CFA 2018 r23 yield curve strategies

Level III Yield Curve Strategies www.ift.world Graphs, charts, tables, examples, and figures are copyright 2017, CFA Institute Reproduced and republished with permission from CFA Institute All rights reserved Contents and Introduction Introduction Foundational Concepts for Active Management of Yield Curve Strategies Major Types of Yield Curve Strategies Formulating a Portfolio Positioning Strategy Given a Market View Comparing the Performance of Various Duration-Neutral Portfolios in Multiple Curve Environments A Framework for Evaluating Yield Curve Trades www.ift.world 2 Foundational Concepts for Active Management of Yield Curve Strategies Multiple forms of the yield curve Some assumptions are made to construct the yield curve Challenges: • Gaps in maturities that require interpolation and/or smoothing • Observations that seem inconsistent with neighboring values • Differences in accounting or regulatory treatment of certain bonds www.ift.world Yield Curve Movements and Slope • • • • • Yield levels have fallen to all time lows Yield curve movements can be represented as changes in 1) level 2) slope and 3) curvature Yield curve slope = spread between yield on long maturity bonds and short maturity bonds Yield curve curvature is measured using the butterfly spread Butterfly spread = – short-term yield + medium-term yield – long-term yield www.ift.world Duration and Convexity • Macaulay duration • Modified duration • Effective duration • Key rate duration • Money duration • Price value of a basis point • Effective convexity www.ift.world Major Types of Yield Curve Strategies Active strategies under assumption of a stable yield curve • Buy and hold • Roll down/ride the yield curve • Sell convexity • The carry trade Active strategies for yield curve movement of level, slope, and curvature • Duration management • Buy convexity • Bullet and barbell structures The application of these strategies depends on: • The investment mandate • The investment guidelines • The investment manager’s expectations • The costs of being wrong www.ift.world 3.1 Strategies under Assumptions of a Stable Yield Curve • Buy and Hold • Riding the Yield Curve • Sell Convexity • Carry Trade www.ift.world 3.2 Strategies for Changes in Market Level, Slope, or Curvature • Duration Management • Buy Convexity • Bullet and Barbell Structures www.ift.world Duration Management (1/2) % P change ≈ –D × ∆Y (in percentage points) How duration is changed impacts final result Position (cash) Sovereign Sovereign Sovereign Sovereign Market-weighted duration Duration 12 Current 33% 33% 33% 0 www.ift.world Alternative 50% 50% 0 Alternative 33% 0 33% 33% Duration Management (2/2) Futures contracts Nf = Required additional PVBP / PVBP of the futures contract Leverage MV of bonds to be purchased = (Additional PVBP / Duration of bonds to be purchased ) x 10,000 Effective portfolio duration ≈ (Notional portfolio value / portfolio equity ) x duration Swaps Maturity 5-Year 10-Year 20-Year Effective PVBP Receive Fixed 0.0485 0.0933 0.1701 Effective PVBP Pay Floating 0.0025 0.0025 0.0025 Net Effective PVBP 0.0460 0.0908 0.1676 www.ift.world PVBP per Million 460 908 1,676 10 Comparing the Performance of Various DurationNeutral Portfolios in Multiple Curve Environments The Baseline Portfolio The Yield Curve Scenarios Extreme Barbell vs Laddered Portfolio Extreme Bullet A Less Extreme Barbell Portfolio vs Laddered Portfolio Comparing the Extreme and Less Extreme Barbell Portfolios www.ift.world 27 5.1 The Baseline Portfolio Laddered Portfolio Bond Portfolio Nominal year year year year 10 year 30 year Market Value (millions) 10 10 10 10 10 10 60 Coupon 0.875 1.250 1.625 2.000 2.250 3.000 Maturity 30 Nov 2017 15 Dec 2018 30 Nov 2020 30 Nov 2022 15 Nov 2025 15 Nov 2045 www.ift.world Price 99.828 99.891 99.672 99.656 99.859 100.172 Yield to Maturity 0.964 1.287 1.694 2.053 2.266 2.991 1.876 Effective Duration 1.939 2.946 4.785 6.550 8.992 20.364 7.596 28 5.2 The Yield Curve Scenarios Maturity(years) 10 20 30 Starting Yield 0.964 1.287 1.490 1.694 2.053 2.266 2.629 2.991 2s–30s Spread Starting yield curve Flatter Steeper Parallel –100 0.010 0.287 0.490 0.694 1.053 1.266 1.629 1.991 2s 0.964 0.964 0.964 30s 2.991 2.491 3.491 