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A Framework for Projecting Interest Rate Spreads and Volatilities January 2000

Although the Congressional Budget Office has routinely projected interest rates on Treasury bills as part of its economic and budget outlook, it has not ordinarily projected commercial paper rates or the London interbank offer rate. With the rate on three-month commercial paper replacing the Treasury bill rate as the benchmark in the student-loan program for the next 42 months, CBO will make projections about the behavior of the new reference rate as part of its outlook. In developing a framework for those projections, plausibility and consistency with CBO's current projection procedures should be guiding principles. CBO formulated its model for projecting interest rate spreads on that basis. After using the model to produce cost estimates for the alternative-rate proposals considered in 1997, CBO has since revised it to incorporate more recent economic data and trends.
 

CBO'S INITIAL ALTERNATIVE-RATE PROJECTIONS

CBO's model for projecting interest rates on commercial paper and London interbank dollar deposits builds on work for its annual economic and budget outlook, which CBO prepares at the beginning of the year and updates at midyear. The outlook's horizon is 10 years; it comprises a short-term projection, or forecast, for a two-year span and a medium-term projection for the remaining eight years.⁽¹⁾ Over the medium term, CBO attempts to approximate average, or trend, relationships rather than project cyclical movements. Nevertheless, its projections take into account the possibility of booms and recessions. To identify trends, analysts use historical data for such factors as the growth of the labor force, the rate of national saving, and the growth of productivity. For Treasury interest rates, CBO bases its projections on underlying trends of real (inflation-adjusted) interest rates and inflation. The projections reflect CBO's baseline figures for government borrowing.

In 1997, CBO projected interest rates on commercial paper and the London interbank offer rate when they were first proposed as alternatives to Treasury bill rates in federal student-loan formulas. Over the projection period, analysts assumed that rates on commercial paper and LIBOR adjusted gradually to levels determined by their historical average spreads, which were calculated against Treasury bill rates using data from the early 1970s to late 1997. As discussed earlier, that period encompassed many shocks that had dissimilar effects on commercial paper and LIBOR spreads.

The Asian financial turmoil of 1998 suggested that CBO needed to augment the approach it took in 1997 for projecting the two alternative-rate spreads. During the crisis, spreads rose sharply but not by as much as during the 1970s to mid-1980s. The weaker hike in 1998 partly reflects the structural changes mentioned earlier (for example, lower inflation) that have encouraged integration of the two segments of the money market. But the spreads' smaller expansion in 1998 also reflects the confluence of favorable cyclical conditions. Following some difficulties in the early 1990s, industrial corporations and financial institutions, as well as the governments of the United States, the United Kingdom, and Western Europe, had come a long way by 1998 toward rebuilding their finances after the turbulence of the 1970s and 1980s. When they went to borrow in the commercial paper and London interbank markets, their improved balance sheets spurred lenders to offer them roughly similar credit-risk and liquidity premiums. Yet as noted earlier, participants in the money markets have not always faced similar premiums. Recognizing the need to factor in as much information as possible, CBO determined that its projections must make some allowance for cyclical circumstances that might have disparate effects on the commercial paper and London interbank markets.
 

CBO'S CURRENT MODEL FOR PROJECTING INTEREST RATE SPREADS

CBO's modeling of the future paths of the alternative rates uses the baseline projections of three-month Treasury bill rates developed for the economic and budget outlook as its core, together with assumptions about certain factors that can affect the direction of those paths. The model projects spreads between Treasury bill rates and the alternative rates as a function of such factors as the rate of inflation and the stance and stability of monetary policy. (Those "determining" factors are also known as explanatory variables.) As discussed in Chapter IV, CBO then uses the baseline spread equations of the model to estimate volatilities for the spreads. The model specifies interest rates as bond-equivalent yields, which requires adjusting yields quoted from the original sources for differences in maturity and type of instrument. The adjustments are necessary because London interbank dollar deposits pay explicit interest computed over the term of the deposit, whereas Treasury bills and commercial paper are discount instruments. That means they pay interest implicitly--by selling at a discounted price relative to the price at which they are redeemed at maturity.

