CFA 2018 level 3 schweser practice exam CFA 2018 level 3 question bank CFA 2018 CFA 2018 r23 yield curve strategies IFT notes

R23 Yield Curve Strategies IFT Notes Table of Contents Introduction 2 Foundational Concepts For Active Management Of Yield Curve Strategies 2.1 A Review of Yield Curve Dynamics 2.2 Duration and Convexity 3 Major Types Of Yield Curve Strategies 3.1 Strategies under Assumptions of a Stable Yield Curve 3.1.1 Buy and Hold 3.1.2 Riding the Yield Curve 3.1.3 Sell Convexity 3.1.4 Carry Trade 3.2 Strategies for Changes in Market Level, Slope, or Curvature 3.2.1 Duration Management 3.2.1.1 Using Derivatives to Alter Portfolio Duration 3.2.2 Buy Convexity 3.2.3 Bullet and Barbell Structures Formulating A Portfolio Positioning Strategy Given A Market View 10 4.1 Duration Positioning in Anticipation of a Parallel Upward Shift in the Yield Curve 10 4.2 Portfolio Positioning in Anticipation of a Change in Interest Rates, Direction Uncertain 12 4.3 Performance of Duration-Neutral Bullets, Barbells, and Butterflies Given a Change in the Yield Curve 13 4.3.1 Bullets and Barbells 13 4.3.2 Butterflies 16 4.4 Using Options 18 4.4.1 Changing Convexity Using Securities with Embedded Options 20 Comparing The Performance Of Various Duration-Neutral Portfolios In Multiple Curve Environment 20 5.1 The Baseline Portfolio 20 5.2 The Yield Curve Scenarios 21 5.3 Extreme Barbell vs Laddered Portfolio 22 5.4 Extreme Bullet 23 5.5 A Less Extreme Barbell Portfolio vs Laddered Portfolio 24 5.6 Comparing the Extreme and Less Extreme Barbell Portfolios 25 A Framework For Evaluating Yield Curve Trades 26 Summary 30 Examples from the Curriculum 32 Example 33 Example 34 Example 35 Example 37 Example 38 IFT Notes for the Level III Exam www.ift.world Page R23 Yield Curve Strategies IFT Notes This document should be read in conjunction with the corresponding reading in the 2018 Level III CFA® Program curriculum Some of the graphs, charts, tables, examples, and figures are copyright 2017, 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 IFT Notes for the Level III Exam www.ift.world Page R23 Yield Curve Strategies IFT Notes Introduction This reading focuses on how different active yield curve strategies can be used to capitalize on expectations regarding the level, slope, or shape (curvature) of yield curves This reading also discusses the comparison of performance of various duration-neutral portfolios in multiple yield curve environments and a framework for analyzing the expected return of a yield curve strategy FOUNDATIONAL CONCEPTS FOR ACTIVE MANAGEMENT OF YIELD CURVE STRATEGIES There are three primary forms of the yield curve: i Par ii Spot iii Forward curve In all the forms, the X-axis represents maturity while the Y-axis represents yield (which can also be spot rate or forward rate) We need to make some assumptions in order to create a yield curve These assumptions may vary depending on the type of investor or by the intended use of the curve There are several challenges associated with constructing a yield curve, such as  Unsynchronized observations of various maturities on the curve  Gaps in maturities that require interpolation and/or smoothing For example, as shown in the yield curve below, the interpolated yield for the January 2017 maturity is about 4.85% However, the actual Treasuries with January 2017 maturity could have been purchased at that time with yields of about 5.35%   Observations that seem inconsistent with neighboring values Differences in accounting or regulatory treatment of certain bonds that may make them look like outliers 2.1 A Review of Yield Curve Dynamics The yield curve movements can be represented as changes in 1) Level: A change in level occurs when all the yields represented on the curve change by the same IFT Notes for the Level III Exam www.ift.world Page R23 Yield Curve Strategies IFT Notes number of basis points This movement is usually referred to as a parallel shift 2) Slope (a flattening or steepening of the yield curve) Yield curve slope represents the spread between yield on long maturity bonds and short maturity bonds As the spread increases or widens, the yield curve is said to steepen As the spread narrows, the yield curve is said to flatten If the spread turns negative, the yield curve is described as inverted 3) Curvature: Yield curve curvature 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 The three changes in yield curve shape are correlated with one another That is, if there is an upward shift in level, the yield curve typically flattens and becomes less curved Conversely, if there is a downward shift in level, the yield curve typically steepens and becomes more curved 2.2 Duration and Convexity   Macaulay duration: Like a bond’s effective maturity, Macaulay duration is a weighted average of time to receive the bond’s promised payments (both principal and interest) The present value of each payment to be received is weighted by the present value of all future payments It is measured in terms of years Modified duration: Modified duration gives us an estimate of the percentage price change (of the full price, including accrued interest) for a bond given a 1% (100 bps) change in its yield to maturity Macaulay duration Modified duration = (1+Yield to maturity for each period)     Effective duration: Effective duration gives us an estimate of the percentage price change for a bond given a 1% (100 bps) change in a benchmark yield curve Unlike modified and Macaulay duration, the effective duration measure can be used for bonds with embedded options Key rate duration (also called partial duration, or partials): Key rate duration gives us a measure