Research Paper No. 2006-01 

IMPLICATIONS OF RETURNS ON 

TREASURY INFLATION-INDEXED SECURITIES FOR 

PROJECTIONS OF THE LONG-TERM REAL INTEREST RATE

James A. Girola 

March, 2006

Abstract:

 This paper updates and extends previous work which considers the real interest rate on 

the Social Security Trust Fund. The paper adds 2005 data to the previous extensive historical 

series, and the resulting average long-term government real interest rate back through 1870 is 

just under 3 percent. Over the last 40 years or so, the Trust Fund rate has been about 24 basis 

points below the long-term government rate. The paper then extends previous work by using 

yield curves for Treasury inflation-indexed securities (TIPS) to develop forward-looking market 

projections for the real return on a hypothetical trust fund made up of TIPS. The comparable 

average real return on the hypothetical trust fund is roughly estimated to be around 2-3/4 percent. 

The author is with the U.S. Department of the Treasury. The views expressed here are those of 

the author and not necessarily those of the Treasury Department. I would like to thank 

Mark Warshawsky, Nada Eissa, Karen Hendershot, Ralph Monaco, and James Duggan for their 

helpful suggestions. 
2

Introduction

 Previous work1 has examined the long-term real interest rate on the Social Security Trust 

Funds. That work included the analysis of historical interest rate data and the examination of 

yield curve estimates of long-term returns implied in the market for Treasury inflation-indexed 

securities (TIPS). 

 The historical analysis was needed because the actual Social Security nominal interest 

rate is not available before the end of September 1960. This gives only about 40 years of data, 

which is a relatively short time period to calculate a historical average. Therefore, the previous 

work developed a historical real interest rate back through 1870 based on a historical nominal 

interest rate series that is similar to the Social Security interest rate and an equivalent price series 

based on the CPI-W. In the first section, this paper presents these series through 2005. 

 However, historical data are, by definition, backward looking, and do not incorporate 

expectations for the future. Therefore, the paper moves on to TIPS to ascertain market 

expectations for future real interest rates. 

 The second section of the paper sets out the updated TIPS yield curves through 2005. 

The third section uses the curves to construct returns on a hypothetical Social Security trust fund 

made up of TIPS. The fourth section draws on the yield curves to estimate the long-run expected 

returns for the hypothetical trust fund and the actual Social Security Trust Fund. 

Historical Series

 The previous paper Girola (2005) presented a historical government nominal interest rate, 

a historical price series based on the CPI-W as adjusted by Social Security for methodological 

improvements, and the resulting historical government real interest rate. The data sources for 

these series are cited in the previous paper, and the series are here updated for 2005. 

 The government nominal interest rate series is updated by the Ibbotson data on long-term 

Treasury bonds for 2005.2

 Chart 1 plots this rate annually back through 1870 and includes the 

updated annual average of the Social Security Trust Fund interest rate back through 1961. 

 

1

 See Girola (2005). 

2

 See Ibbotson Associates (2006). 
3

18

7

0

18

8

0

18

9

0

19

0

0

191019

2

0

19

3

0

19

4

0

19

5

0

19

6

0

19

7

0

19

8

0

19

9

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2

0

0

0

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2

4

6

8

10

12

14

0

2

4

6

8

10

12

14

CHART 1: INTEREST RATES

Annual, Percent

Government

Social

Security

 The chart shows that the government rate tracks the Social Security rate closely. Because 

the Ibbotson data in the government rate are for a 20-year bond while the Social Security rate is 

an average over a range of maturities as low as 4 years, the former can typically be expected to 

be higher than the latter. This is borne out by the fact that the average spread between the two 

for 1961-2005 is 24 basis points. The government nominal interest rate fell from 5.04 percent in 

2004 to 4.64 percent in 2005, whereas the Social Security rate rose from 4.27 percent to 

4.31 percent, reflecting the flattening of the Treasury yield curve last year. 

