THE BEHAVIOUR OF GOVERNMENT OF CANADA REAL RETURN BOND RETURNS: AN EMPIRICAL STUDY

ASAC 2005 Toronto, Ontario David W. Peters Faculty of Social Sciences University of Western Ontario THE BEHAVIOUR OF GOVERNMENT OF CANADA REAL RETURN BOND RETURNS: AN EMPIRICAL STUDY The Government of Canada first issued real return bonds, commonly referred to as indexlinked bonds in the finance literature, in December 1991. This paper empirically examines the holding period returns of real return bonds between 1992 and 2003. This study finds that the real return bond holding period returns were positively related to changes in the year-over-year inflation rate but with a lagged effect, were negatively related to changes in nominal interest rates, but were unrelated to changes in either the stock exchange index or the value of the Canadian dollar. Introduction In an effort to develop a financial security that provided inflation protection to investors and simultaneously lowered its expected financing costs, the Government of Canada developed a security called real return bonds (RRBs). The first issue, with a coupon rate of 4.25% and a maturity date of December 1, 2021 was first opened in December 1991 and has since been reopened several times. There have been three additional RRB issues since the original one with maturity dates of December 1, 2026, December 1, 2031, and December 1, 2036. As of July 2003, the total face value of real return bonds issued by the Canadian government was $16,625 million, which represented approximately 4.5% of its Canadian dollar marketable debt. 1 Further details of the four issues are shown in Table 1. RRBs are bonds issued by the Government of Canada which guarantee the investor a fixed real rate of return if held to maturity, subject to lag effects. When one buys an RRB, both coupon and principal payments are adjusted to changes in the consumer price index (CPI). A detailed description of the indexing process is provided in Appendix 1. The structure of real return bonds has been relatively successful, and the U.S. Treasury decided to structure their indexed bonds in a similar way when they introduced them in 1997. 2 The real return bonds issued by the Government of Canada are a type of bond that is more generally referred to internationally as indexed-linked bonds. A number of arguments have been made for governments to issue index-linked bonds. Some of the arguments for governments to issue index-linked bonds are related to the demand for such instruments by investors while other arguments focus on the cost of index-linked bonds or the motivational aspects of indexlinked bonds. The specific reasons why the British, Swedish and U.S. government made decisions 1 Bank of Canada, Real Return Bond Funding Review, August 2003, www.bankofcanada.ca. 2 Roll (1996) provides a detailed description of how the U.S. Treasury made its decisions about the design of its indexed bonds. 47

to issue index-linked bonds are discussed in articles by Townend (1997), Persson (1997) and Wilcox (1998) respectively. Table 1 Face Value of Real Return Bonds Issued by the Government of Canada as of July 2003 Maturity Date Face Value Amount Issued (Millions of Dollars)* Coupon Rate When Originally Issued December 1, 2021 $5,175 4.25% December 1991 December 1, 2026 5,250 4.25% December 1995 December 1, 2031 5,800 4.00% March 1999 December 1, 2036 400 3.00% June 2003 * The amounts in this column do not include adjustments for changes in the CPI since the issue date. Source: Bank of Canada, Real Return Bond Funding Review, August 2003, www.bankofcanada.ca. There is a significant clientele of investors who are very concerned about the variability of inflation and desire to invest in such financial instruments. In particular, some pension funds and insurance companies that have inflation-indexed liabilities are interested in investing in indexed bonds to hedge inflation risks. Bodie (1980, 1991 and 1997) has argued that indexed bonds are a useful innovation in terms of providing indexed retirement incomes, and that funds could use hedging strategies involving index-linked bonds. Some individual investors may find an index-linked bond useful as it will help these investors provide for themselves a stable real retirement income. From the viewpoint of a government wishing to minimize its cost of financing, it has been argued that governments should be able to reduce their expected cost of financing by issuing index-linked bonds. This is because