of a bond’s sensitivity to a change in the benchmark yield curve at a specific maturity point or segment Key rate durations are useful for measuring the bond’s sensitivity to changes in the shape of the benchmark yield curve (known as “shaping risk”) Money duration: Money duration measures the change in price of the bond in units of the currency in which the bond is denominated In the United States, money duration is commonly called “dollar duration.” Price value of a basis point (PVBP): It is an estimate of the change in a bond’s price given a bp change in yield to maturity PVBP “scales” money duration so that it can be interpreted as money gained or lost for each basis point change in the reference interest rate This measure is also referred to as the “dollar value of an 0.01” (pronounced oh-one) and abbreviated as DV01 For example, for a bond’s par value of 100—a DV01 of $0.08 is equivalent to cents per 100 points Duration is a first-order effect that captures a linear relationship between bond prices and yield to maturity Convexity is a second-order effect that measures the bond’s sensitivity to larger movements in IFT Notes for the Level III Exam www.ift.world Page R23 Yield Curve Strategies IFT Notes yield  If a bond has positive convexity, then the bond price increases more if interest rates decrease (and decreases less if interest rates increase)  For a given change in interest rates, the expected return of a bond with positive convexity will be higher than the return of an identical-duration, lower-convexity bond Therefore, a bond with higher convexity tends to have a lower yield than a similar-duration bond with less convexity For zero-coupon bonds:  Macaulay durations increase linearly with maturity This implies that a 30-year zero-coupon bond has three times the duration of a 10-year zero-coupon bond  Convexity is approximately proportional to duration squared This implies that a 30-year zerocoupon bond has about nine times (three squared) the convexity of a 10-year zero-coupon bond  Coupon-paying bonds have more convexity than zero-coupon bonds of the same duration This means that a 30-year coupon-paying bond with a duration of approximately 18 years has more convexity than an 18-year zero-coupon bond  The more widely dispersed a bond’s cash flows are around the duration point, the more convexity it will exhibit Therefore, a zero-coupon bond has the lowest convexity of all bonds of a given duration  Convexity is more valuable when yields are more volatile This section addresses LO.a: LO.a: describe major types of yield curve strategies; MAJOR TYPES OF YIELD CURVE STRATEGIES The primary active strategies that we can use under the assumption of stable yield curve (i.e., no change in level, slope, or curvature):  Buy and hold  Roll down/ride the yield curve  Sell convexity  The carry trade The primary active strategies that we can use under the assumption of yield curve movement of level, slope, and curvature include the following:  Duration management  Buy convexity  Bullet and barbell structures The application of these strategies depends on several factors, including the following: 1) The investment mandate which the investment manager have to meet 2) The investment guidelines imposed by the asset owner 3) The investment manager’s expectations regarding future yield curve moves 4) The costs of being wrong IFT Notes for the Level III Exam www.ift.world Page R23 Yield Curve Strategies IFT Notes 3.1 Strategies under Assumptions of a Stable Yield Curve 3.1.1 Buy and Hold In an active “buy and hold” strategy, a portfolio is constructed whose characteristics deviate from the benchmark characteristics, and the portfolio is held nearly constant with no active trading during a certain period If the yield curve is expected to remain stable, we may make an active decision to position the portfolio with longer duration and higher yield to maturity in order to generate higher returns than the benchmark 3.1.2 Riding the Yield Curve Riding the yield curve is a strategy which involves purchasing securities with maturities longer than the investment horizon and selling them at the end of the investment horizon For riding the yield curve, if the yield curve is upward sloping, investors can buy bonds with maturity longer than his investment horizon since as the bond approaches the investment horizon, it is valued using successively lower yields and therefore at successively higher price This concept is known as “roll down”—the bond rolls down the (static) curve Like the buy-and-hold strategy, in riding the yield curve the securities, once purchased, are not typically traded However, riding the yield curve differs from buy and hold in its time horizon and expected accumulation This strategy may be particularly effective if the portfolio manager targets portions of the yield curve that are relatively steep and where price appreciation resulting from the bond’s migration to maturity can be significant Example: Assume there is a five-year maturity par bond with yield to maturity of 5% and a four-year maturity par bond with a yield to maturity of 4% After one year, the five-year bond becomes a four-year bond, its price will rise to the point that its yield to maturity equals 4% In addition to collecting the interest income during the period, the portfolio manager can benefit from this price appreciation 3.1.3 Sell Convexity As discussed earlier, convexity is more valuable when yields are more volatile If the yield curve is likely to remain stable, then holding higher-convexity bonds implies that we need to give up yield (since bonds with higher convexity have lower yield) We can sell convexity by selling