CFA level 3 CFA level 3 volume III applications of economic analysis and asset allocation finquiz curriculum note, study session 10, reading 23

Yield Curve Strategies INTRODUCTION In active portfolio management, portfolio returns are assessed with reference to some relevant benchmark, and managers seek to outperform the benchmark 2.1 FOUNDATIONAL CONCEPTS FOR ACTIVE MANAGEMENT OF YIELD CURVE STRATEGIES A Review of Yield Curve Dynamics A dynamic yield curve provides return opportunities to fixed-income managers Three basic movements in the yield curve includes: 1) a change in level (parallel shift in the yield curve) 2) a change in slope (flattening or steepening of the yield curve) 3) a change in curvature Active yield curve strategies are the primary tool for developing and implementing active fixed-income strategies 2.2 Duration, a first order effect, seeks to infer relation between bond price and YTM Some duration measures are as follows I Macaulay Duration is weighted average of time until the bond’s cash flows are received where the weights are the percent of PV of cash flows with respect to sum of PV of all cash flows II A change in level or parallel shift in the yield curve occurs when all the yields on the curve change by the same number of basis points Practically, this assumption is questionable Slope of the yield is measured by the difference between yield on long-maturity bond (e.g 30-yr bond) and yield on short-maturity bond (e.g 2-yr bond) As the spread widens(narrows), the yield curve is considered to be steepen (flatten) and negative value of spread results in inverted yield curve Commonly, yield curve is upward slopping which is also called normal yield curve Curvature of the yield curve is a function of the relationship among three points on the yield curve, short-end, mid-point and long end Common measure of the yield curve curvature is the butterfly spread • • upward shift in level, the yield curve flattens and becomes less curved downward shift in level, the yield curve steepens and becomes more curved Modified Duration is a more direct measure of relation between % change in bond’s price (including accrued interest) for a % change in yield Modified duration is calculated as: Modified Duration = !"#"$%"& ($)"*+,./0"12 3%,4 &+%56 75) 75)+,6 III Effective Duration is bond’s price sensitivity to change in benchmark yield curve Effective duration measure is useful when bond has embedded options IV Key Rate Duration measures bond’s sensitivity to change in the shape of the yield curve i.e change in the benchmark yield curve at some specific point or segment on the yield curve V Money Duration (a.k.a dollar duration) measures the bond’s absolute price change in its denominated currency units i.e approximate dollar change in bond price for 100 basis points change in yield VI Price Value of a basis point (PVBP) estimates change in bond’s price for a basis point change in yield i.e change in dollar value for each basis point change in reference interest rate VII Convexity, a second-order effect, captures bond price behavior for larger movements in yield curve The expected return of a bond with positive convexity will be higher than the return estimated by the duration measure whether interest rates increase or decrease Convexity measure becomes more valuable amid higher expected interest rate volatility Butterfly Spread = -(Short-term yield) + (2 x Mediumterm yield) – Long-term yield Note: These three changes in the yield curve are interrelated Generally, for a (an): Duration and Convexity –––––––––––––––––––––––––––––––––––––– Copyright © FinQuiz.com All rights reserved –––––––––––––––––––––––––––––––––––––– FinQuiz Notes 2 0 1 8 Reading 23 Reading 23 VIII Yield Curve Strategies Effective Convexity like effective duration measures the price behavior of bonds with embedded options such as callable bonds, MBS, whose cash flows change when yields change more the bond’s cash flows are dispersed around the duration point, the higher the convexity • NOTE: • For a zero-coupon bond: Ø there is a linear relation between Macaulay duration and maturity Ø convexity is approximately equal to [duration]2 • Coupon-paying bonds have higher convexity as compared to zero-coupon bonds as the Active strategies have been categorized into the following two groups Active strategies under assumption of a stable yield curve i Buy and hold ii Roll down/ride the yield curve iii Sell convexity iv The carry trade Active strategies for yield curve movement of level, slope, and curvature i Duration management ii Buy convexity iii Bullet and barbell structures The use of the above-mentioned approaches depends on several factors such as: • • • • Convexity (positive or negative) is an important factor in a bond portfolio’s return A portfolio’s convexity can be changed by shifting the duration distribution of bonds either by purchasing bonds of desired convexity properties, or through derivatives MAJOR TYPES OF YIELD CURVE STRATEGIES Active yield curve strategies imply that managers purposely deviate from the relevant benchmark to outperform the benchmark FinQuiz.com Investment