This May 1995 report from Salomon Brothers introduced a series titled Understanding the Yield Curve. The report served as both primer and framework for practitioners seeking to bridge theoretical term structure analysis with actual trading decisions. The document is 22 pages and covers computation methods, economic interpretations, and practical applications.
The report defines three representations of the same term structure information: par rates (yields on bonds priced at 100), spot rates (discount rates for single future cash flows), and forward rates (implied future borrowing rates locked in today). The author notes that while these contain identical information about the term structure, forward rates magnify variations in the spot curve and measure the marginal reward for extending maturity.
The document decomposes the yield curve into three components. First, the market's rate expectations, where the report notes that if markets expect rising rates, current long-term yields must be higher to compensate for expected capital losses. Second, the bond risk premium, defined as the expected return differential between longer-term bonds and the riskless short-term bond. Third, the convexity bias, which accounts for how different bonds' nonlinear price-yield relationships affect relative valuations.
The empirical evidence presented contradicts the pure expectations hypothesis. The report states that the Treasury yield curve has been upward sloping nearly 90% of the time in recent decades. Historical data from 1970-1994 shows that bond risk premia increase steeply with duration in the front end but more slowly after two years, creating a concave return curve. The author says this pattern may reflect demand from pension funds and long-duration liability holders.
On convexity, the report demonstrates that longer-duration zeros exhibit higher convexity, which tends to depress their yields. The lower panel of Figure 4 in the report shows that when all bonds have the same 8% expected return and short-term rates are expected to remain flat, the spot rate curve slopes downward because lower yields are needed to offset the convexity advantage of longer-duration bonds.
The report was published in May 1995, a period following the 1994 bond market selloff when the Federal Reserve raised the federal funds rate from 3% to 6% between February 1994 and February 1995. The document's discussion of curve flattening trades and convexity reflects market conditions where participants were reassessing curve shape expectations after significant losses.
The report references earlier academic work on term structure but explicitly aims to make such analysis accessible for portfolio managers. The author states that advances in theoretical analysis are often very quantitative and rarely emphasize practical investment applications.
The examples use specific dates. Figure 5 shows par yield curves as of March 31, 1995. Figure 6 displays the historical path of three-month rates and implied forward paths as of December 30, 1994 and March 31, 1995. Figure 8 examines the on-the-run yield curve changes between these two dates, noting that the three-month to two-year spread was 200 basis points in December 1994 while the two- to 30-year spread was only 20 basis points.
The report predates several structural market changes. In 1995, Treasury STRIPS (Separate Trading of Registered Interest and Principal of Securities) had been available since 1985, but the zero-coupon bond market remained less liquid than today. The document's discussion of computing spot rates from coupon bond prices reflects this environment.
The on-the-run Treasury curve the report references differs from the current market. In 1995, on-the-run bonds traded at near-par prices and represented the primary liquidity points. Today, ETFs like TLT, IEF, and SHY provide exposure to Treasury duration without trading individual securities.
Interest rate volatility in 1995 was higher than in subsequent decades. The report's convexity bias calculations assume 100 basis point annual yield volatility. From 2008-2020, realized volatility was generally lower, though it increased in 2020-2022.
The report's discussion of curve flattening trades assumes investors can readily short government securities. This was true for institutional investors in 1995. Retail investors today access similar exposures through ETFs, though shorting costs and tracking error differ from direct Treasury positions.
The concepts in the Salomon report translate to strategies using Treasury ETFs. The following approaches illustrate how the report's frameworks could be applied using accessible instruments rather than individual bonds and repo financing. These are conceptual starting points that would require substantial additional work for actual implementation, including proper duration matching, transaction cost analysis, and risk controls.
The report states that one-year forward rates equal an n-year zero's rolling yield for an unchanged yield curve scenario. This suggests a simple rule: extend duration when forward rates are high relative to expected rate changes.
A strategy could use the 2-year to 10-year Treasury spread as a proxy signal. When this spread exceeds its historical average by a threshold (such as one standard deviation), the portfolio shifts from IEF (7-10 Year Treasury) to TLT (20+ Year Treasury). When the spread is below average, the portfolio shifts to SHY (1-3 Year Treasury).
This exploits the report's finding that steeper curves historically have not predicted rate increases sufficient to offset the positive carry. The author notes that on average, small declines in long-term rates, which augment long-term bonds' yield advantage, follow upward-sloping curves.