calls on bonds held in the portfolio, or we can sell puts on bonds that we would be willing to own if, in fact, the put was exercised Selling convexity also results in additional returns in the form of option premiums Selling convexity strategy is not typically used in traditional fixed-income portfolios as the fixed income investment managers are not allowed to engage in option writing However, in case of such restrictions, we can use callable bonds or Mortgage-backed securities that provide an option-writing opportunity 3.1.4 Carry Trade A carry trade involves borrowing in the currency of a low interest rate country, converting the loan proceeds into the currency of a higher interest rate country, and investing in a higher-yielding security of that country In order to execute the trade successfully, we need to close the position (unwind the trade) before any change in interest rates creates a loss in the higher-yielding security that exceeds the carry earned to date The carry trade can be inherently risky, because it frequently involves a high IFT Notes for the Level III Exam www.ift.world Page R23 Yield Curve Strategies IFT Notes degree of leverage and the portfolio holds (typically) longer-term securities financed with short-term securities This section addresses LO.d: LO.d: explain how derivatives may be used to implement yield curve strategies; 3.2 Strategies for Changes in Market Level, Slope, or Curvature 3.2.1 Duration Management Duration management involves shortening the portfolio duration when interest rates are expected to rise (decreasing bond prices) and lengthening the portfolio duration when interest rates are expected to decline (increasing bond prices) The modified duration, D, can be used to estimate the percentage change in a security’s price (or the portfolio’s value), P, given a change in rates as follows: % P change ≈ –D × ΔY (in percentage points) In duration positioning, the pattern of bonds across the maturity spectrum is important for non-parallel changes in the yield curve Let us understand this by the following example Example: Consider a simple portfolio (Portfolio 1) allocated to three positions: one-third in cash, onethird in a sovereign bond with a duration of four years, and one-third in a sovereign bond with a duration of eight years The portfolio would have a market-weighted duration of approximately 4.0 years Suppose the manager wants to increase the duration to 6.0 years The Exhibit below outlines two alternatives to this Alternative 1: The duration can be increased by reducing the cash position to zero, adding half of the cash to the 4-year duration bond and the other half to the 8-year duration bond Alternative 2: A second alternative to increase the duration is leaving the cash position unchanged, selling the 4- and 8-year duration bonds, and buying in their place 6- and 12-year duration bonds The two alternative portfolios would have identical market-weighted durations, but they would respond differently to non-parallel yield curve moves because of their different structures For example, if bonds with durations greater than rallied (rates at the long end declined more than IFT Notes for the Level III Exam www.ift.world Page R23 Yield Curve Strategies IFT Notes rates at the shorter end), Alternative would outperform Alternative because Alternative has no exposure to bonds with durations greater than eight years 3.2.1.1 Using Derivatives to Alter Portfolio Duration Futures contract: We can alter portfolio duration using interest rate derivatives, e.g., by using futures contracts There are two important concepts necessary to calculate the futures trade required to alter a portfolio’s duration i Money duration Money duration is market value multiplied by modified duration, divided by 100 ii Price value of a basis point (PVBP) PVBP is market value multiplied by modified duration, divided by 10,000 For example, a portfolio with $10 million market value and a duration of has PVBP = ($10 million × 6)/10,000 = $6,000 In other words, for every bp shift in the US Treasury curve upward (or downward), the portfolio loses (or gains) $6,000 Example: Assume a $10 million portfolio and a US Treasury 10-year note futures contract with a PVBP of $85 If we want to increase portfolio duration to 7, we need to add $1,000 PVBP to a $10 million portfolio, we would need to buy 12 contracts as calculated below Required additional PVBP Number of contracts required = PVBP of the futures contract = 1000 = 85 11.76 or 12 contracts Leverage: We can also extend portfolio duration using leverage rather than futures The following calculation estimates the value of bonds required to extend the portfolio duration MV of bonds to be purchased = (Additional PVBP / Duration of bonds to be purchased) x 10,000 = (1000/6) X 10,000 = 1.67 million Effective portfolio duration ≈ (Notional portfolio value / portfolio equity) x duration R$11.67 mln ×6 ≈7 $10mln Leverage adds interest rate risk to the portfolio because it increases the portfolio’s sensitivity to changes in rates In addition, using leverage in portfolios which contain credit risk amplifies both credit risk and liquidity risk Interest rate swap: We can increase the portfolio duration using the Interest rate swaps as well We can increase the portfolio duration by using a receive-fixed swap (receive fixed, pay floating) Swaps are not as liquid as Futures contracts and in the short-run, they are not as flexible However, unlike futures (which are standardized contracts), swaps can be available for almost every maturity Example: Consider the following three interest rate swaps (all versus three-month Libor): IFT Notes for the Level III