Title LM1 Yield Curve Strategies IFT Notes.pdf ✅

LM1 Yield Curve Strategies 2024 Level III Notes © IFT. All rights reserved 1 LM1 Yield Curve Strategies 1. Introduction .......................................................................................................................................................1 2. Key Yield Curve and Fixed-Income Concept for Active Managers ................................................2 Yield Curve Dynamics....................................................................................................................................2 Duration and Convexity ................................................................................................................................3 3. Yield Curve Strategies.....................................................................................................................................6 Static Yield Curve.............................................................................................................................................6 Dynamic Yield Curve................................................................................................................................... 10 Key Rate Duration For a Portfolio.......................................................................................................... 23 4. Active Fixed-Income Management Across Currencies ................................................................... 26 5. A Framework for Evaluating Yield Curve Strategies ....................................................................... 31 Summary ............................................................................................................................................................... 34 This document should be read in conjunction with the corresponding reading in the 2024 Level III CFA® Program curriculum. Some of the graphs, charts, tables, examples, and figures are copyright 2023, CFA Institute. Reproduced and republished with permission from CFA Institute. All rights reserved. Required disclaimer: CFA Institute does not endorse, promote, or warrant the accuracy or quality of the products or services offered by IFT. CFA Institute, CFA®, and Chartered Financial Analyst® are trademarks owned by CFA Institute. Version 1.0
LM1 Yield Curve Strategies 2024 Level III Notes © IFT. All rights reserved 2 1. Introduction This reading shows how to position fixed-income portfolios using different active yield curve strategies. These strategies capitalize on expectations regarding the level, slope, or shape (curvature) of yield curves using long and short cash positions, derivatives, and leverage. This reading also discusses active fixed-income management across currencies involving multiple yield curves. Finally, the reading provides a framework for analyzing the expected return of a yield curve strategy. 2. Key Yield Curve and Fixed-Income Concept for Active Managers The factors affecting an investor’s expected fixed-income portfolio returns are given in the following equation: E(R) ≈ Coupon income +/− Rolldown return +/− E (Δ Price due to investor’s view of benchmark yields) +/− E (Δ Price due to investor’s view of yield spreads) +/− E (Δ Price due to investor’s view of currency value changes) Sections 2 and 3 will discuss how to actively manage the first three components of the above equation, and Section 4 will focus on changes in currency. Lastly, Section 5 gives a framework for evaluating yield curve strategies. Yield Curve Dynamics A yield curve shows the yields-to-maturity at various maturities for a specific issuer or group of issuers. Certain assumptions are made to create a yield curve. These depend on the investor type or the curve’s intended use. Several challenges associated with constructing a yield curve are: • Asynchronous observations of various maturities on the curve • Maturity gaps that require interpolation and/or smoothing • Observations that seem inconsistent with neighboring values • Use of on-the-run bonds only versus all marketable bonds (i.e., including off-the-run bonds) • Differences in accounting, regulatory, or tax treatment of certain bonds that may make them look like outliers Two key points about yield curves are: • Yield curves are typically derived from available bond yields-to-maturity using a model that requires interpolating the yields-to-maturity on actively traded bonds. A model frequently used while constructing yield curves is the ‘constant maturity yield’ model. For example, let's say we want to estimate the 4-year yield to maturity
LM1 Yield Curve Strategies 2024 Level III Notes © IFT. All rights reserved 3 and no bonds are available with exactly 4 years remaining to maturity. In this case, we will select other bonds with maturities near 4 years (say 3.9 years and 4.4 years) and use linear interpolation to estimate the 4-year yield to maturity. • A tradeoff exists between yield-to-maturity and liquidity. Off-the-run bonds are typically less liquid than on-the-run bonds; hence they have a lower price (higher yield-to-maturity) and may have higher trading costs. Primary yield curve risk factors are of three types: 1. A change in level (a parallel “shift” in the yield curve)- A change in yield level occurs when all yields-to-maturity represented on the curve change by the same number of basis points. 2. A change in slope (a flattening or steepening “twist” of the yield curve) Yield curve slope is the difference in basis points between the yield-to-maturity on a long-maturity bond and the yield-to-maturity on a shorter-maturity bond. For example, a slope as measured by the 2s 30s spread. • yield curve steepens if the spread increases/widens, • yield curve flattens if the spread decreases/narrows, • yield curve is upward-sloping if the spread is positive, • yield curve is “inverted” if the spread turns negative. 3. A change in shape or curvature (a “butterfly movement”) is measured using the butterfly spread, that is, Butterfly spread = – short-term yield + (2 x medium-term yield) – long-term yield Typically, the butterfly spread is calculated using the on-the-run 2-year, 10-year, and 30-year Treasuries as the short-, medium-, and long-term yields, respectively. For a straight yield curve, the butterfly spread is zero. The greater the curvature, the higher the butterfly spread. Duration and Convexity The price/yield relationship, as explained earlier in the curriculum, is the combination of: • a negative, linear first-order factor (duration) that attempts to capture a linear relationship between bond prices and yield-to-maturity and • a positive, non-linear second-order factor (convexity) that describes a bond’s price behavior for larger movements in yield-to-maturity.
LM1 Yield Curve Strategies 2024 Level III Notes © IFT. All rights reserved 4 The third term in the expected returns equation E (Δ Price due to investor’s view of benchmark yield) for a single bond is given by the expression: %∆PVFull ≈ −(ModDur × ΔYield) + [1⁄2 × Convexity × (ΔYield)2] For a bond portfolio, market value (MV)-weighted averages for modified duration and convexity are substituted in the above equation. AvgModDur = ∑ ModDurj J j=1 × ( MVj MV ) AvgConvexity = ∑ Convexityj J j=1 × ( MVj MV ) EXAMPLE (This is Example 1 of the curriculum) US Treasury Securities Portfolio Consider two $50 million portfolios: Portfolio A is fully invested in the 5-year Treasury bond, and Portfolio B is an investment split between the 2-year (58.94%) and the 10-year (41.06%) bonds. The Portfolio B weights were chosen to (approximately) match the 5-year bond duration of 4.88. How will the value of these portfolios change if all three Treasury yields-to-maturity immediately rise or fall by 50 bps?