Factors That Determine How Spreads Behave

Modeling in full the way spreads between interest rates on three-month Treasury bills and rates for the alternative instruments widen and narrow over time would require an almost limitless set of determining factors. But fewer variables, four of which are among the most important, can explain the broad aspects of the spreads' movements:

• Overall Interest Rates. Higher overall rates should increase (and lower rates decrease) the spreads between Treasury bill rates and the alternatives if the credit-risk premium on commercial paper rates and LIBOR is proportional to those rates. Because CBO routinely projects the rate on three-month Treasury bills, it uses that as a convenient measure of overall interest levels.
  
  
• Monetary Policy Stance. Although many measures are available, a convenient one is the yield curve spread between long- and short-term Treasury rates--convenient because CBO already projects those rates for its economic and budget outlook. (The yield curve is the relationship formed by plotting the yields of otherwise comparable fixed-income securities against their terms of maturity.) Typically, a wider yield curve spread signifies an easier monetary policy, which is often accompanied by narrower spreads of commercial paper rates and LIBOR relative to Treasury bill rates. Spreads may also narrow because a less restrictive monetary policy eases investors' perceptions of risk. (A narrow or sometimes negative yield curve spread would produce opposite effects.)
  
  
• Inflation Rate. Commercial paper and LIBOR spreads have tended to be large when inflation is high, probably because in the past, high inflation has been associated with substantial volatility in markets and, presumably, heightened perceptions of credit risk.
  
  
• Volatility of the Federal Funds Rate (as a measure of the volatility of monetary policy). Historically, the volatility of U.S. monetary policy has had less effect on commercial paper rates than on LIBOR, probably because of the close connection between interbank dollar markets in the United States and in London. By incorporating the volatility of monetary policy in its model, CBO can also gauge the effect of the more stable monetary policy of recent years on the narrowed gap between London interbank and commercial paper rates.

Historical Period

In estimating the relationship between interest rate spreads and the determining factors, CBO used historical data from 1971 to 1998. That span takes in diverse patterns for interest rates, varying levels of inflation, differences in the stance and volatility of monetary policy, and the shifting credit risks of the banks and corporations that participate in commercial paper and interbank markets. The diversity provided a reasonable test of the usefulness of CBO's framework for projecting spreads.

Yet at the same time, using that long a span of data requires analysts to account for structural changes that have influenced the spreads' behavior and especially their volatility. The economy's overall improvement in the 1990s is the most significant structural change affecting interest rate spreads. Compared with the 1970s and 1980s, inflation has subsided, interest rates have declined, large federal deficits have disappeared, and monetary policy has been relatively stable. Those improvements helped narrow interest rate spreads during the 1990s, and CBO has incorporated those structural changes into its projections. Thus, in the model, inflation and interest rates remain lower than in the past, the federal budget shows a surplus, and monetary policy reflects the improved economic outlook. The result is smaller projected commercial paper and LIBOR spreads (measured against three-month Treasury bills) compared with spreads from the early 1970s to the mid-1980s. In CBO's estimates, spreads between commercial paper rates and LIBOR also narrow--for as long as the economy's overall improvement is expected to hold.

Why the spreads' volatilities have lessened is still unclear, even after taking into account the role played by the determining factors. To economic statisticians, the unexplained portion of the observed change in volatility is a condition called heteroskedasticity. Its presence suggests that volatility has changed in response to some underlying factor or set of factors. To account for that change, CBO's model uses a procedure that gives relatively less weight to data from periods when volatility is great (and the spreads are large) and relatively more weight to data from times when volatility is less (see Table 7). Smoothing the volatility in that way reduces the influence of extreme, chaotic factors, such as the oil price shocks that occurred in the 1970s, and yields a more accurate estimate. (For more details of the weighting procedure, see the appendix.)
 

Adjusting the model for the change in volatility achieves two objectives. First, it allows analysts to use a sufficiently long historical sequence to detect the role played by each determinant of a spread. (Another approach would have been to discard data when volatility was substantial, but that would needlessly throw away valuable information and prevent a more complete understanding of a spread's behavior.) Second, as explained in Chapter IV, accounting for the decline in volatility with such procedures improves estimates of the probability distribution of the range of variation in the spreads.