Exam www.ift.world Page R23 Yield Curve Strategies IFT Notes Assume a $10 million portfolio with a duration of and PVBP of $6,000 We can increase the portfolio duration up to as follows:  Using five-year swaps: Add 1,000/460 or $2.17 million in swaps  Using 10-year swaps: Add 1,000/908 or $1.1 million in swaps  Using 20-year swaps: Add 1,000/1,676 or $0.60 million in swaps This section addresses LO.b: LO.b: explain why and how a fixed-income portfolio manager might choose to alter portfolio convexity; 3.2.2 Buy Convexity We can alter portfolio convexity without changing duration in order to increase or decrease the portfolio’s sensitivity to an anticipated change in the yield curve   If yields rise, a portfolio of a given duration but with higher convexity will outperform a lowerconvexity portfolio with a similar duration Similarly, if yields fall, the higher-convexity portfolio will outperform a lower-convexity portfolio of the same duration As discussed earlier, a bond with higher convexity has a lower yield than a bond without that higher convexity The lower yield creates a drag on returns Hence, in order to benefit from higher convexity, the anticipated decline in interest rates must happen within short period Otherwise, over too long a period, the yield sacrificed will be larger than the expected price effect We can add more curvature to the price–yield function of our portfolio by adding instruments that have a lot of curvature in their price response to yield changes Refer to Exhibit below which shows the trajectory of the value of a call option on a bond relative to the bond price As the price of the underlying bond declines, the option value also declines, although at a slower pace than the price of the bond itself  If the bond price falls below the option’s strike price, the intrinsic value of the option is zero; any further decline in the bond price will have no effect on the (terminal) value of the option  When the price of the underlying bond rises, the option’s value quickly increases and its “delta (the IFT Notes for the Level III Exam www.ift.world Page R23 Yield Curve Strategies IFT Notes sensitivity of the option’s price to changes in the price of the underlying bond) approaches 1.0 3.2.3 Bullet and Barbell Structures Bullet and barbell structures can be used to capitalize on the non-parallel shifts in the yield curve Bullet Portfolio:  A bullet portfolio is made up of securities targeting a single segment of the curve  A bullet structure is typically used to take advantage of a steepening yield curve If the yield curve steepens through increase in long rates, the bulleted portfolio will lose less than a portfolio of similar duration If the yield curve steepens through a reduction in short rates, the bulleted portfolio loses less given the small magnitude of price changes at the short end of the curve Barbells Portfolio:  A barbell portfolio is made of securities concentrated in short and long maturities relative to the benchmark  A barbell structure is typically used to take advantage of a flattening yield curve If long rates fall more than short rates (and the yield curve flattens) the portfolio’s long-duration securities will gain more If the yield curve flattens through rising short-term rates, portfolio will outperform the benchmark due to lower price sensitivity to the change in yields at the short end of the curve Key rate durations (KRDs): KRDs (also called partial durations) are to measure the duration of fixed-income instruments at key points on the yield curve, such as 2-year, 5-year, 7-year, 10-year and 30-year maturities It is important to note that the sum of the KRDs must closely approximate the effective duration of a bond or portfolio Example: Consider the two portfolios, Portfolio and Portfolio  The effective duration of both portfolios is close to that of the index (5.85)  The convexity of Portfolio is also close to that of the index (0.779 versus 0.801)  The convexity of Portfolio is higher than that of the Portfolio (0.877 versus 0.779) and of the index (0.877 versus 0.801) The sums of the partial PVBPs for each of the two portfolios are the same (0.059) and close to the benchmark partial PVBPs (0.061)  Portfolio has key rate PVBPs distributed along the yield curve, underweighting the 5- and 20-year relative to the index, but the 2-, 3-, 10-, and 30-year maturities are well represented, evidencing a bullet structure  Portfolio materially overweights the 2s and 30s relative to the index and underweights the 3-, 5and 20-year segments, evidencing a barbell structure Performance of the two portfolio under different yield curve:  For parallel shifts, Portfolio is likely to perform similarly to Portfolio and the index because of their similar overall durations  In a curve flattening, Portfolio will outperform based on its barbell structure  If yield curve steepens, Portfolio outperforms IFT Notes for the Level III Exam www.ift.world Page 10 R23 Yield Curve Strategies IFT Notes 5.6 Comparing the Extreme and Less Extreme Barbell Portfolios Exhibit 52 displays return comparison of a less extreme barbell portfolio versus extreme barbell portfolio      The extreme barbell outperforms the less extreme barbell slightly in the parallel shifts because the extreme barbell portfolio has greater convexity If the curve flattens, the extreme barbell portfolio outperforms the less extreme barbell portfolio due to a large position in the longest bond (30-year Treasury) If the yield curve steepens, the extreme barbell portfolio underperforms the less extreme barbell portfolio If the curve loses curvature, then the less extreme barbell outperforms the extreme barbell by 118 