mandate Investment constraints regarding duration, deviation from the benchmark, credit quality, geographical constraints, turnover, concentration limits etc Investment manager’s expectations about yield curve The costs of being wrong, such as relative loss, absolute loss in money terms, reputational impairment etc Several tools, portfolio managers generally use, to increase portfolio returns are duration adjustment, leverage, sector weighting and convexity Duration adjustment is considered to be the most powerful tool 3.1 Strategies under Assumptions of a Stable Yield Curve 3.1.1) Buy and Hold Active ‘buy & hold’ strategy may involve in constructing a portfolio whose features deviate from the benchmark, and the portfolio is held constant for certain time period For example, a portfolio manager estimates that the current normal yield curve is expected to remain stable for a certain time period, the portfolio manager may generate higher return by increasing the weights of longer maturity bonds This is not a passive strategy as it may appear due to low portfolio turnover 3.1.2) Riding the Yield Curve Riding the Yield Curve (RYC) is an aggressive version of buy & hold strategy Like buy & hold strategy, RYC works if the yield curve is upward sloping and manager believes that the yield curve is likely to remain static RYC is based on the concept of “roll down” As bond’s maturity approaches, its yield lowers and price rises Manager sells the bond and not only earns higher coupon but also benefits from the price appreciation of the bond The manager purchases another bond of original maturity and this process is repeated periodically until his curve view remains the same Managers particularly target the steeper portion of the curve as the steeper the curve, the higher the price appreciation gain For example, a manager who currently owns a 3-year 7% bond, anticipates that the yield curve will remain stable for the next two years Exhibit below shows maturity and yield for three bonds at time Reading 23 Yield Curve Strategies FinQuiz.com At time T0 Maturity Yield 4% 5% 7% As one year passes, the 3-year bond now becomes 2year bond and its price rises at the level that its yield equals 5%, (same as 2-year bond’s yield) The manager will sell that bond and will buy another 3-year 7% bond The manager earns 7% coupon during the year and sells the bond at higher price 3.1.3) Sell Convexity Consider two bonds of equal duration but varying convexity, the expected return will be higher for the bond with higher convexity if interest rates change (↑ 𝑜𝑟 ↓), therefore, this bond will have lower yield (higher price) compared to the bond with lower convexity A manager who anticipates lower future volatility or stable yield curve can enhance portfolio returns by reducing/selling the portfolio convexity i.e receiving option premiums by selling the calls and puts on the bonds Though many institutions prohibit option writing, however, investing in some securities inherently offer option-writing features such as callable bonds, mortgage-backed securities etc 3.1.4) Carry Trade Carry trade is another strategy to position a portfolio in anticipation of stable yield curve In a carry trade, manager purchases higher yield security, which is financed at a rate lower than the yield on that security, and earns the spread between the two rates This strategy frequently involves higher leverage Carry trade can be executed using two securities of same currency or of different currencies Cross-currency carry trade implies borrowing in a currency of a lower interest rate country and investing proceeds is a currency of a higher interest rate country In order to execute carry trade successfully, managers should be aware of currency risk or unfavorable interest rate changes Another risk is that before closing out the position, a substantial decline in price of high-yield bonds may wipe-off the spread earned to date When executed in large volume, carry trades are subject to Crowding risk i.e prices can become extreme volatile, if large number of investors try to exit from the positions at the same time 3.2 Strategies for Changes in Market Level, Slope, or Curvature 3.2.1) Duration Management Duration management, the basic fixed-income manager’s tool, offers active return opportunities if managers correctly predict the changes in interest rates Managers shorten portfolio duration in anticipation of rising interest rates and lengthen portfolio duration in anticipation of declining interest rates Duration measure assumes parallel shifts in the yield curve, % change in portfolio value = −Duration × ∆ Yield Therefore, for a bond with no embedded options, the relation among duration, price change and yield is straightforward To estimate the portfolio return, simply add all the anticipated bonds’ price changes based on duration and yield change Further incorporate prediction about extra price volatility and convexity measures If there are non-parallel shifts, portfolio values may deviate from the estimates Under such conditions, key rate duration is an essential tool in monitoring the portfolio’s duration distribution 3.2.1.1) Using Derivatives to Alter Portfolio Duration Portfolio duration can be altered using futures contract, leverage and interest rate swaps One way to adjust portfolio duration using derivatives is by means of futures contracts Futures contracts are sensitive to changes in the price of the underlying bonds and no cash outlay is required except posting and maintaining margin Two relevant concepts in this regard are money duration and PVBP Money Duration = Market value x Modified duration PVBP = !")