 Charts 2 and 3 show the annual average of the CPI-W through 2005. Annual average 

inflation accelerated from 2.6 percent in 2004 to 3.5 percent in 2005. 
4

1870

1880189019001910192019301940195019601970198019902

0

0

0

10

20

40

80

160

300

CHART 2: ADJUSTED CPI-W

Annual Level, Ratio Scale

1870

1880189019001910192019301940195019601970198019902000

-15

-10

-5

0

5

10

15

20

-15

-10

-5

0

5

10

15

20

Annual

Trend Line

CHART 3: ADJUSTED CPI-W

Annual Percent Change and

Annualized Trend-Line Percent Change over 10 Years
5

18

7

0

18

8

0

18

9

0

19

0

0

191019

2

0

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5

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0

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2

0

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0

-15

-10

-5

0

5

10

15

20

-15

-10

-5

0

5

10

15

20

Annual

10-Year

CHART 4: GOVERNMENT REAL INTEREST RATE

Annual Percent, and Annualized 10-Year Compound Return

Average Compound

Annual Return = 2.96%

 The government nominal interest rate and the price series are put together in Chart 4 to 

get the real return as computed by the Social Security formula. The real return series stops in 

2004 because the calculation requires the CPI-W for the year ahead and 2005 is the last year for 

which the CPI-W is available.3

 The long-term average compound government real interest rate over the entire period 

1870-2004 is 2.96 percent. For the years 1961-2004, the average government real interest rate is 

3.44 percent, compared with 3.20 percent for the average compound real Social Security rate; the 

difference is 24 basis points, the same as the average difference between the two nominal rates in 

Chart 1. For 2004 the government real interest rate is 1.53 percent and the real Social Security 

rate is 0.77 percent, compared with 2003 values of 2.29 percent and 1.44 percent, respectively.4

 

3

 The Social Security formula for computing real return uses the average nominal interest rate for each year and the 

price indexes for that year and the following year. The formula first calculates the semiannually compounded 

nominal return from a bond bought at par with that interest rate and then sold at par, where it is assumed that this 

bond pays a coupon of half the interest rate at midyear which is reinvested at the same rate, and another coupon at 

the end of the year. The real return is then obtained by dividing the nominal return by the ratio of next year’s price 

to the current year’s price. For more information, see Girola (2005), p. 7. 

4

 Calculations including 2004 are done by the author. See the Trustees Report (2005) for more information on 

Social Security interest rates. 
6

The TIPS Yield Curve

 The following sections of the paper focus on the market for Treasury inflation-indexed 

securities (TIPS) and examine what this market has to say about the long-term Social Security 

interest rate. 

 TIPS are important for the Social Security interest rate because the TIPS market can 

reveal market expectations for long-term real interest rates. Consequently, analysis of the TIPS 

market is forward looking, in that such analysis concentrates on expected future economic 

conditions. In contrast, historical data as presented in the previous section are backward looking, 

and even though history is an important guide for the future, historical averages do not include 

future expectations. 

 Of course, market expectations may shift over time and expectations at any particular 

point in time may not be fulfilled. Even so, expectations which are sustained for a significant 

period of time can be assumed to embody information that should inform judgment about the 

future of interest rates. 

 Use of TIPS is somewhat limited by the lack of past data. TIPS were first issued in 1997, 

but it appears that the TIPS market did not reach maturity until about June, 2002 when Treasury 

renewed the commitment to TIPS in the May 2002 Quarterly Refunding Statement. As a result, 

there is about 3-1/2 years worth of reasonably mature TIPS data for analysis. Nevertheless, if 

current market expectations are the center of attention, a long record of TIPS data may not be 

needed. 

 The empirical analysis of the TIPS market done in this paper continues and deepens the 

yield curve approach presented in previous work. Among other features, this approach provides 

a projected TIPS long-term forward real interest rate which can reveal market expectations. 

Details of this approach are outlined in the Appendix. 

 For this paper, the TIPS yield curves were fitted to daily TIPS quotes for 1,678 business 

days from April 15, 1999 through the last business day of 2005 which was December 30, 2005.5

 

Chart 5 depicts the spot rates from all the yield curves and includes projections out to 80 years 

maturity. At the short end, spot rates have been moving up along with Federal Reserve increases 

in the federal funds rate target. Moreover, the curve has flattened out recently. 

 

5

 In this paper, TIPS quotes were provided by Treasury’s Office of Debt Management. The yield curves in this 

paper are not used to compute the inflation-indexed rates published in the Federal Reserve Board’s H.15 release. 
7

1999 2000 2001 2002 2003 2004 2005

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

30-Year

10-Year

5-Year

CHART 6: TIPS PAR YIELDS

4/15/1999 - 12/30/2005, Percent

 Chart 6 plots daily par yields which were read off the fitted yield curves for maturities 5, 

10, and 30 years. This chart shows that yields were low since mid 2002, and have stayed at 

2 percent or below recently. 
8

TIPS Trust Fund Returns

 The charts in the previous section depicted spot and par rates for the TIPS yield curves. 