Illustrative Projections

CBO conducted an exercise to illustrate its approach for projecting the approximate behavior of interest rate spreads. As explanatory variables, CBO used interest rates on three-month Treasury bills; the yield curve spread, measured by the difference between rates on 10-year Treasury notes and three-month Treasury bills; inflation, measured by the percentage change in the consumer price index (specifically, the index for all urban consumers, or CPI-U); and monetary policy volatility, measured as the volatility of the federal funds rate. Projections of Treasury bill rates, the yield curve spread, and CPI-U inflation were based on CBO's December 1998 baseline. As noted earlier, the 1990s have seen much less volatility in monetary policy than in the past. Including the volatility of the federal funds rate as a factor thus assumes that monetary policy and the economy will remain relatively stable. Although the same determining factors were used throughout the exercise, the factors' effects can be expected to differ according to the spread being considered and the alternative instrument's maturity (whether one month or three months). All of the interest rate spreads discussed below were calculated against the three-month Treasury bill.

One-Month Commercial Paper. The results from CBO's model for the one-month commercial paper spread appear satisfactory for two reasons (see Figure 8). First, for the 1971-1998 period, the model's estimate of the spread as a function of the determining factors tracks reasonably closely with the actual spread during that time. Second, the projected spreads for 1999 to 2009 move much closer to the average of the 1985-1998 period than to the average of the earlier period, which indicates that the model's projections are consistent with the economy's overall expected improvement.
 

FIGURE 8. ACTUAL AND PROJECTED INTEREST RATE SPREADS FOR ONE-MONTH COMMERCIAL PAPER

SOURCES: Actual values are Congressional Budget Office calculations based on data from the Board of Governors of the Federal Reserve. Projected values are derived from CBO's model for estimating alternative interest rates for the federal student-loan program.

NOTES: Spreads (the differences between rates) are computed against the rate for three-month Treasury bills. Interest rates have been converted to bond-equivalent yields.

Commercial paper is defined here as short-term debt issued by financial companies.

Three-Month Commercial Paper. In the past, the average for the three-month commercial paper spread was less than that for the one-month spread; however, in CBO's model, projections of the three-month spread for 1999 to 2009 are slightly above the historical average and close to recent experience (see Figure 9). The spread's stability reflects the lack of economic shocks during the projection period in contrast to the mid-1970s and early 1980s, when sudden economic jolts drove one-month commercial paper rates to much higher levels than rates on three-month commercial paper.
 

FIGURE 9. ACTUAL AND PROJECTED INTEREST RATE SPREADS FOR THREE-MONTH COMMERCIAL PAPER

SOURCES: Actual values are Congressional Budget Office calculations based on data from the Board of Governors of the Federal Reserve. Projected values are derived from CBO's model for estimating alternative interest rates for the federal student-loan program.

NOTES: Spreads (the differences between rates) are computed against the rate for three-month Treasury bills. Interest rates have been converted to bond-equivalent yields.

Commercial paper is defined here as short-term debt issued by financial companies.

One-Month LIBOR. The model's results for the one-month LIBOR spread show that CBO's approach can explain the spread's historical behavior, including the narrowing described earlier (see Figure 10). The determining factors affect LIBOR spreads differently from commercial paper spreads. For example, fluctuations in three-month Treasury bill rates influence the one-month LIBOR spread more strongly than the commercial paper spread, probably because interbank premiums for credit and liquidity risks are more influenced by overall movements in interest rates. A steep yield curve also affects the LIBOR spreads more than the commercial paper spreads, suggesting that an easier monetary policy influences the interbank market more than the market for commercial paper. Furthermore, high levels of inflation and more volatility in monetary policy have stronger effects on credit-risk premiums in interbank markets. But the model also projects future LIBOR spreads that are much lower than in the past. Those lower spreads stem from CBO's baseline assumptions of lower overall rates of interest and inflation and a stable monetary policy.
 

FIGURE 10. ACTUAL AND PROJECTED INTEREST RATE SPREADS FOR ONE-MONTH LONDON INTERBANK DOLLAR DEPOSITS

SOURCES: Actual values are Congressional Budget Office calculations based on data from the Board of Governors of the Federal Reserve. Projected values are derived from CBO's model for estimating alternative interest rates for the federal student-loan program.

NOTES: Spreads (the differences between rates) are computed against the rate for three-month Treasury bills. Interest rates have been converted to bond-equivalent yields.

The rate on London interbank dollar deposits is known as LIBOR--the London interbank offer rate.