?5* @"%$5 × !,6+3+56 6$)"*+,.A,AAA PVBP specifies money gain/loss for each basis point change in the interest rate Another way to adjust portfolio duration is by using leverage rather than futures To increase the portfolio duration, add desired PVBP by purchasing bonds through leverage The managers are not obligated to use bonds of the same duration as the portfolio, they can either use bonds of shorter duration and increase the market value to get the desired PVBP or use bonds of longer duration and decrease amount borrowed to attain the desired PVBP However, selection of bonds at shorter or longer point on the curve can add curve risk to the portfolio Reading 23 Yield Curve Strategies FinQuiz.com Interest rate swaps can also be used to alter the portfolio duration Swaps can be created for every maturity; however, they are less liquid than futures and less flexible than using leverage To lengthen(shorten) duration add a receive-fixed (pay-fixed) swap Bullet and barbell structures are the most common approaches to benefit from non-parallel shifts in the yield curve Based on the anticipation of the yield curve changes, two portfolios with similar duration can perform differently if their maturity structures are dissimilar Theoretically, swaps position can be created equivalent to either futures or leverage A receive-fixed swap (receive fixed, pay floating) is essentially a long position in a bond and short position in short-term security, similar to long bond, short financing in case of leverage or long bond, short repo position in a futures contract A bullet portfolio contains securities that target a single segment of the curve with the bonds aggregated around the portfolio’s target duration Therefore, a bulleted portfolio will have little exposure away from the target segment of the curve (at longer or shorter maturity points) For parallel shifts in the yield curve, all the three approaches will add same dollar volatility However, if the curve moves in a non-parallel manner, the results will be different due to curve risk (distinctive exposure to different parts of the curve) A barbell portfolio contains securities gathered at long and short maturity points compared to the benchmark A barbell portfolio exhibits higher convexity than a bullet portfolio The following discussion assumes the yield curve is linear Please refer to curriculum section 3.2.1.1 for illustration of all three approaches through examples 3.2.2) Buy Convexity Buying convexity is valuable when interest rates are expected to be volatile Managers can change the portfolio convexity (change in portfolio’s sensitivity to an anticipated change in the yield curve) to earn additional return, without any alteration in the portfolio duration Using options to enhance portfolio convexity is an alternative for managers who find it difficult to change the portfolio structure easily, especially when operating under tight duration constraints or when managing portfolios with broader mandates that also include credit securities Credit securities add illiquidity concerns, and managers can alter convexity using derivatives Consider two portfolios A and B of same duration but portfolio A has higher convexity than portfolio B Whether yields rise or fall, portfolio A will outperform the portfolio B Since the higher convexity portfolio offers lower yield, to benefit from higher convexity, the expected price effect must be higher than the yield sacrificed The longer it takes for price impact to unfold, the lesser is the benefit of adding convexity Enhancing portfolio convexity by shifting the distribution of bonds can be performed using derivatives such as options, swaptions, callable bonds and MBS 3.2.3) Bullet and Barbell Structures Relative to the benchmark, an active portfolio manager can shift the portfolio to be more laddered (securities distributed equally around various maturities), bullet (securities concentrated around single point on yield curve) or barbell (securities concentrated at longer and shorter points) Bullet structure is usually used to take advantage of a steepening yield curve Yield curve steepens when short-term yields decrease and the long-term yields increase Barbell structure underperforms the bullet structure because losses in longer duration securities will be higher compared to little price gains from shorter duration securities The bullet structure relatively performs better having all securities concentrated in the middle Barbell structure is usually used to take advantage of a flattening yield curve If the yield curve flattens, short-term yields increase, longterm