In order to use the curves to project the interest rate relevant to Social Security, however, the 

Social Security real interest rate method must be applied. The appropriate real interest rate 

concept for Social Security is the real rate of return from TIPS computed analogously to the real 

rate of return for the Social Security Trust Funds.6

 By this concept, the TIPS real return is the real return that would be produced by a trust 

fund made up of TIPS. Moreover, the return as so defined is an estimate of the actual Trust Fund 

real return (based on nominal Treasury securities) after possible adjustments, including the 

addition of an inflation risk premium to the TIPS return, and the subtraction from the return of 

adjustments for the tax treatment of TIPS and for the lower liquidity of TIPS relative to nominal 

Treasuries. 

 Chart 7 plots the daily real returns on a hypothetical Social Security trust fund made up of 

TIPS using the yield curves computed in the last section. For the purpose of calculating the 

returns, the yield curves provide estimates of what the arrays of TIPS yields would have been in 

the past if there had been a fully filled out TIPS market at that time. The weights applied to the 

TIPS yields to get the trust fund returns are the same as were actually used for the nominal Trust 

Fund returns. 

 The chart shows that returns on this simulated TIPS trust fund have averaged only about 

2 percent for the 3-1/2 years through the end of 2005, and over the last year they were even 

lower. 

 

6

 Specifically, the TIPS return is the semiannually compounded market weighted average yield on TIPS, ignoring 

capital gains and losses. 
9

1999 2000 2001 2002 2003 2004 2005

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

4/15/1999 - 12/30/2005, Percent

CHART 7: TIPS TRUST FUND

REAL RETURN*

* Hypothetical market-weighted TIPS trust fund return,

 estimated from TIPS yield curves

Averages:

From 1/1/2001: 2.37

From 6/1/2002: 1.99

From 1/1/2005: 1.76

 The charts in this and the previous section indicate that if the last several years are 

representative of the TIPS market into the future, TIPS returns may remain near 2 percent or 

below indefinitely. This could lead to a sustained period of low real returns like the one after 

World War II, which would continue to depress the average long-term real interest rate. 

 However, there are various special factors which may have temporarily pushed down real 

interest rates over the last several years, including the low real rates following the recession in 

2001, the accommodative monetary policy which brought the federal funds rate target down to 

1 percent from mid 2003 to mid 2004 followed by tightening, and an exceptionally large pool of 

foreign savings. 

 Therefore, the future levels of real returns, and whether returns will continue to be low, 

cannot be inferred simply from the fact that returns have been low the last several years. 

However, the yield curves also contain information about market expectations of future returns. 

Therefore, in the next section the curves are examined further to see whether the market expects 

the current levels of low returns to persist. 
10

1999 2000 2001 2002 2003 2004 2005

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

4/15/1999 - 12/30/2005, Percent

Averages:

From 1/1/2001: 2.83

From 6/1/2002: 2.58

From 1/1/2005: 2.00

CHART 8:

 TIPS LONG-RUN FORWARD RATE

Expected TIPS Returns

 The starting point for studying long-run expectations is the long-run forward rate derived 

from the yield curves. The forward rate is the short-term interest rate for future periods implied 

by the yield curve, and the long-run forward rate is the constant forward rate at longer maturities. 

The yield curve approach used here and in previous work produces a value for the long-run 

forward rate.7

 Chart 8 plots the daily TIPS long-run forward rate from the yield curves. The chart 

shows that the forward rate has been declining. However, it seems to have evolved a bit more 

smoothly than shorter-term rates such as the TIPS returns in Chart 7. The greater smoothness 

suggests that the long-run forward rate may be less influenced by short-run effects such as 

market immaturity, and so may be more useful as a monitor of expectations. 

 However, the TIPS long-run forward rate does not directly translate into long-term trust 

fund return expectations because it must be adjusted for term premia. Conceptually, the 

adjustment can be broken into two parts. First, the long-run forward rate term premium must be 

subtracted from the long-run forward rate to get the expected short interest rate. And second, the 

term premium for the TIPS trust fund return must be added back to the expected short rate to get 

long-term expectations for the TIPS trust fund return. 