bps If the curve adds curvature, then the less extreme barbell portfolio underperforms the extreme barbell portfolio by about 115 bps The following table provides a summary of the relative performance of bullet and barbell portfolios under various yield curve scenarios Yield Curve Scenario Barbell Bullet Level change Parallel shift Outperforms Underperforms Slope change Flattening Outperforms Underperforms Steepening Underperforms Outperforms Less curvature Underperforms Outperforms More curvature Outperforms Underperforms Decreased rate volatility Underperforms Outperforms Increased rate volatility Outperforms Underperforms Curvature change Rate volatility change Refer to Example from the curriculum IFT Notes for the Level III Exam www.ift.world Page 26 R23 Yield Curve Strategies IFT Notes This section addresses LO.g: LO.g: evaluate the expected return of a yield curve strategy; A FRAMEWORK FOR EVALUATING YIELD CURVE TRADES The expected return of a fixed income portfolio can be estimated using the following formula: 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) where E( ) indicates the analyst’s expectations based on his forecast Example: Victoria Lim is a fixed-income portfolio manager in the Singapore office of a large US wealth management company Her investment horizon is one year, and she is considering following two strategies: 1) Buy and hold: It consists of buying a portfolio of baht-denominated, one-year, zero-coupon notes issued by the Thai government (currently yielding 1.0%) 2) Riding the yield curve It consists of buying a portfolio of two-year zero-coupon Thai government notes and selling them in one year Exhibit 54 summarizes the key information for the two yield curve strategies Lim is considering Because the securities being considered for purchase are baht-denominated zero-coupon notes, the expected returns on the portfolio include expected currency gains and losses, as shown in Exhibit 55 IFT Notes for the Level III Exam www.ift.world Page 27 R23 Yield Curve Strategies  IFT Notes Notice that due to greater price appreciation (higher rolldown return) of the two-year zero-coupon note over the investment horizon (3.01% for the two-year zero versus 1.00% for the one-year zero) as its time to maturity shortens to one year and its yield declines from 2.0% to 1.0%, the expected return from simply riding the yield curve is higher than the expected return from the buy-and-hold strategy The implied one-year rate, one year forward can be estimated as follows: (1.02)2 / 1.01 − = 3.01%  This indicates that the yield curve contains an expectation that one-year rates will rise over the 12-month horizon  The bank’s forecast for a 1% one-year rate one year from now implies that the bank’s forecast is a decline in rates relative to the expectations embedded in the yield curve In summary,   If forecasted ending yield on a particular bond < forward rate  expected return > one-period rate If forecasted ending yield on a particular bond > forward rate  expected return < one-period rate Example: Lamont Cranston is a trader on the government securities desk of a US investment bank He expects that the US Treasury security zero-coupon yield curve will experience an upward shift by 50 bps in the next 12 months Cranston is considering following two strategies for the year ahead: 1) Bullet portfolio: 100% of its funds invested in five-year 2) Barbell portfolio: 62.97% of its funds invested in two-year Treasury zero-coupon notes, priced at 98.7816, and the remaining 37.03% of funds invested in 10-year Treasury zero-coupon bonds, priced at 83.7906 Other key assumptions are summarized in Exhibit 56 below IFT Notes for the Level III Exam www.ift.world Page 28 R23 Yield Curve Strategies IFT Notes With an expectation of a 50 bp upward shift at all points along the curve, the expected loss from the increase in rates is calculated as follows Expected gain/loss from change in yield [-MD ì Yield] + [ẵ ì Convexity × (∆Yield)2] Bullet portfolio: (–3.98 × 0.005) + [1/2 × 17.82 × (0.005)2] = –1.9677% Barbell portfolio: (–3.98 × 0.005) + [1/2 × 32.57 × (0.005)2] = –1.9493% The rolldown return is calculated as follows: (Bond priceeh − Bond pricebh ) Bond pricebh where the subscript bh indicates the bond price at the beginning of the horizon and the subscript eh indicates the bond price at the end of the horizon Bullet portfolio: (96.0503 – 94.5392) ÷ 94.5392 = 1.5984% Barbell portfolio: (94.3525 – 92.6437) ÷ 92.6437 = 1.8444% It is important to note that there is no yield income since both portfolios contain only zero-coupon bonds Total expected return over the one-year investment horizon for the bullet portfolio = -1.9677% + 1.5984%= 0.369% Total expected return for the barbell portfolio = -1.9493% + 1.8444% = –0.105% The derivation of the expected return is summarized in Exhibit 57 IFT Notes for the Level III Exam www.ift.world Page 29 R23 Yield Curve Strategies IFT Notes Refer to Example from the curriculum Using Structured Notes in Active Fixed-Income Management Structured notes are a type of fixed-income securities that provide highly customized exposures to alter a portfolio’s sensitivity to yield curve changes Examples of structured notes used in fixed-income portfolio management include the following:  Inverse floaters  Deleveraged floaters  Range accrual notes  Extinguishing accrual notes  Interest rate differential notes  Ratchet floaters Benefits:   Structured notes are relatively less costly compared with traditional financing Structured notes can be used to package certain risks or bets (if used by sophisticated investors) Limitations:    Structured notes can be extremely complicated, with