Parallel +100 1.964 2.287 2.490 2.694 3.053 3.266 3.629 3.991 Spread 2.027 1.527 2.527 Flatter 0.964 1.269 1.455 1.640 1.964 2.123 2.308 2.491 Steeper 0.964 1.305 1.526 1.748 2.142 2.409 2.950 3.491 Butterfly spread Starting yield curve Less curvature More curvature Less Curvature 0.892 1.174 1.337 1.499 1.776 1.866 2.429 2.991 2s 0.964 0.892 1.036 More Curvature 1.036 1.400 1.644 1.889 2.330 2.666 2.829 2.991 10s 2.266 1.866 2.666 30s 2.991 2.991 2.991 Spread 0.577 –0.151 1.305 Butterfly spread = – 2-Year yield + (2 × 10-Year yield) – 30-Year yield www.ift.world 29 5.3 Extreme Barbell vs Laddered Portfolio Bond Portfolio Nominal year year year year 10 year 30 year Duration Convexity Yield Curve Scenario -100 +100 Flatter Steeper Less curvature More curvature Market Value (millions) 41.58 18.42 60.00 Coupon 0.875 1.250 1.625 2.000 2.250 3.000 Extreme Barbell Portfolio 7.595 1.578 Return 8.517 –6.823 3.243 –2.971 0.107 –0.107 Maturity 30 Nov 2017 15 Dec 2018 30 Nov 2020 30 Nov 2022 15 Nov 2025 15 Nov 2045 Price 99.828 99.891 99.672 99.656 99.859 100.172 Benchmark Portfolio 7.596 1.134 Return 8.241 –7.041 2.125 –1.974 1.146 –1.124 www.ift.world Yield to Maturity 0.964 1.287 1.694 2.053 2.266 2.991 1.586 Effective Duration 1.939 2.946 4.785 6.550 8.992 20.364 7.595 Return Difference 0.276 0.218 1.118 –0.997 –1.039 1.017 30 5.4 Extreme Bullet Bond Portfolio Nominal year year year year 10 year 30 year Duration Convexity Yield Curve Scenario -100 +100 Flatter Steeper Less curvature More curvature Market Value (millions) 34.25 25.75 Coupon 0.875 1.250 1.625 2.000 2.250 3.000 Maturity 30 Nov 2017 15 Dec 2018 30 Nov 2020 30 Nov 2022 15 Nov 2025 15 Nov 2045 60.00 Extreme Bullet Portfolio 7.598 0.643 Return 7.939 –7.277 0.881 –0.875 2.590 –2.534 Benchmark Portfolio 7.596 1.134 Return 8.241 –7.041 2.125 –1.974 1.146 –1.124 www.ift.world Price 99.828 99.891 99.672 99.656 99.859 100.172 Yield to Maturity 0.964 1.287 1.694 2.053 2.266 2.991 2.144 Effective Duration 1.939 2.946 4.785 6.550 8.992 20.364 7.598 Return Difference –0.302 –0.236 –1.244 1.099 1.444 –1.410 31 5.5 A Less Extreme Barbell Portfolio vs Laddered Portfolio Bond Portfolio Nominal year year year year 10 year 30 year Duration Convexity Yield Curve Scenario -100 +100 Flatter Steeper Less curvature More curvature Market Value (millions) 17.66 12.65 19.35 10.34 60.00 Less Extreme Barbell Portfolio 7.601 1.183 Return 8.269 –7.012 2.239 –2.083 1.287 –1.256 Coupon 0.875 1.250 1.625 2.000 2.250 3.000 Maturity 30 Nov 2017 15 Dec 2018 30 Nov 2020 30 Nov 2022 15 Nov 2025 15 Nov 2045 Benchmark Portfolio 7.596 1.134 Return 8.241 –7.041 2.125 –1.974 1.146 –1.124 www.ift.world Price 99.828 99.891 99.672 99.656 99.859 100.172 Yield to Maturity 0.964 1.287 1.694 2.053 2.266 2.991 1.801 Effective Duration 1.939 2.946 4.785 6.550 8.992 20.364 7.601 Return Difference 0.028 0.029 0.114 –0.109 0.141 –0.132 32 5.6 Comparing the Extreme and Less Extreme Barbell Portfolios Duration Convexity Yield Curve Scenario -100 +100 Flatter Steeper Less curvature More curvature Extreme Barbell 7.595 1.578 Return 8.517 -6.823 3.243 -2.971 0.107 -0.107 Less Extreme Barbell 7.601 1.183 Return 8.269 -7.012 2.239 -2.083 1.287 -1.256 Return Difference 0.248 0.189 1.004 -0.888 -1.180 1.149 www.ift.world 33 Exhibit 53 Relative Performance of Bullets and Barbells under Different Yield Curve Scenarios Yield Curve Scenario Level change Slope change Curvature change Rate volatility change Parallel shift Barbell Outperforms Bullet Underperforms Flattening Outperforms Underperforms Steepening Underperforms Outperforms Less curvature Underperforms Outperforms More curvature Outperforms Underperforms Decreased rate volatility Underperforms Outperforms Increased rate volatility Outperforms Underperforms www.ift.world 34 Example 4: Positioning for Changes in Curvature and Slope Heather Wilson, CFA, works for a New York hedge fund managing its US Treasury portfolio Her role is to take positions that profit from changes in the curvature of the yield curve Wilson’s positions must be duration neutral, and the maximum position that she can take in 30-year bonds is $100 million On-the-run Treasuries have the characteristics shown in the following table: Maturity Year Year 10 Year 30 Year Coupon 1.0% 