Real Return Bonds

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. 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. 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) 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. At the end of 2018, RRBs represented about 9% of all marketable federal debt outstanding. In other words, RRBs are only a small part of the federal debt, which itself represents only a portion of the Canadian fixed income market. Furthermore, trading of RRBs on the secondary market represented a relatively small share (about 2-5%) of overall trading in Government of Canada securities.

When issued, federal RRBs have 30 year maturities. There have been calls (e.g., ) for the government to issue RRBs with shorter maturities.

The key benefits of RRBs are:

• a known real rate of return (if held to maturity)
• 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 CPI_base. Thereafter, both the principal and the coupon are indexed according to the CPI_base. 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 CPI_base. The new base CPIs of the current federal RRBs are as follows:

CPI_base Values for Canadian RRBs

Coupon (%)	Bond maturity	New CPIbase
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
0.50	1 December 2050	129.96667
0.25	1 December 2054	139.67000

The reference CPI and index ratio

The "Reference CPI" (or "Ref CPI_Date") is calculated for each day of the month and used to calculate the value of the coupons and principal. On the first day of each month, Ref CPI_Date is "the CPI for the third preceding calendar month". For example, "the reference CPI for December 1 in any year will be the CPI for September in that year". For days other than the 1st of the month, it is calculated by "linear interpolation between the reference CPI applicable to the first day of the month in which such day falls and the reference CPI applicable to the first day of the month immediately following".

This Reference CPI is divided by the base CPI for each bond to calculate an Index Ratio which is used to adjust the price and coupon 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 maintained by FWF member Shakespeare. 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.

Principal and coupons

At maturity, the principal is returned to the bond holder with an inflation adjustment called "inflation compensation":

Final Payment = Principal + Inflation Compensation.

This Inflation Compensation accrues daily and is related to the Index Ratio:

Inflation compensation = ((Principal x Index Ratio) – Principal).

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 payment_i = real coupon rate/2 x (Principal + Inflation Compensation_i).

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.

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. Here was the Canadian Fixed Income's (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

Individual issues

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:
   • 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 (TSX: XRB) and the BMO Real Return Bond Index ETF (TSX: ZRR). Note that these ETFs have long durations, so they are sensitive to changes in interest rates. This means a volatile share price.

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

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 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.

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.

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.

Treasury Inflation-Protected Securities (TIPs)

Similar indexed bonds offered in the United States are 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.

A US-listed ETF with the symbol TIP is also available. Recently, Canadian-listed ETFs offering exposure to TIPS have appeared, with or without hedging back to Canadian dollars (CAD). The following ones have been discussed on the Financial Wisdom Forum:

• BMO Short-Term US TIPS Index ETF (Hedged Units) (ZTIP.F)
• Mackenzie US TIPS Index ETF (CAD-Hedged) (QTIP)
• iShares 0-5 Year TIPS Bond Index ETF (CAD-Hedged) (XSTH)

These TIPS ETFs have much lower durations relative to RRB ETFs, so should be less volatile, but don't protect directly against Canadian inflation (instead, they track US inflation). Only the CAD-hedged funds are listed above since most Canadian investors want Canadian dollars to spend.

Historical rates and return data

Historical rates are available from the Bank of Canada.

Total return data, before and after inflation, are available from Libra Investment Management 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.

See also

• Tax-efficient investing
• Fixed income

Further reading

• Financial Wisdom Forum topic: "Real Return Bonds"
• Financial Wisdom Forum topic: "Barclay's Real Return Bond ETF (Symbol-XRB)"
• Financial Wisdom Forum topic: "PH&N Inflation-Linked Bond Fund"
• Financial Wisdom Forum topic: "What are you going to do with the 2021 RRB?"

External links

• Bank of Canada, Inflation expectations and Real Return Bonds, Summer 1996
• Department of Finance Canada, Tax Treatment of Government of Canada Securities (Government of Canada Securities - Technical Guide)
• TD Canada Trust, Government of Canada Real Return Bonds, a brief summary of RRBs by one of the principal dealers in the bond market.
• Libra Investment Management, Nominal bonds, indexed bonds, or some of each? , a couple of intriguing charts to help you decide how to divide your portfolio between RRBs and nominal bonds.
• Bylo Selhi's website, Real Return Bonds for Canadian Dummies
• Bogleheads:Treasury Inflation Protected Security
• Bank of Canada, Government of Canada Real Return Bond Consultations Summary, March 2020
• David W. Peters (2007) The behavior of government of Canada real return bond returns, International Review of Financial Analysis 16:152-171