investors, in equilibrium, will not demand a premium for inflation volatility when they invest in index-linked bonds in the same way that they do from conventional nominal bonds. The term structure theory of Cox, Ingersoll and Ross (1985) suggest that the interest rate on a nominal zero coupon bond should be equal to the real rate of interest plus the expected inflation rate plus an inflation risk premium. Barone and Masera (1997) suggest that a government can annul the inflation risk premium by issuing index-linked bonds. It should be noted that the value of real return bonds in Canada are adjusted to the CPI with a 2.5 month lag, and it seems reasonable that investors should require a very small inflation risk premium on real return bonds. If the Cox, Ingersoll and Ross model is an accurate explanation of how required yields on bonds are determined, governments should be able to reduce their financing costs by issuing index-linked bonds. This paper will empirically examine the behaviour of real return bond returns. Since real return bonds have now been traded in Canada for over 12 years, there is now a sufficiently large amount of data that it is possible to test a number of hypotheses about the behaviour of real return bond prices. Literature on index-linked bonds will be reviewed in the second section, followed by an empirical analysis of RRB holding period returns in the third section and, finally, concluding remarks in the last section. 48

Literature Review There has been a significant amount of research published on index-linked bonds, especially during the past 15 years. This literature review will focus on studies that have looked theoretically at the factors that affect index-linked bond prices, empirical studies that have examined the cost of issuing index-linked bonds, and empirical research related to the behaviour of index-linked bond holding period returns and yields. The empirical modeling of the factors affecting real return bond returns is based on a theoretical model of the behaviour of real return bond prices developed by Peters (1996). Peters found that real return bond prices were theoretically affected by a number of factors. He found that (1) the price of an RRB should be negatively related to the real rate of interest, (2) a change in nominal yields of conventional bonds should cause the value of an RRB to move in the opposite direction but the impact will depend on how much the real rate of interest changes when the nominal yield changes, (3) a change in the inflation rate should have no significant impact on the price of an RRB as long as the change in the inflation rate does not affect the real rate of interest or the inflation risk premium, (4) an unexpected shock to the price level should cause the value of an RRB to change slightly less than proportionately to the change in the price level if the next coupon date is less than two months away, 3 and (5) a change in the volatility of the inflation rate should have no significant impact on the price of an RRB. There have been a few studies that have looked empirically looked at the cost of issuing index-linked bonds versus the cost of issuing conventional nominal bonds. These studies should also be interesting from an investment point of view since the costs incurred by governments also represent the returns earned by RRB investors. Empirically, it has been found that the cost of issuing index-linked bonds has been cheaper than that of conventional bonds. Townend (1997) found that the cost of index-linked bonds had been lower than the cost of conventional bonds in Britain where inflation after the bonds were issued has been lower than the difference between the nominal yield on conventional bonds and the real yield on indexed bonds. Foresi, Penati and Pennacchi (1997) and Barone and Masera (1997) found that Italy s savings between 1983 and 1993 by issuing indexed-linked bonds versus conventional nominal bonds were very substantial. 4 There have been a small number of studies that have empirically examined what factors affect yields and holding period returns on Canadian real return bonds. Lewis and Adamo (1994) examined the RRB real yields and found that they were positively affected by the difference 3 If the unexpected price shock occurs between 2 and 3 months before the coupon date, the effect on the value of RRBs will depend on the exact procedures used by Statistics Canada in calculating the CPI for the month in which the price shock occurs. The change in the value of RRBs should be proportionate if the next coupon payment is at least 3 months away. 4 The yield on conventional debt was between 13.45% and 13.79%, while the initial real yield on the indexed-linked bonds was 2.5% and the inflation rate during this period was 6.05%. This would suggest either that the inflation risk premium demanded by investors was very large, perhaps as large as 5%, or that inflation ended up being far below initial expectations. 49