Three-Month LIBOR. CBO's model produced three-month LIBOR spreads that are quite similar to those described above for one-month LIBOR (see Figure 11). The determining factors appear to account for the broad movements of the spread over all three decades--the 1970s, 1980s, and 1990s--which in turn suggests why LIBOR spreads were wide before the 1990s and why they have not only narrowed in this decade but also come close to commercial paper spreads. The determining factors also lead to narrow projected spreads for the decade ahead--as long as the CBO economic outlook remains favorable.
 

FIGURE 11. ACTUAL AND PROJECTED INTEREST RATE SPREADS FOR THREE-MONTH LONDON INTERBANK DOLLAR DEPOSITS

SOURCES: Actual values are Congressional Budget Office calculations based on data from the Board of Governors of the Federal Reserve. Projected values are derived from CBO's model for estimating alternative interest rates for the federal student-loan program.

NOTES: Spreads (the differences between rates) are computed against the rate for three-month Treasury bills. Interest rates have been converted to bond-equivalent yields.

The rate on London interbank dollar deposits is known as LIBOR--the London interbank offer rate.

Eurodollar Deposits. Closely associated with LIBOR are Eurodollar deposit rates--the rates paid on deposits of dollar-denominated funds by banks in London and in cities outside the United States to corporations and other investors that are not part of the interbank community. Unlike LIBOR, which is not published regularly or even frequently by the U.S. government, estimates of Eurodollar deposit rates are available daily from the Federal Reserve (for reference purposes only) on maturities of one, three, and six months. Those estimates are bid rates for deposits in London. Spreads between LIBOR and rates on Eurodollar deposits have tended to be relatively narrow (see Table 8).
 

One criterion for any benchmark rate for the student-loan program might be whether the rates could be provided by the Federal Reserve. Consequently, CBO developed equations to estimate the spreads between one-month and three-month Eurodollar deposit rates and rates on three-month Treasury bills. In both cases, the framework was the same as that used for the LIBOR spreads, and the results were as satisfactory (see Figures 12 and 13).
 

FIGURE 12. ACTUAL AND PROJECTED INTEREST RATE SPREADS FOR ONE-MONTH EURODOLLAR DEPOSITS

SOURCES: Actual values are Congressional Budget Office calculations based on data from the Board of Governors of the Federal Reserve. Projected values are derived from CBO's model for estimating alternative interest rates for the federal student-loan program.

NOTES: Spreads (the differences between rates) are computed against the rate for three-month Treasury bills. Interest rates have been converted to bond-equivalent yields.

Eurodollar deposits are dollar-denominated funds placed in banks in London and in cities outside the United States by investors that are not part of the interbank community.

FIGURE 13. ACTUAL AND PROJECTED INTEREST RATE SPREADS FOR THREE-MONTH EURODOLLAR DEPOSITS

SOURCES: Actual values are Congressional Budget Office calculations based on data from the Board of Governors of the Federal Reserve. Projected values are derived from CBO's model for estimating alternative interest rates for the federal student-loan program.

NOTES: Spreads (the differences between rates) are computed against the rate for three-month Treasury bills. Interest rates have been converted to bond-equivalent yields.

Eurodollar deposits are dollar-denominated funds placed in banks in London and in cities outside the United States by investors that are not part of the interbank community.

Conclusion

The results from CBO's model indicate that with one exception, spreads between interest rates on three-month Treasury bills and the rates on the alternative financial instruments are narrow compared with past averages (see the top panel of Table 9). The largest declines relative to the past occur in LIBOR and Eurodollar spreads. The exception is the spread for three-month commercial paper, which is projected to be slightly larger than the spread for one-month commercial paper instead of slightly smaller, as in the past.
 

Over the long run, why have the projected spreads fallen below their historical averages in almost all cases? The main reason is CBO's economic outlook for the next several years. Compared with historical trends, Treasury bill rates are lower (see the bottom panel of Table 9). Furthermore, yield curves are flatter, inflation rates are more modest, and the volatility of the federal funds rate is assumed to be less (see Table 10). Those projected improvements in the economic outlook feed directly into CBO's projections of the spreads and help narrow them.
 

1. The two-year forecast describes the likely evolution of the business cycle and is usually similar to the Blue Chip consensus (an average of the forecasts produced by approximately 40 to 50 private-sector economists).

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