Real Return Bonds

Introduction

A Real Return Bond (RRB) is an inflation-indexed bond issued by the Government of Canada and/or certain provincial governments. Historical rates are available from the Bank of Canada. Total return data are available from Libra Investment Management and real returns for various investments from this pdf A Study of Real Real Returns.

Because the inflation indexing of the capital results in deemed income from individual bonds with no cash immediately received, they should be held in registered accounts. See Tax-Efficient Investing.

How they work

The Base CPI

The Bank of Canada (BoC) will issue an RRB with a certain maturity. At the date of issue, a base value of the Consumer Price Index (CPI) is associated with the bond. Thereafter, both the principal and the coupon are indexed according to the CPI. The effect is that both the principal and interest pay in constant dollars (as defined by CPI indexing), thus providing protection from future inflation. The details of the calculation are given by the Bank of Canada. However, since that report was issued, there has been an adjustment in the base CPI. The new base CPIs of the current federal RRBs are as follows:

Base CPI Values for Canadian RRBs

Coupon (%)	Bond Maturity	New CPIBase
4.25	1 December 2021	83.07713
4.25	1 December 2026	87.82571
4.00	1 December 2031	91.38249
3.00	1 December 2036	102.99160
2.00	1 December 2041	111.21849
1.50	1 December 2044	115.60000

The Reference CPI and Index Ratio

The "Reference CPI" is calculated for each day of the month by linear interpolation of the CPI data measured in the two preceding months. This Reference CPI is divided by the base CPI for each bond to calculate an Index Ratio which is used to adjust the price of each bond:

Index Ratio = Reference CPI ÷ Base CPI

Tables of these ratios are provided by the Bank of Canada and used by financial institutions to determine purchase and sale prices. A spreadsheet that calculates the index ratios is here. For an RRB purchase or sale, the index ratio is calculated for the settlement date, which is three business days after the transaction.

An example of the index ratio calculation is as follows:

For a bond purchased on Feb. 13, 2009, settlement date is Feb. 19. On Feb. 19, the Reference CPI calculated by interpolation of the November 2008 CPI of 114.1 and December 2008 CPI of 113.3 is 113.58571. For each bond, 113.58571 is divided by the bond's base CPI and rounded to five decimal places. These index ratios are:

Index Ratios for
Feb. 19 2009

Bond	Index Ratio
Dec 01/21	1.36723
Dec 01/26	1.29331
Dec 01/31	1.24297
Dec 01/36	1.10286
Dec 01/41	1.02128
Dec 01/44	N/A 1

1. The 2044 bond was issued after the example was calculated.

Once the index ratio is known, it is multiplied by the real price of the bond (in constant dollars) to get the price in current dollars:

Corrected Price = Real Price × Index Ratio

The price shown for the 2021 bond on closing Friday, Feb. 13 2009 was $120.39 in constant dollars. The corrected price for settlement at this price on Feb. 19 is $120.39 × 1.36723 or $164.60, not including accrued interest. The purchase of $10000 face value this bond would require over $16500 once interest (about $128) is included.

RRBs pay interest semi-annually on June 1 and Dec. 1. The interest payments, like the principal, are adjusted for CPI changes by multiplying constant-dollar amounts by the index ratio.

Effect of Deflation

In the event of deflation, the nominal dollar amount received for an RRB at maturity would decrease with a decrease in the index ratio. However, the CPI adjustment would mean that the real value would remain constant.

RRBs do not offer a $100 guarantee on the principal, so in the event of extended deflation, the final value of the bond could drop below $100, although its inflation-adjusted value would still remain constant. Since that eventuality would require the Reference CPI of the bond to drop below its Base CPI, it is considered extremely unlikely. For the oldest RRB, the 2021 issue, the Index Ratio as of Feb. 19 2009 is about 1.37; a drop in the CPI of over 27% over the next 13 years would be necessary to move the Index Ratio below 1.00 and the terminal value below $100. For the more recent issues, less deflation would be required; the 2041 bond would require only 2% deflation over the next 33 years to have an index ratio below 1.00.

Comparison with regular bonds

Regular bonds are not indexed for inflation. RRBs therefore provide protection against unanticipated future inflation. Since RRBs and regular bonds trade on secondary markets, anticipated inflation is built into the current price.

RRBs will not provide protection against unanticipated future deflation.

A common simplification is to derive the anticipated inflation value by subtracting the RRB yield from the regular bond yield. This is not quite correct, as a more comprehensive equation is:

regular bond yield = RRB yield + anticipated inflation + insurance against inflation changes

Or, rearranging:

RRB yield = regular bond yield - anticipated inflation - insurance against inflation changes

The insurance component thus decreases RRB yields compared to regular bonds. This insurance component, also known as the inflation risk premium, is hard to precisely estimate, but may be in the vicinity of half a percent.

A more detailed analysis of this relationship for TIPS, the US counterpart of RRBs, can be found here.

A comparison of various combinations of RRBs and normal bonds is here.

Buying RRBs

RRBs are generally not listed on line by discount brokerages, and usually have to be bought by calling in. As the calculation example above shows, the amount required for a certain face value, particularly for the earliest RRB series, may be significantly larger than the nominal amount for that bond.

An ETF for Canadian RRBs, iShares DEX Real Return Bond Index Fund, trades under the symbol XRB. There is a dedicated FWF thread discussing it. Philips, Hagar and North also has an inflation-linked bond fund., also discussed on FWF. One major difference between XRB and the PH&N fund is the way the CPI distribution is handled. This distribution must be made each year because the Canada Revenue Agency deems it to be a taxable gain. iShares consolidates the distribution in XRB, so no cash is available; the consolidation increases the holder's cost base if the ETF is held in a taxable account. The 2008 consolidation amounted to $0.43942/unit, or about 2.5%. PH&N intends to distribute the CPI adjustment as cash or reinvest it in fund units at the unitholder's choice. The cash yield of the PH&N fund will therefore be greater than the cash yield of XRB. However, if a PH&N unitholder elects to receive those distributions in cash, the value of his principal will be eroded by inflation unless he manually reinvests the CPI adjustment. iShares' automatic reinvestment and consolidation of the CPI adjustment preserves the principal in real terms but provides a more modest cash flow.

TIPS

A similar indexed bond offered in the United States is called American Treasury Inflation-Protected Securities (TIPs). These bonds can be purchased directly from any major brokerage, and should be held in a tax-deferred account if purchased directly. An ETF with the symbol TIP is also available.