Real Return Bonds

From finiki
Jump to: navigation, search

A Real Return Bond (RRB) is a bond issued by the Government of Canada (GoC) and/or certain provincial governments that pay you a rate of return that is adjusted for inflation.[1] RRBs are unsecured, unconditional obligations of Her Majesty in right of Canada, may not be called for redemption prior to maturity and have a nominal principal amount of $1000.[2] With conventional bonds, inflation erodes the real return (yield minus inflation). RRBs assure that your rate of return is maintained regardless of the future rate of inflation. RRBs pay interest semi-annually based on an inflation-adjusted principal, and at maturity they repay the principal in inflation-adjusted dollars.

RRBs can be difficult to understand, particularly because of the ongoing inflation-adjustments to their interest payments and market price, but also because of the way in which they are taxed. The purpose of this article is to provide a convenient summary.

At the date of issue, RRBs have a nominal coupon rate plus a base value of the consumer price index (CPI)[note 1] 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.

Because the inflation indexing of the capital results in deemed income from individual bonds with no cash immediately received, they should be held in tax sheltered accounts.

RRBs are not as liquid as other Canada bonds and are generally recommended as primarily buy and hold investments.

The key benefits of RRBs are:

  • a known real rate of return
  • returns are highly correlated with inflation
  • low correlation with other asset classes

How they work

The base CPI

The Bank of Canada (BoC) issues a RRB with a specified maturity. At the date of issue, a base value of CPI is associated with the bond, this is known as the CPIbase. Thereafter, both the principal and the coupon are indexed according to the CPIbase. 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.[2] However, since that report was issued, there has been an adjustment in the CPIbase. The new base CPIs of the current federal RRBs are as follows:

CPIbase Values for Canadian RRBs[3]
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
1.25 1 December 2047 123.29032

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[4] and used by financial institutions to determine purchase and sale prices. A spreadsheet that calculates the index ratios is maintained by FWF member Shakespeare.[5] For a 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 February 13, 2009, settlement date is February 19, 2009. On February 19, 2009 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 February 19 2009
Bond maturity Index ratio
1 December 2021 1.36723
1 December 2026 1.29331
1 December 2031 1.24297
1 December 2036 1.10286
1 December 2041 1.02128
1 December 2044 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 February 13, 2009 was $120.39 in constant dollars. The corrected price for settlement at this price on February 19, 2009 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 December 1. The interest payments, like the principal, are adjusted for CPI changes by multiplying constant-dollar amounts by the index ratio. The semi-annual nominal coupon payments are calculated as follows:

coupon paymenti = real coupon rate/2 x (principal + inflation compensationi) where inflation compensationi = ((principal x reference CPIi/reference CPIbase) – principal). [6]

Simple example

On a $1,000 bond, if the coupon interest rate is 3% and inflation is 1% after six months, the principal is adjusted to $1,010. You then receive a semi-annual interest payment of $15.15. If inflation rises to 3% by year end, the principal is adjusted to $1,030. You then receive another interest payment of $15.45. Assuming similar inflation over 10 years, you will receive $351.64 in interest payments while the principal will have risen to $1,343.92.[7]

Effect of deflation

In the event of deflation, the nominal dollar amount received for a 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 February 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 Treasury Inflation-Protected Securities (TIPS), the US counterpart of RRBs, can be found here.

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

Understanding RRB quotes

How to determine the price of an RRB

You can obtain the most authoritative RRB pricing by contacting the bond desk at your broker. The Globe and Mail's GlobeInvestor publishes RRB prices on a daily basis. You can also get RRB pricing at Canadian Fixed Income's (CFI) RRB Offer Prices and Yields. While these numbers will vary somewhat from your broker's quotes, they're much more convenient to obtain. Here is the CFI quote from 04Dec09:

Canadian Fixed Income quotes
December 4, 2009
Coupon Maturity Price Yield
Canada 4.250 2021-Dec-01 131.92 1.35
Canada 4.250 2026-Dec-01 140.57 1.53
Canada 4.000 2031-Dec-01 146.59 1.50
Canada 3.000 2036-Dec-01 132.92 1.51

An RRB quote consists of two numbers, Real Price and Real Yield. You can determine the approximate market value of an RRB by multiplying the real price by the Index Ratio1. Using CFI's real price, 131.92, and the index ratio (based on the spreadsheet cited in the footnote), 1.38045, the price of the 01Dec21 4.25% RRB was $182.11. This means that for every $100 of face value you buy you'll pay approximately $182.11. In practice you'll pay somewhat more and, if you sell, you'll get somewhat less because your broker adds a commission on every transaction.