complex formulas for coupon payments and redemption values Structured notes often lack liquidity Investments in structured notes require thorough due diligence and a high level of investment expertise Summary LO.a: describe major types of yield curve strategies; Active strategies under assumption of a stable yield curve IFT Notes for the Level III Exam www.ift.world Page 30 R23 Yield Curve Strategies IFT Notes Buy and hold Build portfolio with characteristics different from benchmark; minimize trading over investment horizon Roll down (ride) yield curve Works with upward sloping yield curve As bond ages  yield down  price up Target steep portion of yield curve  significant price appreciation Sell convexity If yields are stable then convexity does not help  sell convexity Sell options or buy callable bonds and MBS Carry trade Buy securities with high yield and finance with low-yield securities Active strategies for yield curve movement of level, slope, and curvature Duration management % P change ≈ –D × ∆Y (in percentage points) Duration management methods: • Number of futures contracts = Required additional PVBP / PVBP of the futures contract • MV of purchased bonds = (Additional PVBP / Duration of bonds to be purchased ) x 10,000 • Effective portfolio duration ≈ (Notional portfolio value / portfolio equity ) x duration • Notional value of swaps = Additional PVBP / PVBP of swap How the duration is changed does matter Bullet and barbell structures Bullets target a single segment of the yield curve; barbells target short and long yields Bullet structures well when yield curve steepens Barbell structures well when yield curve flattens Buy convexity If yield is expected to change  add convexity Higher convexity bonds are more expensive (lower yield) Convexity can be bought by 1) altering portfolio structure or 2) buying call options LO.b: explain why and how a fixed-income portfolio manager might choose to alter portfolio convexity; Adding Convexity Reducing Convexity Make structure more barbelled Make structure more bulleted Buy options Sell options Buy callable bonds IFT Notes for the Level III Exam www.ift.world Page 31 R23 Yield Curve Strategies IFT Notes Buy mortgage backed securities LO c: formulate a portfolio positioning strategy given forward interest rates and an interest rate view; View Strategy Upward sloping yield curve which will remain stable Roll down the yield curve Parallel shift up Lower duration Parallel shift down Higher duration High interest rate volatility Add convexity • Buy options • More barbelled structure If yield change does not materialize the higher convexity will cause a yield drag Low interest rate volatility Sell convexity • Sell options • More bulleted structure Flatter yield curve Barbell Steeper yield curve Bullet LO d: explain how derivatives may be used to implement yield curve strategies; Altering Duration  Number of futures contracts = Required additional PVBP / PVBP of the futures contract  Notional value of swaps = Additional PVBP / PVBP of swap Altering Convexity To add convexity of portfolio:  Sell bonds and buy options Par value of options needed = Par value of bonds being sold x (bond’s PVBP / option’s PVBP) To reduced convexity of portfolio:  Sell options  Replace regular bonds with callable bonds or MBS LO e evaluate a portfolio’s sensitivity to a change in curve slope using key rate durations of the IFT Notes for the Level III Exam www.ift.world Page 32 R23 Yield Curve Strategies IFT Notes portfolio and its benchmark; Key rate durations (KRD, partial durations) measure duration at key points on the yield curve    Used to identify bullets and barbells Sum of KRDs ≈ effective duration Predicted change = Portfolio par amount × Partial PVBP × (–Curve shift) LO f construct a duration-neutral government bond portfolio to profit from a change in yield curve curvature;  Long barbell and a short bullet o Benefit from flattening yield curve o Benefit from increase in curvature o More valuable when interest rate volatility is high  Short barbell and a long bullet o Benefit from steepening yield curve o Benefit from decrease in curvature o More valuable when interest rates are stable  Condor: positions Examples: o o  Long 2s Short 5s and Short 10s Long 30s Short 2s Long 5s and Long 10s Short 30s Relative Performance of Bullets and Barbells under Different Yield Curve Scenarios: Yield Curve Scenario Barbell Bullet Level change Parallel shift Outperforms Underperforms Slope change Flattening Outperforms Underperforms Steepening Underperforms Outperforms Less curvature Underperforms Outperforms More curvature Outperforms Underperforms Decreased rate volatility Underperforms Outperforms Increased rate volatility Outperforms Underperforms Curvature change Rate volatility change LO g evaluate the expected return of a yield curve strategy; 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)  If forecasted ending yield < forward rate  expected return > one-period rate IFT Notes for the Level III Exam www.ift.world Page 33 R23 Yield Curve Strategies  IFT Notes If forecasted ending yield > forward rate  expected return < one-period rate Expected gain/loss from change in yield [-MD ì Yield] + [ẵ ì Convexity ì (∆Yield)2] Examples from the Curriculum Example Yield Curve Strategies During a recent meeting of the investment committee of Sanjit Capital Management Co (Mumbai), the portfolio managers for the firm’s flagship fixed-income fund were asked to discuss their expectations on Indian interest rates over the course of the next 12 months Indira Gupta expects the yield curve to steepen significantly, with short rates falling in response to a government stimulus package