I know who they are I notice, though, that they only have one yield posted for all bonds, whereas Bylo's link has a different yield for each maturity. What's up with that?

[DanielCarrera]

"how do I find the coupon rate?".

It's the second column....

Sorry for asking stupid questions. I didn't see it.

Shakespeare, do you know who Perimiter Financial is? I've never heard of them.

[Bylo Selhi]

I trust the Bank of Canada, at least I know who they are I notice, though, that they only have one yield posted for all bonds, whereas Bylo's link has a different yield for each maturity. What's up with that?

The BoC's number is based on an aggregation of the issues outstanding. Also I believe it's based on mid-market prices.

Perimeter Financial is "Canada's only electronic, multi-dealer Canadian fixed income marketplace operated specifically for the wealth management marketplace.. Our fixed income prices represent firm offers to sell through the CBID™ fixed income marketplace... Offer prices represent the wholesale prices that investors can expect to pay to purchase the securities." You can find lots more info about them using Google.

[IdOp]

My first attempt to calculate the yield used nominal dollars and it included a bunch of inflation factors. I was not able to find a clear answe this way, so on my second try I expressed all amounts in dollars at a common time.

There are two things that one can do (or think of doing). As in your first attempt, you could express all cash flows in nominal terms (that you actually pay, or receive). Then solve for the rate of return (just IRR) and it will be the nominal return. This works well for an ordinary bond that you buy today, because the (nominal) amounts to be paid are known in advance (assuming no default!). This isn't practical for an RRB you buy today, because future inflation is unknown and hence the actual nominal amounts you'll be paid in the future are not known. The best you could do is make assumptions to model future inflation and calculate the nominal yield of the RRB based on that model.

To get around this problem for RRBs, the real yield is used instead, which is gotten by using the real payments (nominal with inflation stripped out). These are known in advance, so the calculation is possible. OTOH, try to apply this to an ordinary bond, and you have a problem there because you don't know the inflation factors to strip off the known nominal payments.

OTOH yet again, if you don't buy the bond today, but look at one from the past that has matured, then you know all the inflation factors and you can calculate both real or nominal yields for ordinary and RR bonds without assumptions.

On the fourth hand, in all of the above pictures you could layer on the calculation of real or nominal durations.

[squash500]

This is slightly off-topic but the xrb with an mer of .35% has a yield to-date of 11.16% as of July2/08. TDW has also started to synthetic drip the xrb shares . It shows you how things can change from one year to the next. Last year, the xrb was a real dog of an etf with a return of around -5% for 2007. IMHO, xrb might be a good alternative for someone who doesn't have the knowledge or wants to go through the hassle of buying individual bonds or individual real-return bonds .

[Bylo Selhi]

yield to-date of 11.16% as of July2/08... It shows you how things can change from one year to the next. Last year, the xrb was a real dog of an etf with a return of around -5% for 2007.

Be verrry careful with that.

[squash500]

Be verrry careful with that.

Thanks for posting those threads Bylo . I will read them very carefully too try and improve my knowledge of rrbs.

[parvus]

Shakespeare, do you know who Perimiter Financial is? I've never heard of them.

Perimeter Financial is also, in a way, Doug Steiner's columns in ROB mag (one of which mentions bylo).

[DanielCarrera]

Shakespeare, do you know who Perimiter Financial is? I've never heard of them.

Perimeter Financial is also, in a way, Doug Steiner's columns in ROB mag

Maybe I'm dumb, but I don't know what you are trying to tell me.

(one of which mentions bylo).

This is an interesting article. I didn't know that about Bylo or FWR. Besides Bylo, who were the other two founding members of FWR? I'm curious to know. Not that it has anything to do with RRBs...

[Bylo Selhi]

who were the other [s]two[/s]three founding members of FWR?

Shakespeare, Yielder and Norbert.

[DanielCarrera]

who were the other [s]two[/s]three founding members of FWR?

Shakespeare, Yielder and Norbert.

You guys have all done a great job with FWR. I've received invaluable information here. Thanks for making this place.

[northbeach]

You guys have all done a great job with FWR. I've received invaluable information here. Thanks for making this place.

I thank all contributors and in particular the founders and moderators who have made this site non commercial and free from spam.

[Small Investor Activist]

I wouldn't buy real reburn bonds, nobody understands or can explain how they trade.

[parvus]

Shakespeare, do you know who Perimiter Financial is? I've never heard of them.

Perimeter Financial is also, in a way, Doug Steiner's columns in ROB mag

Maybe I'm dumb, but I don't know what you are trying to tell me.