As with any bond, you must also add the interest that's accrued since the last coupon interest payment. You'll have to pay that if you're buying and you'll receive that much extra if you're selling.

Meaning of real yield

This is the inflation-adjusted yield that you'll earn on an RRB that you buy now at the listed real price and hold to maturity. This represents the coupon rate (4.25% for the 2021 series in the example) discounted by the current real price (131.92 in the example.)

Determining the value of an interest payment

All series of RRBs pay interest on June 1st and December 1st. For every $1,000 face value you'll receive an interest payment of $1,000 times half the coupon rate (e.g. 0.0425/2) times the then current index ratio.

Determining the value when RRB matures

When an RRB matures, you'll get the face (par) value times the then current index ratio. In other words, you'll get the face value indexed for inflation. This will probably be more than the original face value, but if there's been a period of deflation, it could be less.

Inflation expectation impact to RRB price

This can be estimated by comparing the yield of a nominal bond with a similar maturity as the RRB. If the 01Dec21 RRB yields 3.79% and the closest nominal GoC bonds, the Jun 2021 and Jun 2022 bonds, yield 5.87% and 5.91% respectively, the implied nominal yield for the RRB is about 5.89% (the average of the two closest nominal bonds) and the inflation expectation is about 5.89%-3.79%, or 2.1%. If the average inflation rate from now until 2021 exceeds 2.1%, then the RRB will have been the better investment. Conversely if inflation is lower than 2.1%, the nominal bond will have been a better investment.

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.

Use this checklist to ensure that you have all the information you need to make an informed purchase.

  1. Check the current approximate real yield and real price in the newspaper or at the Bank of Canada website.
  2. Call your broker and ask for the following information about your prospective RRB purchase:
    • Face value:
    • Maturity date:
    • Coupon yield:
    • Real yield to maturity:
    • Current market price:
    • Real price:
    • Index ratio[note 2]:
    • Accrued interest:
  3. Confirm that Current market price = Real price x Index ratio
  4. Confirm total cost = (Face value/100 x Current market price) + Accrued interest
  5. Confirm that the Index ratio matches the Bank of Canada's number. (See link at top of this page and remember to use the settlement date.)
  6. Check that the real yield you're quoted is plausible using a bond calculator. (For Price use Current market price divided by Index ratio.)
  7. When you make a purchase record the above information along with the date/time and the name of the representative with whom you spoke.
  8. When your confirmation slip arrives make sure it agrees with the information you recorded.

RRB exchange traded and mutual funds

The are two exchange-traded funds (ETFs) for Canadian RRBs, the iShares Canadian Real Return Bond Index ETF[8] (TSX: XRB) and the BMO Real Return Bond Index ETF[9] (TSX: ZRR).

Philips, Hagar and North also has a mutual fund, the PH&N Inflation-Linked Bond Fund.[10]

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 adjusted cost base if the ETF is held in a taxable account. The 2013 capital gains distribution was $0.90523 per share, i.e. over 3% of the share price [11] PH&N intends to distribute the CPI adjustment as cash or reinvest it in fund units at the unitholder's choice.[12] 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.

Stripped RRBs

Some securities dealers strip the coupons from RRBs, sell them individually, as well as selling the remaining principal (called the residual.) Note that each of the stripped coupons behaves just like the residual, i.e. they each make only a single payment at a specified date in the future. A word of caution is in order here, stripped RRBs tend to be illiquid, not often available, and should be held to maturity.

Taxation of RRBs

Like nominal bonds, RRB interest is taxed as ordinary income at your marginal tax rate. Inflation adjustments are also taxed annually as ordinary income as they accrue even though you won't receive them until the bond matures, possibly many years later. There are also regular CPI inflation adjustments on the principal. In taxable accounts these are taxed every year as they accrue even though you may not see the cash for up to 30 years when the RRB matures. This tax treatment means they should be held in registered accounts, such as a Registered Retirement Savings Plan, Registered Retirement Income Fund or other tax sheltered accounts.