and long rates rising as non-domestic investors sell their bonds in response to a possible sovereign credit rating downgrade Vikram Sharma also sees short rates declining as the Reserve Bank of India substantially lowers its policy rate to stimulate economic growth, but he expects the long end of the curve to remain unchanged He has only moderate conviction in his forecast for the long end of the curve Ashok Pal disagrees with his co-workers He believes the Indian economy is doing quite nicely and expects interest rates to remain stable during the next year From the following list, identify which yield curve strategy each of the three portfolio managers would most likely use to express his or her yield curve view Justify your response Strategy:        Roll down/ride the yield curve Sell convexity Carry trade Duration management Buy convexity Bullet Barbell Solution: Based on her view that the yield curve will steepen significantly with short rates falling and long rates rising, Gupta would most likely implement a bullet structure, concentrating the portfolio holdings in bonds whose duration are closely matched to the duration of the index The bullet structure offers protection against a steepening yield curve Based on his view that short rates will decline significantly while long rates remain unchanged, Sharma is unlikely to shorten duration but would adopt a bullet portfolio structure This approach avoids longer-maturity securities to insulate the portfolio against possible adverse moves at the long end of the curve The duration of his portfolio holdings may be less concentrated than Gupta’s given his more benign view of long rates Based on his view that interest rates will remain stable during the next 12 months, Pal is most likely to sell convexity for the year ahead With an expectation for stable interest rates, he sees little value in the convexity that currently exists in his portfolio Pal can sell convexity through the sale of IFT Notes for the Level III Exam www.ift.world Page 34 R23 Yield Curve Strategies IFT Notes options on bonds in his portfolio, or he could replace some of the current positions with callable bonds or mortgage backed securities Back to Notes Example Using Partial Durations to Estimate Portfolio Sensitivity to a Curve Change Assume Haskell revises his yield curve forecast as shown in Exhibit 31: Yields for the 2-year through 10year maturities each decline by bps, and the yield for the 30-year maturity increases by 23 bps Using the data from Exhibit 31, we compare the partial durations of the two portfolios Haskell is considering: Which portfolio would Haskell prefer to own under this scenario? Solution: If the curve becomes steeper and less curved, intuitively Haskell should prefer Portfolio Portfolio has significantly more partial duration at the intermediate maturities of and years, as well as substantially less partial duration at the shorter (2-year) and longer (30-year) maturities compared with Portfolio Portfolio thus would be expected to outperform Portfolio under a scenario in which the yield curve steepens and its curvature decreases This is confirmed as shown in the following table, which estimates the portfolio change using the portfolio’s key rate durations: IFT Notes for the Level III Exam www.ift.world Page 35 R23 Yield Curve Strategies IFT Notes Back to Notes Example Bullets and Barbells Observe the three US government Treasury bond portfolios in Exhibit 33—Base Portfolio, Portfolio A, and Portfolio B Each has the same market value of $60 million These portfolios differ significantly in terms of key characteristics, however—including yield to maturity, effective duration, and effective convexity—because of their different portfolio structures IFT Notes for the Level III Exam www.ift.world Page 36 R23 Yield Curve Strategies IFT Notes Discuss which portfolio (A or B) would be preferred to the base portfolio under each of the following yield curve scenarios   Scenario 1: The 2s–30s spread is expected to widen by 100 bps as short and intermediate rates fall and long rates remain stable Also, interest rate volatility is expected to be low during the next year Scenario 2: The 2s–30s spread is expected to narrow by 100 bps as short and intermediate rates rise and long rates fall Also, interest rate volatility is expected to be high during the next year Your answer should make reference to the expected shape of the yield curve; the allocation of notes and/or bonds in the selected portfolio; and the effective duration, effective convexity, and yield to maturity of the selected portfolio Solution for Scenario 1: A widening spread indicates a steepening yield curve A steeper yield curve and low volatility favors a bulleted portfolio (concentrated in the intermediate maturities—the 5-, 7-, and 10- year notes) because the intermediate maturities should perform better than the combination of the short- end and long- end positions in the expected steepening environment    Portfolio B is the portfolio best positioned for this scenario The higher effective duration (6.910) of Portfolio B relative to the base portfolio will benefit Portfolio B as intermediate interest rates decline Portfolio B will also benefit through the yield pickup of 32.1 bps (1.660%– 1.339%) received in exchange for giving up convexity of 0.287 (0.541 – 0.828) Solution for Scenario 2:       A narrowing spread defines a flattening yield curve A flatter yield curve and high volatility favors a barbelled portfolio (concentrated in the short and long maturities—the 2-year notes and 30-year bonds, respectively) Portfolio A is the portfolio best positioned for this scenario Together, the short and