between conventional long bond yields and the current inflation rate, positively affected by inflation expectations as measured by the 36-month average of the year-over-year CPI, and negatively related to inflation direction. Quick (2001) examined the price sensitivity of RRBs between April 1996 and August 2001 and found that they had an implied modified duration of 4.82 during this period but the relationship was not stable throughout this period. 5 Peters (1996) examined the holding period returns on real return bonds between January 1992 and June 1995, and found that they were negatively related to the changes in long-term bond yields, positively related to returns on TSE total return index, but that the relationship between RRB returns and changes in the inflation rate appeared to be weak. This current paper tries to improve on the study of Peters (1996) by looking at holding period returns on two different RRB issues, including a much larger number of observations, and by examining the lagged effect of changes in inflation on RRB holding period returns. Empirical Analysis of RRB Holding Period Returns Nominal monthly holding period returns for the first two Government of Canada Real Return Bond issues, i.e., the 4.25% RRB issue due in December 2021, and the 4.25% RRB issue due in December 2026, were computed based on raw data provided by Beutel Goodman Canada. It was felt there were too few observations to analyze the holding period returns on the 4.00% RRB issue due in 2031, which was issued in March 1999, and the 3.00% RRB issue due in December 2036, which was issued in 2003. The results are shown in Table 2. The holding period returns for the RRB due in 2021 were analyzed from January 1992 to December 2003, while the holding period returns for the RRB due in 2026 were analyzed from January 1996 to December 2003. The average monthly holding returns on the RRB due in 2021 was 0.66% between 1992 and 2003, which is equivalent to 7.9% on an annual basis. The average monthly holding period return on the RRB due in 2026 was 0.77% between 1996 and 2003, which is equivalent to 9.2% on an annual basis. The higher average holding period return for the latter bond was because real yields rates stayed at about the same level between January 1992 and December 1995 while real yields declined since January 1996. The standard deviations of the monthly returns were 1.60% for the RRB due in 2021 and 1.52% for the RRB due in 2026; the riskiness of the real return bonds was much lower than the risk of conventional bonds of similar maturities. Table 2 Statistical Summary of RRB Holding Period Returns RRB Issue RRB Due Dec. 2021 RRB Due Dec. 2026 Average Monthly Holding Period Return 0.66% 0.77% Standard Deviation of Monthly Holding Period Returns 1.60% 1.52% Number of Observations 144 96 5 The implied duration was 7.68 between April 1996 and December 1998 but only 1.03 between January 1999 and August 2001. During the latter period, changes in nominal bond yields were primarily driven by increases in the CPI. 50

Regression analysis was used to try to explain the pattern in monthly holding period returns. The theoretical model of real return bond prices by Peters (1996) showed that the major force behind changes in RRB values should be changes in the real yield. The real yield should be a function of the nominal required yield and the expected inflation rate. Therefore, variables representing changes in the long-term bond yield and changes in the CPI inflation rate were used as independent variables. Since the CPI index is announced with a lag of 20 days on average (although astute observers might be able to guess its level before the announcement), it was decided to include lagged independent variables for changes in the CPI inflation rate as well. 6 Historically, stock prices have moved inversely with real interest rates. Therefore, an explanatory variable representing the holding period return on the TSE Total Return Index was used as an independent