Risks of RRBs

All securities, including bonds that are guaranteed by the Government of Canada, carry some risks. However, RRBs are among the least risky investments.

Like nominal fixed-coupon marketable bonds, if you sell an RRB prior to maturity the price you realize will be based on the prevailing interest rate and could be less than what you originally paid.

In addition, if you buy an RRB on the secondary market, it's possible that after a period of deflation you may receive a principal repayment that's based on a lower index ratio than when you bought the bond.

Moreover, even if you buy an RRB at issue, in the unlikely event that there is net deflation over the 30-year holding period, you could receive less than face value. But keep in mind that even if you were to get less than face value at maturity, your purchasing power would still be preserved. Indeed, if you had reinvested the coupons in more RRBs inside a tax-sheltered account, at maturity the purchasing power of your initial investment would have grown significantly.

And, although extremely unlikely, RRB values may also be subject to changes in how the CPI is calculated or even issuer default.

Investors need to be aware that the semi-annual interest payment received may rise or fall from one payment date to the next due to the impact of the Index Ratio and such variations may be material during periods of significant changes in the CPI.[2]

There is also an indexing lag as the calculation of the Index Ratio incorporates an approximate three-month lag, which may have an impact on the trading price of a series of Bonds, particularly during periods of significant changes in the CPI.[2]

Treasury Inflation-Protected Securities (TIPs)

Similar indexed bonds offered in the United States are called American Treasury Inflation-Protected Securities (TIPs)[13]. These bonds can be purchased directly from any major brokerage, and should be held in a tax-deferred account if purchased directly. An US ETF with the symbol TIP is also available.[14]

Historical rates and return data

Historical rates are available from the Bank of Canada.[15]

Total return data, before and after inflation, are available from Libra Investment Management[16] and plotted year by year at Canadian asset class returns. The worse nominal returns for RRBs were -14% in 1994, and -13% in 2013. The highest nominal return was +19% in 1993. Over the period 1993-2013, the standard deviation of RRBs was about 10%, compared to about 6% for all Canadian conventional bonds.

Real returns for various investments are also available from Thornburg Investment Management.[17]


  1. CPI for purposes of the Bonds is defined as the All-items Consumer Price Index for Canada, not seasonally adjusted, as published by Statistics Canada (or its successor government department or agency).
  2. The index ratio that you'll be quoted by a broker is based on the settlement date, three trading days later, rather than the date you place the trade.

See also


  1. Hank Cunningham, Defending Against Rising Inflation and Interest Rates. Viewed April 5, 2006.
  2. 2.0 2.1 2.2 2.3 Bank of Canada, Canada Real Return Bonds, November 25, 1994. Accessed December 8, 2013.
  3. Bank of Canada. Real Return Bonds:Index Ratio in PDF Format 2013-December, viewed December 7, 2013.
  4. Bank of Canada, Government Securities Auctions: Real Return Bonds. Viewed November 25, 2016.
  5. Shakespeare's RRB Index Ratio Worksheet, viewed March 9, 2016.
  6. Government of Canada Market Debt Instruments (Government of Canada Securities - Technical Guide), viewed December 7, 2013.
  7. Business Week, How Inflation-Indexed Bonds Work, June 23, 1997. Accessed December 8, 2013.
  8. iShares Canadian Real Return Bond Index ETF. Viewed Dec. 26, 2014.
  9. BMO Real Return Bond Index ETF - Fixed Income - BMO Exchange Traded Funds (ETFs), accessed December 8, 2013.
  10. Philips, Hagar, and North. Inflation-Linked Bond Fund. Accessed December 8, 2013.
  11. BlackRock Canada, iShares Canadian Real Return Bond Index ETF. Viewed Dec 26 2014.
  12. Philips, Hager, and North, personal communication to K.R. Betty, dated October 8 2009.
  13. Wikipedia, TIPS. Viewed February 17, 2009
  14. BlackRock US, iShares TIPS Bond ETF (TIP). Viewed Dec. 26 2014.
  15. Selected Bond Yields - Bank of Canada. Viewed December 16, 2014
  16. Libra Investment Management Inc., viewed December 16, 2014.
  17. Thornburg Investment Management, A Study of Real Real Returns, Viewed December 16, 2014.

Further reading

External links