1.5% 2.5% 3.0% Price 100 100 100 100 Yield to Maturity 1.0 1.5 2.5 3.0 Duration 1.98 4.80 8.80 19.72 PVBP/$ Million 198 480 880 1,972 If Wilson takes the maximum allowed position in the 30-year bonds and all four positions have the same (absolute value) money duration, what portfolio structure involving 2s, 5s, 10s, and 30s will profit from a decrease in the curvature of the yield curve? www.ift.world 35 A Framework for Evaluating Yield Curve Trades E(R) ≈ Yield income + Rolldown return + E(Change in price based on investor’s views of yields and spreads) - E(Credit losses) + E(Currency gains or losses) Expected gain/loss from change in yield ≈ [-MD × Yield] + [ẵ ì Convexity ì (Yield)2] Calculation of forward rates www.ift.world 36 Victoria Lim Investment horizon (years) Bonds maturity at purchase (years) Coupon rate Yield to maturity Current average bond price for portfolio Buy-and-Hold Portfolio 1.0 1.0 0.00% 1.00% 99.0090 Ride the Yield Curve Portfolio 1.0 2.0 0.00% 2.00% 96.1169 100.00 99.0090 1.5% 1.5% Expected average bond price in one year for portfolio Expected currency gains or losses If forecasted ending yield < forward rate  expected return > one-period rate If forecasted ending yield > forward rate  expected return < one-period rate www.ift.world 37 Lamont Cranston Investment horizon (years) Average bond price for portfolio currently Average bond price for portfolio in one year (assuming stable yield curve) Current modified duration for portfolio Expected effective duration for portfolio (at the horizon) Expected convexity for portfolio (at the horizon)* Expected change in US Treasury zero-coupon yield curve Bullet 1.0 94.5392 96.0503 Barbell 1.0 92.6437 94.3525 4.97 3.98 17.82 0.50% 4.93 3.98 32.57 0.50% www.ift.world 38 Example 5: Components of Expected Returns Investment horizon (years) Average annual coupon rate for portfolio Average beginning bond price for portfolio Average ending bond price for portfolio (assuming rolldown and stable yield curve) Expected effective duration for portfolio (at the horizon) Expected convexity for portfolio (at the horizon) Expected change in government bond yield curve www.ift.world Initial Portfolio 1.0 2.01% 100.00 100.46 1.313 0.9 — Yield Curve Shift Initial Portfolio Revised Portfolio 1.0 1.0 2.01% 1.91% 100.00 100.00 100.46 100.40 1.305 0.9 0.60% 0.979 0.60% 39 Using Structured Notes in Active Fixed-Income Management There is a class of fixed-income securities that can provide highly customized exposures to alter a portfolio’s sensitivity to yield curve changes These securities fall under the broad heading of structured notes Among the many types of structured notes used in fixed-income portfolio management are the following: • Inverse floaters • Deleveraged floaters • Range accrual notes • Extinguishing accrual notes • Interest rate differential notes • Ratchet floaters Structured notes can offer significantly lower all-in costs compared with traditional financing When used by sophisticated investors, structured notes allow the packaging of certain risks or bets Some structured notes can be extremely complicated, with complex formulas for coupon payments and redemption values Structured notes can be complicated and often lack liquidity Thorough due diligence and a high level of investment expertise are essential to effectively invest in these securities Many unsophisticated investors have purchased these securities without truly understanding their idiosyncratic characteristics and risks The Orange County debacle of 1994 is one notable example www.ift.world 40 Conclusion • Learning objectives • Summary • Examples • Practice Problems www.ift.world 41 ... of Yield Curve Strategies Active strategies under assumption of a stable yield curve • Buy and hold • Roll down/ride the yield curve • Sell convexity • The carry trade Active strategies for yield. .. Multiple Curve Environments A Framework for Evaluating Yield Curve Trades www.ift.world 2 Foundational Concepts for Active Management of Yield Curve Strategies Multiple forms of the yield curve. .. www.ift.world Yield Curve Movements and Slope • • • • • Yield levels have fallen to all time lows Yield curve movements can be represented as changes in 1) level 2) slope and 3) curvature Yield curve