yields decrease, barbell portfolio outperforms the bullet portfolio because price gains in longer duration securities will generally be higher (due to higher sensitivity) than price decline in shorter duration securities (due to lower sensitivity) Key rate durations (KRDs) measure duration of bonds at key points on the yield curve and help identifying bullets and barbells as KRDs Practice: Example 1, Reading 23, Curriculum Reading 23 Yield Curve Strategies FinQuiz.com FORMULATING A PORTFOLIO POSITIONING STRATEGY GIVEN A MARKET VIEW Following are some crucial elements required to modify a portfolio for the predicted changes in the yield curve Properly understand • • • • 4.1 the characteristics of the current portfolio and the benchmark against which the portfolio is being evaluated any client-imposed constraints a yield forecast portfolio positioning strategies suitable for the anticipated yield-curve changes Duration Positioning in Anticipation of a Parallel Upward Shift in the Yield Curve Refer to the CFA Institute’s curriculum section 4.1 for demonstration of the strategy through an example 4.2 Portfolio Positioning in Anticipation of a Change in Interest Rates, Direction Uncertain If a portfolio manager anticipates that rate will move by certain basis points but is unsure about the direction, he can improve the portfolio returns under such scenario by increasing the portfolio convexity By giving up yield (adding convexity), the manager can enhance returns i.e if rates rise the portfolio will bear less losses and if rates drop, the gains will be higher Suppose a manager currently holds a portfolio of 10-year Treasury bonds He can increase portfolio convexity by selling these bonds and investing the proceeds into a duration-matched barbell portfolio of shorter and longer maturities Refer to the CFA Institute’s curriculum section 4.2 for demonstration of the strategy through an example 4.3 Performance of Duration-Neutral Bullets, Barbells, and Butterflies Given a Change in the Yield Curve 4.3.1) Bullets and Barbells Consider two duration-matched portfolios of equal market value, a barbell portfolio containing 5-year bonds and a bullet portfolio containing two bonds of zero maturity (cash like) and 10-year maturity respectively If there is an instant downward parallel shift in the yield curve, barbell portfolio will outperform bullet portfolio because of barbell portfolio’s higher sensitivity to declining yields If the yield curve flattens in a way that short term rates rise but long-term rates remain unchanged, the barbell portfolio will outperform the bullet portfolio because barbell portfolio’s zero duration bond will not decline in value, whereas, bullet portfolio’s bond will lose money If the yield curve flattens in a way that short-term rates rise and long-term rates decline, the barbell portfolio will outperform the bullet portfolio in a way that the price of bullet portfolio will remain unchanged whereas, the price of barbell portfolio’s shorter maturity bond will remain stable (due to its cash-like feature) and longermaturity bond will rise If the yield curve steepens, the bullet portfolio will outperform the barbell portfolio because the price of intermediate maturity bonds will rise, whereas, both the bonds of barbell portfolio will experience no change in price Refer to the CFA Institute’s curriculum, exhibits 21, 22 and 23 for graphical illustration of the abovementioned scenarios of the changes in the yield curve Refer to the CFA Institute’s curriculum in blue box “How are partials calculated” 4.3.2) Butterflies A butterfly is a long-short combination of bullet and barbell portfolio structures, where bullet symbolizes the body of the butterfly and barbell represents the wings of the butterfly The butterfly structure is created by taking position in three securities; short-term, intermediate term and long-term As the butterfly structure is a money duration-neutral long- short position, therefore, the weights are selected in a way that the money duration of long and short portfolios are equal in value but reverse in signs If the yield curve changes in a parallel fashion, both the portfolios offset each other Though butterfly portfolios often use leverage, however, in case of an unlevered portfolio, short position can be created by underweighting the corresponding section of the yield curve relative to the benchmark Two types of butterfly structures include: Long barbell and short bullet – higher convexity position, benefit from a flattening of the yield curve Convexity become more valuable in a volatile interest rate situation Reading 23 Yield Curve Strategies Long bullet and short barbell – lower/selling convexity position, beneficial amid stable interest rate prediction or steepening of the yield curve In a butterfly portfolio, the weights of the wings (long & short ends) can be selected in many different ways Some common ones are: i ii iii Duration neutral – money duration neutral position i.e the weights are selected in a manner that the duration of the wings = the duration of the body and market values are also equal 50/50 – In 50/50 