variable. The combination of purchasing power parity and interest rate parity theories suggests that the value of the Canadian dollar should be inversely related to real interest rates, and therefore a variable representing the percentage change in the value of the Canadian dollar was used as an independent variable. The full model estimated is as follows: HPR + β 6 t = α + β1( DCP) t + β 2 ( DCP) t 1 + β3( DCP) t 2 + β 4 ( DCP) t 3 + β5 ( DBY ) t ( DTS ) + β ( DCD) + ε t 7 t t where HPR t is the holding period return on the RRB in month t, DCP t is the change in the unadjusted year-over-year CPI inflation rate for month t, DCP t-1, DCP t-2 and DCP t-3 are the changes in the unadjusted year-over-year CPI inflation rate for months t-1, t-2 and t-3 respectively, DBY t = the change in the long-term bond yield in month t, DTS t = the percentage change in the TSX total return index in month t, and DCD t = the percentage change in the Canadian dollar versus the US dollar in month t. All of the independent variables were calculated based on raw data from the Bank of Canada Review and the Bank of Canada website. The results of estimating the model using ordinary least squares regression analysis for the RRB issues due in 2021 and 2026 are shown in Tables 3 and 4 respectively. Changes in the inflation rate appear to have a lagged effect on the holding period returns of real return bonds. To examine the lagged effect, the holding period returns in month t were regressed on changes in the annual inflation rate in month t in equation 1, and then lagged inflation rate change variables were introduced in equations 2, 3 and 4. The results show that changes in the annual inflation rate have a significant effect, with most of the effect happening with a lag of one or two months. Given the coefficients in equation 4 in Table 3 and 4, the cumulative effect of a 0.1% change in the inflation rate was to change the value of the RRBs by 0.24%. In equation 10, where all variables were included in the regression equations, the cumulative effect of a 0.1% change in the inflation rate appears to have been a 0.21% change in the value of the first RRB and a 0.25% change in the value of the second RRB. If the changes in the inflation rate had only been temporary and had represented unexpected price shocks, one would expect the response of the RRB holding period returns to be approximately proportional to the changes in the inflation rate. The observation that the change in RRB holding period returns (1) 6 The CPI is announced somewhere between 16 and 24 days after the end of the month. 51

was more than proportional suggests that changes in the year-over-year inflation rate are sometimes temporary but sometimes reflect changes in the expected long-run inflation rate. The observation that most of the effect of changes in inflation on RRB returns happens with a lag of one or two months requires some further explanation; it would seem plausible that investors do not actually react to changes in inflation until Statistics Canada actually announces the consumer price index, which occurs, on average, 20 days after the month for which it is being calculated. Table 3 OLS Regression Estimation Dependent Variable= Monthly Holding Period Return on RRB Due in December 2021 EQ. # Const. DCP t DCP t-1 DCP t-2 DCP t-3 DBY t DTS t DCD t R 2 / Adj. R 2 F/ D.W. 1.007*.306.007 1.02 T-Stat (4.96) (1.01).000 1.15** 2.007*.164 1.050*.089 6.91 T-Stat (5.29) (.56) (3.57).076 1.23** 3.007*.230.923*.856*.144 7.83 T-Stat (5.55) (.80) (3.18) (2.98).125 1.25** 4.007*.162.962*.771*.512.163 6.78 T-Stat (5.67) (.56) (3.34) (2.67) (1.81).139 1.27** 5.006* -3.084*.221 40.40 T-Stat (4.85) (-6.36).216 1.39** 6.006*.081*.053 8.01 T-Stat (4.43) (2.83).047 1.16** 7.007*.166.026 3.86 T-Stat (5.07) (1.96).020 1.16** 8.006*.050.914*.652*.458-2.857*.351 14.90 T-Stat (5.63) (.20) (3.59) (2.54) (1.83) (-6.31).327 1.52** 9.006*.042.904*.649*.463-2.673*.040.363 13.00 T-Stat (5.31) (.17) (3.57) (2.55) (1.86) (-5.76) (1.62).335 1.53** 10.006*.041.904*.647*.463-2.671*.040.004.363 11.06 T-Stat (5.25) (.16) (3.55) (2.51) (1.85) (-5.72) (1.47) (.05).330 1.53** DCP t = change in the year-over-year unadjusted CPI inflation rate in month t. DCP t-1, DCP t-2, DCP t-3 = change in the year-over-year unadjusted CPI inflation rate for the months t-1, t-2 and t-3 respectively. DBY t = change in the long-term bond yield in month t. DTS t = the return on the Toronto Stock Exchange total return index in month t. DCD t = the percentage change in the value of the Canadian dollar versus the US dollar in month t. * Statistically significant at the 5% level. ** Positive serial correlation was detected using an α = 5%. The effect of changes in the conventional long-term bond yield on RRB holding returns is estimated using equation 5. The results are quite statistically significant. The results of estimating 52