 

7

 Specifically, the long-run forward rate is the average forward rate for maturities 10 through 31-1/2 years, which is 

held constant at higher maturities for projections. The Appendix has more details. 
11

1999 2000 2001 2002 2003 2004 2005

-50

-25

0

25

50

75

100

125

-50

-25

0

25

50

75

100

125

CHART 9: SPREAD: LONG-RUN

FORWARD RATE TO MARKET RETURN

4/15/1999 - 12/30/2005, Basis Points

Averages:

From 1/1/2001: 46

From 6/1/2002: 59

From 1/1/2005: 24

 More concisely, the net term premium, that is, the difference between the term premium 

for the long-run forward rate and the term premium for the TIPS trust fund return, must be 

subtracted from the long-run forward rate. The net term premium is simply an adjustment factor 

to convert the forward rate into the expected TIPS trust fund return. 

 To estimate the net term premium, Chart 9 plots the hypothetical trust fund return 

(Chart 7) subtracted from the long-run forward rate (Chart 8): 

 Chart 9 suggests an average net term premium of 50 basis points or more over the last 

several years. However, a confident estimate of the net term premium would require a much 

longer historical record in order to smooth out the idiosyncrasies of the various historical 

episodes. So estimates from the TIPS data available at this time must be seen as a work in 

progress. 

 To get another estimate of the net term premium, data from nominal Treasuries can 

supplement the limited historical record from TIPS. Charts 10 and 11 display data for a nominal 

long-run forward rate from coupon STRIPS and returns derived from the Trust Fund nominal 

interest rate and the 10-year Treasury constant maturity yield.8

 

8

 The two charts end in August 2005 because data for the 30-year STRIPS series for monthly averages were not 

available as a result of the absence of a current 30-year Treasury bond. Recently, because of the return of the 30-

year bond, this 30-year STRIPS series has started again. 
12

1987 1990 1995 2000 2005

0

1

2

3

4

5

6

7

8

9

10

0

1

2

3

4

5

6

7

8

9

10

Forward Rate

Trust Fund Return

10-Year Return

CHART 10: NOMINAL TREASURY RATES*

Monthly Average 10/1987 - 8/2005, Percent

* Long-term forward rate computed from Bloomberg

 Generic Coupon Strips of 10 and 30 years maturity.

 Returns computed from Trust Fund and Treasury

 constant maturity yields.

1987 1990 1995 2000 2005

-200

-150

-100

-50

0

50

100

150

200

250

-200

-150

-100

-50

0

50

100

150

200

250

Trust Fund

10-Year

CHART 11: NOMINAL TREASURY SPREADS:

 LONG-TERM FORWARD RATE

 TO NOMINAL RETURNS

Monthly Average 10/1987 - 8/2005, Basis Points

Averages, Whole Period:

Trust Fund: 11

10-Year: 25

Averages, Last 10 Years:

Trust Fund: 36

10-Year: 54
13

 Changes in inflation can affect this premium in the nominal market. By focusing on the 

last ten years when inflation was relatively stable, these two charts point to a net term premium 

of at least 35 basis points. Because Chart 9 might imply a higher premium, the TIPS and 

nominal markets together suggest a lower limit for the net term premium of 35 basis points. 

 Given the term premium, the expected TIPS long-run real return can be estimated by 

subtracting the net term premium from the TIPS long-run forward rate. Therefore, the average 

long-run forward rate of 2.58 percent since mid 2002 together with a net term premium of 

35 basis points or more implies a long-run expected return of about 2-1/4 percent or less. Recent 

long-run forward rates at around 2 percent may indicate an even lower expectation. 

 Of course, if current TIPS rates are abnormally low, long-run forward rates may also be 

biased down if markets simply extrapolate expectations from the present. Nevertheless, the 

apparent low expectations for future TIPS returns have persisted for several years or more, so it 

must be considered a real possibility that markets are looking to a future of low real interest 

rates. 

 In sum, TIPS markets have solidly priced in a TIPS long-term real return which is at most 

2-1/4 percent. Current returns are around 2 percent, and so are expected future returns. 

 The preceding calculations provide the expected return on a TIPS trust fund. The 

expected long-term real return for the actual Trust Funds made up of nominal Treasuries can be 

derived by adjusting the expected TIPS long-term real return. 

 The adjustment includes the inflation risk premium net of offsetting effects. Early 

analytical work suggests that the most likely upper limit of the inflation risk premium is 50 basis 

points.9

 After allowing for offsetting effects such as the tax effects of TIPS and the lesser 

liquidity of TIPS, the net adjustment may be lower. 

 However, even with the upper adjustment limit of 50 basis points, the TIPS long-term 

real return of 2-1/4 percent or less would imply that the expected long-term real return on the 

nominal Trust Funds would fall below 2-3/4 percent. 