weighting, half the duration value (market value x modified duration) is allocated to each wing of the barbell portfolio Regression weighting – using the regression analysis for calculating the weights at long and short end of the curve Additional structures might involve using four-position trade (sometimes called condor) much like, butterfly with elongated body e.g a position involving a money duration-neutral: • long 2-yr bond • short 5-yr bond • short 10-yr bond • long 30-yr bond Long 2-yr Short 5-yr Short 10-yr Long 30-yr In the above-mentioned position, both the long and short pairs (long 2-yr, short 5-yr and short 10-yr, long 30-yr) become profitable if the curvature of the yield curve increases Refer to the CFA Institute’s curriculum Exhibit 32 for graphical illustration of the four-position trade Practice: Example 3, Reading 23, Curriculum 4.4 Using Options It is easier to increase the portfolio duration or convexity by using options e.g short maturity at-or near-the money call options on long-term bonds (such as 30-yr) exhibit high convexity Adding convexity using options can be performed by selling some bonds and purchasing call options on those FinQuiz.com bonds in a way that the portfolio’s effective duration and market value remains unchanged In order to maintain the initial PVBP of the portfolio, the required par value of the options can be estimated as follows: Par value of the options = Par value of the bonds sold × C,-6 D 1 EFGE ,7*+,-D 1 EFGE Some of the bonds’ sale proceeds are used to purchase options while the remaining can be invested in cash to maintain the portfolio duration Costs include: Initial purchase price of the options + forgone interest income on the bonds sold The post trade portfolio outperforms the pre-trade portfolio whether interest rates increase (even options expire worthless) or decrease (options’ own convexity become valuable), as long as the rate change is greater than certain basis points If large number of market participants are expecting movements in interest rates but are uncertain about the direction, the demand for convexity will increase and the strong demand will lead to higher option prices Under such circumstances, the purchase of convexity will not be very profitable even if volatility turns out to be high 4.4.1) Changing Convexity Using Securities with embedded Options A manager, expecting a stable yield curve or low yield volatility for a short horizon, can increase portfolio return by decreasing the portfolio convexity Convexity can be reduced by selling options or buying mortgage-backed securities (MBS) Buying MBS is equivalent to selling call options as MBS exhibits negative convexity because of the prepayment option that borrowers (homeowners) retain Given a manager’s expectation of stable yield curve, he will sell the treasury bonds and will purchase MBS If yields remain stable, the yield advantage of MBS will increase the portfolio returns However, the portfolio will suffer if rates change significantly in either direction Compared to treasury bonds, MBS due to their negative convexity feature, are more sensitive to increase in rates (drop in prepayments lengthens the duration) and less sensitive to decline in rates (increase in prepayments shortens the duration) Reading 23 Yield Curve Strategies FinQuiz.com COMPARING THE PERFORMANCE OF VARIOUS DURATION-NEUTRAL PORTFOLIOS IN MULTIPLE CURVE ENVIRONMENTS Relative performance of Bullet and Barbell under different yield curve scenarios Yield Curve Scenarios Outperforms Underperforms Level ∆ Parallel Shift Barbell Bullet Slope ∆ Flattening Steepening Less More Decreased Increased Barbell Bullet Bullet Barbell Bullet Barbell Bullet Barbell Barbell Bullet Barbell Bullet Curvature ∆ Rate Volatility ∆ Refer to CFA Institute’s curriculum section for illustration of performance comparisons of various duration-neutral portfolios in multiple yield curve environments through examples Practice: Example 4, Reading 23, Curriculum A FRAMEWORK FOR EVALUATING YIELD CURVE TRADES Expected return can be decomposed into five subcomponents This decomposition can help understanding the relative contribution of each component in the performance of the strategy E(R) ≈ Yield income + Rolldown return + E(∆ in price based on investor’s views on yields and yield spread) − E(Credit losses) + E(currency gains & losses) where E( ) stands for analyst’s expectations Refer CFA Curriculum section for the Case Studies: Victoria Lim and Lamont Cranston Practice: Example 5, Reading 23, Curriculum  ... measure duration of bonds at key points on the yield curve and help identifying bullets and barbells as KRDs Practice: Example 1, Reading 23, Curriculum Reading 23 Yield Curve Strategies FinQuiz. com... the curvature of the yield curve increases Refer to the CFA Institute’s curriculum Exhibit 32 for graphical illustration of the four-position trade Practice: Example 3, Reading 23, Curriculum 4.4... bonds of barbell portfolio will experience no change in price Refer to the CFA Institute’s curriculum, exhibits 21, 22 and 23 for graphical illustration of the abovementioned scenarios of the