equation 5 shows that a 1 basis point change in the conventional long-term bond yield caused a 0.031% reduction in the value of the first RRB and 0.028% reduction in the value of the second RRB. As shown in equation 10, the effect was only slightly different when all variables were included in the regression equations. The results suggest that RRBs have interest rate sensitivities similar to conventional bonds that have maturities in the range of three to four years. Since the RRBs studied actually had maturities of at least 19 years and the value of RRBs should vary significantly with changes in real interest rates, these results seem plausible if most of the changes in conventional long-term yields over the period from 1992 to 2003 were accompanied by changes in expectations about long-term inflation. Table 4 F/ OLS Regression Estimation Dependent Variable = Monthly Holding Period Return on RRB Due in December 2026 EQ. # Const. DCP t DCP t-1 DCP t-2 DCP t-3 DBY t DTS t DCD t R 2 / Adj. R 2 D.W. 1.008*.215.004.33 T-Stat (4.95) (.58) NM 1.30** 2.008*.103.929*.069 3.44 T-Stat (5.14) (.28) (2.56).049 1.40** 3.008*.318.788* 1.010*.143 5.12 T-Stat (5.35) (.88) (2.23) (2.82).115 1.37** 4.008*.299.839*.972*.249.147 3.93 T-Stat (5.34) (.82) (2.31) (2.67) (.69).110 1.37** 5.007* -2.847*.152 16.90 T-Stat (4.83) (-4.11).143 1.45** 6.007*.043.021 1.97 T-Stat (4.69) (1.40).010 1.27** 7.008*.156.028 2.74 T-Stat (4.96) (1.65).018 1.31** 8.007*.238 1.007*.866*.405-3.002*.313 8.22 T-Stat (5.31) (.73) (3.06) (2.64) (1.23) (-4.66).275 1.65*** 9.007*.222 1.010*.880*.422-2.896*.031.324 7.10 T-Stat (5.09) (.68) (3.07) (2.68) (1.28) (-4.46) (1.17).278 1.66*** 10.007*.218 1.014*.855*.414-2.875*.019.077.329 6.17 T-Stat (5.12) (.67) (3.08) (2.59) (1.26) (-4.42) (.64) (.83).276 1.68*** DCP t = change in the year-over-year unadjusted CPI inflation rate in month t. DCP t-1, DCP t-2, DCP t-3 = change in the year-over-year unadjusted CPI inflation rate for the months t-1, t-2 and t-3 respectively. DBY t = change in the long-term bond yield in month t. DTS t = the return on the Toronto Stock Exchange total return index in month t. DCD t = the percentage change in the value of the Canadian dollar versus the US dollar in month t. * Statistically significant at the 5% level. ** Positive serial correlation was detected using an α = 5%. *** Tests for positive serial correlation were inconclusive using α = 5%. NM = Not Meaningful since reported Adjusted R 2 is less than zero. 53

The relationship between RRB holding period returns and TSX index returns is estimated using equation 6. To be more precise, the coefficients estimated in equation 6 are the betas of the RRBs as if they were stocks. The first RRB had a very small but statistically significant beta of 0.081 while the beta of the second RRB appears to be statistically insignificant. As shown in equation 10, the relationship between RRB holding period returns and TSX index returns was statistically insignificant when all variables were included in the estimation. The results show that the behaviour of RRBs and stocks are very dissimilar. The effect of changes in the Canadian dollar on RRB holding returns is estimated using equation 7. The estimated coefficients are positive, as one would expect, but not quite statistically significant at the 5% level. The estimated coefficients remain statistically insignificant when all variables are included in the estimation, as shown in equation 10. The Durbin-Watson statistics were tested for significance at an α level of 5%. Positive serial correlation was detected in all equations explaining the returns on the RRB due in 2021 and in the first 7 equations explaining the holding period returns for the RRB due in 2026. Tests of positive serial correlation were inconclusive for equations 8 through 10 that explain the holding period returns on the RRB due in 2026. Because of the serial correlation detected, the equations were re-estimated using maximum likelihood estimation, and are shown in Tables 5 and 6. The maximum likelihood estimation results are fairly similar to the OLS