The limitation is that curve slope is an imperfect proxy for actual forward carry, particularly when ETF durations differ from the curve points being measured. A more sophisticated approach would compute expected returns for each ETF directly from fitted forward rates, but the slope-based rule captures the essential insight.
The report discusses duration-neutral positions that exploit curve shape. A barbell (short and long maturities) versus a bullet (intermediate maturity) was the classic example.
Using ETFs, this becomes: long SHY and TLT versus short IEF. The critical requirement is duration neutrality, achieved by weighting the barbell components so their combined duration matches IEF's duration. Without this, the position becomes a directional rate bet rather than a pure curve trade. ETF providers publish effective duration, which enables the necessary calculations.
The position profits from curve steepening or increased volatility (which increases the convexity value of the barbell).
The report's Figure 8 shows a specific case from December 1994 when the curve exhibited high curvature (three-month to two-year spread of 200 basis points, two- to 30-year spread of 20 basis points). The article says that by March 1995, the front end flattened by 108 basis points and the long end steepened by 45 basis points.
A systematic version monitors the curve's curvature. When curvature is historically wide (bullets appear cheap), favor bullet positions. When narrow (barbells appear cheap), favor barbell positions. The challenge lies in measuring curvature consistently when using ETFs rather than individual bonds.
The report notes that more convex bonds tend to have lower yields than less convex bonds with the same duration. This yield disadvantage exists because investors pay for the convexity benefit. Long-term Treasury ETFs (TLT) have higher convexity than intermediate ETFs (IEF) when duration-matched.
The question is when the convexity benefit justifies its cost. The report states that the value of convexity increases with the magnitude of yield changes. When volatility is low, the yield penalty of high-convexity positions exceeds their option value. When volatility rises sufficiently, the convexity benefit can outweigh the yield disadvantage.
A systematic approach would compare the estimated value of convexity (which depends on expected volatility) against the yield penalty. The strategy increases TLT exposure relative to IEF when this calculation favors convexity, maintaining constant duration through position sizing.
This requires estimating how much yield spread compensates for convexity differences, which in turn depends on volatility expectations. The report's framework provides the logic, but implementation requires specific assumptions about future rate distributions.
The report provides no discussion of:
These omissions reflect the report's scope: a framework for understanding Treasury curve relationships. The author notes that subsequent reports would provide detailed analysis, and indeed the series continued with papers on duration extension, forecasting returns, and convexity bias.
The report also predates modern term structure models that were developed in the late 1990s and 2000s. Affine models, Heath-Jarrow-Morton framework, and more sophisticated approaches to extracting market expectations from the curve came later.
The report's framework assumes government bonds can be valued separately from the broader portfolio context. In practice, Treasury positions interact with equity exposures, currency positions, and other portfolio components.
The forward rate decomposition into expectations, risk premia, and convexity bias is conceptually clean but operationally difficult. The report acknowledges that exact decomposition is not possible because the three components vary over time and are not directly observable but must be estimated.
The assumption of an unchanged yield curve as the base case scenario may not hold during all regimes. The report notes this assumption is more accurate than assuming forward rates reflect expected future yields, but neither assumption is universally correct.
Transaction costs matter for systematic implementations. The report provides no guidance on rebalancing frequency, position sizing, or the trade-off between signal strength and implementation costs.
The core insight that forward rates reflect the combination of expectations, risk premia, and convexity remains the standard framework for fixed income analysis. The report's decomposition appears in virtually every modern textbook on term structure modeling.
The empirical finding that bond risk premia are positive on average and time-varying continues to drive research and practical strategies. The report's Figure 3 showing the concave shape of average returns by duration has been replicated in subsequent studies using longer time periods.
The observation that curve steepness predicts future bond returns better than it predicts future rate changes remains true. Academic papers published in the 2000s and 2010s confirmed this relationship using more sophisticated econometric techniques.
The practical applications of forward rates as break-even rates for active positions continue in use. Portfolio managers still compare their rate forecasts to the forward curve to determine if a position has favorable odds.
For retail investors using ETFs, the report's framework remains useful despite changes in market structure. The relationships between curve shape, carry, and expected returns still hold. The advantage of ETFs is that they package these concepts into tradable instruments without requiring individual bond selection or repo market access.
The 1995 report established a vocabulary and framework that persists. Terms like rolling yield, forward-spot premium, and convexity bias appear regularly in fixed income research three decades later. The report succeeded in its stated goal of bridging the gap between theory and practice.