long ends of the curve should perform better than the intermediate maturities in the expected flattening environment Note that for the same rate rise, the short end will lose less money than the intermediate maturities in Portfolio B The higher effective duration (6.903) of Portfolio A relative to the base portfolio will benefit Portfolio A as long-term interest rates decline The small give-up in yield (1.298% – 1.339%) is a reasonable exchange for the added convexity of IFT Notes for the Level III Exam www.ift.world Page 37 R23 Yield Curve Strategies IFT Notes 0.696 (1.524 – 0.828) Back to Notes Example 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-therun Treasuries have the characteristics shown in the following table: 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? Solution: To profit from a decrease in yield curve curvature, Wilson should structure a condor: short 2s, long 5s, long 10s, and short 30s If the curvature decreases, the short positions in the 2s and 30s will profit as rates at either end of the curve rise, and the long positions in 5s and 10s will maintain their value If curvature decreases as a result of a decline in intermediate (5s and 10s) yields, the long positions at the intermediate maturities are likely to profit while the short positions in the 2s and 30s maintain their value To determine the portfolio positioning:   100 million 30-year bonds have a money duration of 100 × 1,972 = 197,200 (the maximum allowed position) To establish the remaining positions, each with the same money duration:  The 10s position should be 197,200/880 = 224.09 or 224 million (long)  The 5s position should be 197,200/480 = 410.83 or 411 million (long)  The 2s position should be 197,200/198 = 995.96 or 996 million (short) Wilson’s position should be short 996 million 2s, long 411 million 5s and long 224 million 10s, short 100 million 30s Details of the portfolio positioning are shown in the following table: IFT Notes for the Level III Exam www.ift.world Page 38 R23 Yield Curve Strategies IFT Notes Back to Notes Example Components of Expected Returns In Section 4.1, we introduced Hillary Lloyd, a fixed-income portfolio manager at AusBank, and demonstrated how she might choose to position her portfolio in anticipation of a 60 bp parallel upward shift in the yield curve Recall that she has a strong conviction that interest rates will increase Comparing the implied forward rates with the expected yields and returns on the bonds in her portfolio given her interest rate forecast, she concludes the best expected return will be earned with a portfolio invested 100% in the two-year bonds We now look to evaluate that decision Exhibit 58 provides information on the characteristics of Lloyd’s ending portfolio under such a scenario Information is also shown for her initial portfolio (with no restructuring) assuming it is held over the investment horizon given both a stable yield curve and the +60 bp curve shift Using the return decomposition framework provided, calculate the expected return for each portfolio and discuss the factors that contribute to the differences Exhibit 59 shows the decomposition of the portfolios’ expected returns into yield income, rolldown return, and expected price change based on yield view The initial portfolio holds all six (short- to intermediate-term) bonds The ending portfolio holds only the two-year bonds, the ones with the highest expected holding-period return IFT Notes for the Level III Exam www.ift.world Page 39 R23 Yield Curve Strategies IFT Notes Under Lloyd’s rising interest rate scenario, the revised portfolio generates a total expected return of 1.73% versus the initial portfolio’s expected return of 1.69% The portfolio holding only two-year bonds gave up 10 bps of yield income and bps of rolldown return in exchange for 19 bps of price protection from the shorter duration, resulting in bps of outperformance relative to the initial portfolio Yield income is 2.01% for the initial portfolio and 1.91% for the revised portfolio This difference is the result of the higher coupon income from the six-bond portfolio, because it holds the intermediatematurity, higher-coupon bonds The rolldown return for the initial portfolio is 0.463%, slightly higher than the 0.404% rolldown return for the revised portfolio The intermediate-term bonds in the initial portfolio contribute to this portfolio’s higher rolldown return—these intermediate-maturity bonds experience a larger price increase than the shorter-term bonds (2s), which are the only bonds in the revised portfolio The price change attributable to the yield view is −0.5874% for the revised portfolio, versus −0.7814% for the initial portfolio Due primarily to the revised portfolio’s shorter duration (0.979) relative to the initial portfolio (1.305), its losses are more moderate than those of the initial portfolio Taken together, these components explain the revised portfolio’s outperformance of bps under the anticipated rise in interest rates Back to Notes IFT Notes for the Level III Exam www.ift.world Page 40 ... offered by IFT CFA Institute, CFA , and Chartered Financial Analyst® are trademarks owned by CFA Institute IFT Notes for the Level III Exam www .ift. world Page R 23 Yield Curve Strategies IFT Notes. .. Forward Yieldb Implied Yield Change Yield Curve Forecast Holding Period Returnc Maturity [B] Coupon IFT Notes for the Level III Exam [E] www .ift. world Page 11 R 23 Yield Curve Strategies IFT Notes. .. owner 3) The investment manager’s expectations regarding future yield curve moves 4) The costs of being wrong IFT Notes for the Level III Exam www .ift. world Page R 23 Yield Curve Strategies IFT Notes