results. Conclusions The behaviour of Government of Canada real return bonds has been examined in this study. There have been a number of interesting findings. The holding periods of real return bonds move positively with changes in the year-over-year inflation rate, but with a lag where the bonds respond one or two months after the inflation rate has increased; a change of 0.1% in the inflation rate caused the value of RRBs to change by about 0.24%, on average, including the lagged effects. The RRB holding returns move negatively with changes in the yields on long-term conventional bonds; on average, they respond similarly to conventional nominal bonds that have a maturity in the range of 3 to 4 years. RRB returns do not tend to move systematically with stock market returns. RRB holding period returns are unaffected by changes in the Canadian dollar. Further research related to Canadian real return bonds and index-linked bonds in an international context could take a number of directions. Empirical research could be done to assess whether the differences in return between real return bonds and conventional bonds reflects their relative risks. It would be interesting to compare this difference between nominal yields on conventional bonds and real yields on RRBs to inflation forecasts provided by major economic forecasters. Research could also be directed at examining the holdings of RRBs by institutional investors in an attempt to answer the question as to why some funds invest in RRBs while others do not. Such research would also be helpful to the Canadian government and investment bankers in terms of focussing their marketing efforts. Given that Canadian real return bonds have been outstanding now for over 13 years, it would be interesting to assess whether the issuance of real return bonds by the federal government has been good from a public policy perspective. Such a perspective could be both in providing a needed new investment vehicle for the public as well a 54

whether the RRBs have had the effect of reducing the public cost of the national debt in Canada as well as the effects in those other nations issuing index-linked bonds. Table 5 Maximum Likelihood Estimation Dependent Variable = Monthly Holding Period Return on RRB Due in December 2021 EQ. # Const. Rho DCP t DCP t-1 DCP t-2 DCP t-3 DBY t DTS t DCD t Log Likelihood 1.007*.427*.105 406.60 T-St. (3.12) (5.75) (.39) 2.007*.399*.273.760* 410.54 T-St. (3.44) (5.27) (1.01) (2.84) 3.007*.382*.391.931*.701* 413.97 T-St. (3.73) (4.86) (1.46) (3.44) (2.62) 4.007*.375*.375.997*.787*.399 415.12 T-St. (3.86) (4.68) (1.41) (3.66) (2.89) (1.51) 5.006*.367* -2.182* 418.47 T-St. (3.40) (5.01) (-5.13) 6.006*.424*.065* 409.79 T-St. (2.91) (5.64) (2.56) 7.007*.423*.110 407.70 T-St. (3.21) (5.63) (1.53) 8.006*.294*.209.942*.694*.408-2.215* 428.13 T-St. (4.28) (3.87) (.85) (3.83) (2.81) (1.69) (-5.33) 9.006*.288*.197.930*.690*.403-2.070*.035 429.21 T-St. (4.12) (3.80) (.80) (3.79) (2.81) (1.67) (-4.83) (1.45) 10.006*.288*.196.930*.689*.403-2.070*.035.000 429.18 T-St. (4.08) (3.78) (.80) (3.78) (2.78) (1.66) (-4.79) (1.35) (.01) DCP t = change in the year-over-year unadjusted CPI inflation rate in month t. DCP t-1, DCP t-2, DCP t-3 = change in the year-over-year unadjusted CPI inflation rate for the months t-1, t-2 and t-3 respectively. DBY t = change in the long-term bond yield in month t. DTS t = the return on the Toronto Stock Exchange total return index in month t. DCD t = the percentage change in the value of the Canadian dollar versus the US dollar in month t. * Statistically significant at the 5% level. 55

Table 6 Maximum Likelihood Estimation Dependent Variable = Monthly Holding Period Return on RRB Due in December 2026 EQ. # Const. Rho DCP t DCP t-1 DCP t-2 DCP t-3 DBY t DTS t DCD t Log Likeli-hood 1.008*.354*.027 272.32 T-St. (3.42) (3.71) (.08) 2.008*.316*.119.642* 274.02 T-St. (3.69) (3.30) (.35) (1.87) 3.008*.308*.379.797*.964* 277.96 T-St. (3.90) (3.06) (1.10) (2.37) (2.80) 4.008*.308*.390.858* 1.003*.239 278.18 T-St. (3.90) (3.04) (1.12) (2.46) (2.87) (.69) 5.007*.307* -2.143* 278.03 T-St. (3.60) (3.21) (-3.47) 6.007*.357*.042 273.41 T-St. (3.25) (3.69) (1.46) 7.008*.344*.111 273.18 T-St. (3.47) (3.57) (1.30) 8.007*.209*.299.988*.902*.393-2.443* 285.56 T-St. (4.37) (2.12) (.92) (3.06) (2.80) (1.21) (-4.00) 9.007*.207*.286.986*.915*.392-2.346*.030 286.20 T-St. (4.22) (2.09) (.89) (3.06) (2.84) (1.21) (-3.80) (1.13) 10.007*.198*.273.990*.894*.393-2.353*.022.054 286.34 