 Therefore, based on the hypothetical TIPS trust fund derived from the TIPS yield curves, 

the expected long-term real return adjusted to be comparable to the real return on the Social 

Security Trust Funds is around 2-3/4 percent. 

 

9

 For more on estimating the inflation risk premium, see Hammond (2002). 
14

Conclusions

 This paper updates and extends previous work which considers the real interest rate on 

the Social Security Trust Fund. The paper adds 2005 data to the previous extensive historical 

series, and the resulting average long-term government real interest rate back through 1870 is 

just under 3 percent. Over the last 40 years or so, the Trust Fund rate has been about 24 basis 

points below the long-term government rate. The paper then extends previous work by using 

yield curves for Treasury inflation-indexed securities (TIPS) to develop forward-looking market 

projections for the real return on a hypothetical trust fund made up of TIPS. The comparable 

average real return on the hypothetical trust fund is roughly estimated to be around 2-3/4 percent. 
15

Appendix

The Yield Curve for TIPS

 The TIPS yield curves presented in this paper use the yield curve methodology developed 

in this Office.10

 The price quotes used to compute these curves were provided by Treasury’s Office of 

Debt Management. They consist of daily quotes for business days from April 15, 1999 through 

December 30, 2005, where the choice of early 1999 as the start date minimizes some of the 

abnormalities in the prices when these securities were new in the market. Price quotes for days 

before each security’s issue date were removed. 

 As of December 30, 2005, there had been a total of 18 inflation-indexed securities issued 

with 17 still outstanding and an early 5-year issue having matured in 2002 (quotes for this 

security during the last year of its existence were eliminated). The resulting sample of quotes 

contained at least 6 securities outstanding for each quote day. 

 The methodology for computing the yield curves starts by expressing the price of each 

security as the discounted sum of the security’s real cash flows, where the discount factors are 

given by a discount function. The spot and par yield curves are calculated from the discount 

function. 

 The discount function is written in terms of the forward rate, which, in turn, is modeled 

as a cubic spline. The knots of the spline are placed at maturities 0, 7, 10, and 31-1/2 years. The 

quote sample for each day includes at least one security whose maturity is within each of these 

knot ranges. 

 In addition, the spline is constrained in several ways including endpoint constraints for 

smoothness. And in order to generate a seamless projection, the forward rate at and beyond 

31-1/2 years maturity is made to equal its average from 10 to 31-1/2 years. 

 The parameters of the spline are estimated for each daily quote sample by nonlinear least 

squares with no weighting. The splines are written in terms of B-spline bases for estimation. 

The resulting spline parameters define the discount function from which the various yield curves 

are derived. And the long-run forward rate is given as the resulting average of the forward rate 

from 10 to 31-1/2 years maturity.

 

10 See the discussion on p. 10 of the previous paper Girola (2005). For more information about this methodology as 

applied to the corporate bond market, see U.S. Department of the Treasury (2005a, 2005b, and 2006). 
16

References

Girola, James A., 2005, “The Long-Term Real Interest Rate for Social Security,” Economic 

Policy Research Paper 0502, March 30. Available at 

http://www.treas.gov/offices/economic-policy/long_term_rates_socialsecurity.pdf

Hammond, P. Brett, 2002, “Understanding and Using Inflation Bonds,” TIAA-CREF Research 

Dialogue, Issue 73, September. 

Ibbotson Associates, 2006, Stocks, Bonds, Bills, and Inflation 2006 Yearbook. 

The 2005 Annual Report of the Board of Trustees of the Federal Old-Age and Survivors 

Insurance and Disability Insurance Trust Funds, March 23, Washington, D.C. 

U.S. Department of the Treasury, 2005a, Creating a Corporate Bond Spot Yield Curve for 

Pension Discounting, February 7, Washington, D.C. Available at 

http://www.treas.gov/offices/economic-policy/reports/pension_yieldcurve_020705.pdf

U.S. Department of the Treasury, 2005b, Supplement to Creating a Corporate Bond Spot Yield 

Curve for Pension Discounting, February 7, Washington, D.C. Available at 

http://www.treas.gov/offices/economic-policy/reports/t05ax.pdf

U.S. Department of the Treasury, 2006, The Corporate Bond High Quality Centered Yield Curve 

for Pension Discounting, January 24, Washington, D.C. Available at 

http://www.treas.gov/offices/economic-policy/reports/wp_up_x.pdf