He's a good read, if you're in Toronto and get ROB magazine — as thoughtful in his writings as he is in his financial innovations. (Sometimes I'm a little vague; sorry. )

[Inquisitive]

I wouldn't buy real reburn bonds

Actually,Moderator, I have been wondering if the spelling on the thread title could be corrected so it will be easily found in a search?

Parvus, ROB comes free with the Globe to Vancouver as well and I assume everywhere the Globe is sold.

[Bylo Selhi]

Web reference tool helps traders pick the best bond price and yield

There's only one problem with buying bonds on your own without an adviser.

How do you know if you're getting a good deal?

The bond market, unlike the stock market, is not transparent. Each dealer carries an inventory of bonds and marks up the price to cover the cost of selling the bond.

The exact size of the markup is a well-kept secret. Only by comparing bond prices and yields at many dealers can you know if you're paying too much.

Comparison shopping was tough for do-it-yourself investors until a new website launched this year...

N.B. Shakes' caveat in the Comments section!

[BRIAN5000]

yield to-date of 11.16% as of July2/08... It shows you how things can change from one year to the next. Last year, the xrb was a real dog of an etf with a return of around -5% for 2007.

Be verrry careful with that.

So is there any studies arround on how chasing bad performace in previous time frames works, I guess this is just market timing. Buying beaten up sectors or perhaps PH & N US dividend fund now as an example?

[Norbert Schlenker]

Wouldn't RRB coupons fill that niche?

They would, if you could find them. Back in the TWB days Norbert explained why brokers are loath to strip coupons "on spec." I don't recall the details or I'd post them here and Norbert is currently at sea (so to speak )

Back on land after a few weeks and it's impossible to catch up on everything without resorting to marking everything read, but I'll respond here and apologize for any other request specifically to me that I've missed.

The problem with stripping RRBs on spec is that the volume generated is quite paltry. RRBs have small coupons, so the best case scenario - from the dealer's point of view - goes something like this:

• Buy a million of the 4.25% of 1Dec2021.
• Apply to CDS to strip the million.
• End up (these days) with about 25 coupons, each worth a real $20k or thereabouts at payment, and a million of the principal at maturity.
• Discount everything to the present day, ending up with about 25 coupons worth $10-20k, and principal of maybe $600k.
• Mark everything up so that we get paid.
• Flog all the bits to customers.

The problem is the last step. There's not much difficulty selling little chunks worth $10-20k to retail customers for their RRSPs: investors are pretty used to building ladders that way with stripped coupons built from nominal bonds, so this is no different. Think it would be nice to have an inflation adjusted $20k paying off in 2012, just when you expect to retire and need it in the RRSP? Then this is the product for you.

It's easy to imagine flogging every coupon like this from the original million to fewer than five people. Fred and Wilma each want five year ladders starting next year (which takes care of both semi-annual coupons), Tom and Jerry each want five year ladders from 2014-2018, and there's an occasional vulture who will clean up the few remaining dregs.

So retail brokers blow out all the shorter coupons in about five minutes with almost no work and the investment dealer gets left with what in inventory? $600k of the longest maturity, i.e. the Dec 2021 principal. If there's no pension fund customer willing to take it right now, how does the dealer get rid of a big chunk like that? It doesn't have the attributes of all the other coupons that appeal to retail investors. It can't be laddered. It's all one date, so it's harder to find customers to take that particular one. It's as far away in time as you can get so projections are harder to make for the likely buyer. (Fred's quite sure he's retiring next year. It's not nearly as easy for Fred's sister, 12 years his junior, to be so precise about her retirement date.) And it's about 30 times the size of all the others so, if you're counting on retail, you probably need more than 30x as many difficult phone calls to find the equivalents of the easy sales to Fred et al.

I expect this problem will eventually go away. A speculative strip of the 2021 RRB, which has the above described problem today, won't be much of a problem come, say, 2016. Then the big principal chunk is only five years out and it's much easier to flog.

[Bylo Selhi]

$600k of the longest maturity, i.e. the Dec 2021 principal. If there's no pension fund customer willing to take it right now, how does the dealer get rid of a big chunk like that? It doesn't have the attributes of all the other coupons that appeal to retail investors.

Thanks for the explanation, Norbert.

As one of those who managed to pick up some of the 2021 principals the main attraction was the guaranteed ~3.5% real on accrued interest from 2003 to 2021. Contrast with the complete 2021 and the need to reinvest interest payments every 6 months at prevailing rates.

Of course that's all in hindsight. I might not be quite so happy with the strips if RRBs currently yielded 5% real.