T-St. (4.27) (1.99) (.84) (3.06) (2.75) (1.21) (-3.78) (.73) (.59) DCP t = change in the year-over-year unadjusted CPI inflation rate in month t. DCP t-1, DCP t-2, DCP t-3 = change in the year-over-year unadjusted CPI inflation rate for the months t-1, t-2 and t-3 respectively. DBY t = change in the long-term bond yield in month t. DTS t = the return on the Toronto Stock Exchange total return index in month t. DCD t = the percentage change in the value of the Canadian dollar versus the US dollar in month t. * Statistically significant at the 5% level. Appendix 1: The RRB Indexing Process The indexing process for the 4.25% RRB issue due December 1, 2021 is shown below. The reference CPI on December 10, 1991 when the bond was first issued was 98. 86178. On the first day of any month, the principal amount of the RRB is adjusted so that the revised principal of the bond is equal to the original principal times the reference CPI on the first day of the month, divided by 98.86178 (the reference CPI at the time of issue). The reference CPI on the first day of any month is the unadjusted CPI for the third preceding month. For example, the reference CPI on November 1, 2003 is the unadjusted CPI for August 2003. For any other day other than the first day of the month, the reference CPI is calculated by interpolating between the reference CPIs 56

for the first days of the third and second preceding months. For example, the reference CPI on November 10, 2003 would be calculated as follows: 9 Reference CPI November 10, 2003 = CPI August 2003 + CPISeptember 2003 31 (2) At maturity on December 31, 2021, the payment to bondholders will be equal to the original principal times the reference CPI for September 2021, divided by 98.86178 (the reference CPI at the time of issue). The coupon payments are made every six months on June 1 and December 1, and are equal to 2.125% of the revised principal at the time of the coupon payment. Thus, the values of principal and coupon payments are adjusted to inflation with an average lag of 2.5 months. The indexing process for the 4.25% RRB issue due December 1, 2026 is similar to that for the RRB issue due December 1, 2021, except that the payment calculations are based on the ratios between the reference CPIs at the time of the payments and the reference CPI at the time of the original issue. The reference CPI on December 7, 1995 when the bond was originally issued was 104.51260. References Barone, E. and Masera, R.S. Index-linked Bonds from an Academic, Market and Policy-making Standpoint, in: Managing Public Debt: Index-linked Bonds in Theory and Practice, Edward Elgar Publishing, 1997, 117-47. Bodie, Z. An Innovation for Stable Retirement Income, Journal of Portfolio Management, 7(1), (Fall 1980), 5-13. Bodie, Z. Inflation, Index-linked Bonds and Asset Allocation, Journal of Portfolio Management, 16(2), (Winter 1990), 48-53. Bodie, Z. Inflation-Protected Retirement Plans, in Managing Public Debt: Index-linked Bonds in Theory and Practice, Edward Elgar Publishing, 1997, 33-49. Cox, J.C., Ingersoll, J.E. and Ross, S.A. A Theory of the Term Structure of Interest Rates, Econometrica, 53(2), (March 1985), 385-407. Foresi, S., Penati, A. and Pennacchi, G. Reducing the Cost of Government Debt: The Role of Indexed-linked Bonds, in: Managing Public Debt: Index-linked Bonds in Theory and Practice, Edward Elgar Publishing, 1997, 93-116. Lewis, M. and Adamo, D. A Valuation Model for Canadian Real Return Bonds, Scotia McLeod, 1994. 57

Persson, M. Index-linked Bonds: The Swedish Experience, in: Managing Public Debt: Indexlinked Bonds in Theory and Practice, Edward Elgar Publishing, 1997, 18-32. Peters, D.W. Government of Canada Real Return Bonds, Proceedings of the 1996 Annual Conference of the Administrative Sciences Association of Canada, Finance Division, Vol. 17, No. 1, G. Tannous (ed.), 81-90. Quick, R. Real Return Bond Effective Duration: The Price Sensitivity of Real Return Bonds to Changes in Nominal Bond Yields, Scotia Capital, 2001. Roll, R. U.S. Treasury Inflation-Indexed Bonds: The Design of a New Security, Journal of Fixed Income, 6(3), (December 1996), 9-28. Townend, J. Index-linked Government Securities: The UK Experience and Perspective, in: Managing Public Debt: Index-linked Bonds in Theory and Practice, Edward Elgar Publishing, 1997, 1-17. Wilox, D.W. Policy Watch: The Introduction of Indexed Government Debt in the United States, Journal of Economic Perspectives, 12(1), (Winter 1998), 219-27. 58