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

 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 yiel

Table of Contents

1 Introduction 2

2 Foundational Concepts For Active Management Of Yield Curve Strategies 2

2.1 A Review of Yield Curve Dynamics 3

2.2 Duration and Convexity 3

3 Major Types Of Yield Curve Strategies 4

3.1 Strategies under Assumptions of a Stable Yield Curve 5

3.1.1 Buy and Hold 5

3.1.2 Riding the Yield Curve 5

3.1.3 Sell Convexity 6

3.1.4 Carry Trade 6

3.2 Strategies for Changes in Market Level, Slope, or Curvature 6

3.2.1 Duration Management 6

3.2.1.1 Using Derivatives to Alter Portfolio Duration 7

3.2.2 Buy Convexity 8

3.2.3 Bullet and Barbell Structures 9

4 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

5 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

6 A Framework For Evaluating Yield Curve Trades 26

Summary 30

Examples from the Curriculum 32

Example 1 33

Example 2 34

Example 3 35

Example 4 37

Example 5 38

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

1 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

2 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

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

Modified duration = (1+Yield to maturity for each period)Macaulay duration

 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 1 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 8 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

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 coupon bond has about nine times (three squared) the convexity of a 10-year zero-coupon bond

zero- 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;

3 MAJOR TYPES OF YIELD CURVE STRATEGIES

1 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

2 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

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

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: third in cash,

one-third in a sovereign bond with a duration of four years, and one-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 7 below outlines two alternatives to do 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 9 rallied (rates at the long end declined more than

rates at the shorter end), Alternative 2 would outperform Alternative 1 because Alternative 1 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 6 has PVBP = ($10 million × 6)/10,000 = $6,000

In other words, for every 1 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

Number of contracts required = PVBP of the futures contractRequired additional PVBP = 100085 = 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

$10mln × 6 ≈ 7 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):

Assume a $10 million portfolio with a duration of 6 and PVBP of $6,000 We can increase the portfolio duration up to 7 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 convexity portfolio with a similar duration

lower- 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 8 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

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

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 1 and Portfolio 2

 The effective duration of both portfolios is close to that of the index (5.85)

 The convexity of Portfolio 1 is also close to that of the index (0.779 versus 0.801)

 The convexity of Portfolio 2 is higher than that of the Portfolio 1 (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 1 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 2 materially overweights the 2s and 30s relative to the index and underweights the 3-, 5- and 20-year segments, evidencing a barbell structure

Performance of the two portfolio under different yield curve:

 For parallel shifts, Portfolio 2 is likely to perform similarly to Portfolio 1 and the index because of their similar overall durations

 In a curve flattening, Portfolio 2 will outperform based on its barbell structure

 If yield curve steepens, Portfolio 1 outperforms

 If yield curve flattens, Portfolio 2 outperforms

Refer to Example 1 from the curriculum

This section addresses LO.c:

LO.c: formulate a portfolio positioning strategy given forward interest rates and an interest rate view;

4 FORMULATING A PORTFOLIO POSITIONING STRATEGY GIVEN A MARKET VIEW

Modifying a portfolio for the anticipated yield curve change requires an understanding of the following:

 Benchmark against which the portfolio is being evaluated

 Role the portfolio is intended to fill in the client’s portfolio;

 Any client-imposed constraints, such as duration, minimum and overall credit quality, diversification,

or leverage;

 Current portfolio characteristics;

 A yield forecast (of course); and

 Knowledge of the portfolio positioning strategies most applicable to the anticipated yield curve environment

Analyst should have a yield forecast and knowledge of the portfolio positioning strategies most

applicable to the anticipated yield curve environment

4.1 Duration Positioning in Anticipation of a Parallel Upward Shift in the Yield Curve

In this section we will discuss the duration positioning in anticipation of a parallel upward shift in the yield curve using the following example

Hillary Lloyd is a portfolio manager at AusBank She manages a portfolio benchmarked to the XYZ Short- and Intermediate-Term Sovereign Bond Index, which has an effective duration of 2.00 Her mandate allows her portfolio duration to fluctuate ±0.30 year from the benchmark duration Lloyd is highly confident that yields will increase by 60 bps across the curve in the next 12 months

Security Descriptor (all are par

Implied Forward Yield and Implied Yield Change

Next 12-Month Yield Forecast and Holding Period Return Estimation under Forecast Interest Rate Change (+60 bps) [A] [B] [C] [D] [E] [F] [G] [H] [I]

Maturity Coupon

Current price

New Price with Rolldowna

Holding Period Return

Implied Forward Yieldb

Implied Yield Change

Yield Curve Forecast

Holding Period Returnc

Total Return ≈ −1 × Ending effective duration

× (Ending yield to maturity − Beginning yield to maturity)+ Beginning yield to maturity

For example, consider the two-year bond If the yield on the bond evolves to its implied forward yield of 2.33% (column F) as a one-year bond one year from now, it will return 1.50% But if, instead of changing

in yield by 83 bps to reach the forward yield, it changes by only +60 bps to reach the forecast yield of 2.10% (column H), the 23 bps of “unused” forward migration can be thought of as a last-minute rally in the one-year bond at the horizon For a duration just under one year (0.98) at the horizon, this 23 bp

“rally” would add just under 23 bps to a bond priced near par Using the above equation, the two-year bond has a holding period return of 1.72%, 22 bps higher than it would have had it simply moved to its implied forward yield

Total Return ≈ −1 × 0.98 × (2.10 − 1.91) + 1.91 ≈ 1.72%

Assuming no portfolio constraints, a manager can sell all current bond holdings except for the two-year bond and use all of the sales proceeds to buy more two-year bonds, because these offer the highest one-year return The portfolio duration would be 1.944 (given in Exhibit 17) and would meet the requirement of being 2.00 ± 0.30

4.2 Portfolio Positioning in Anticipation of a Change in Interest Rates, Direction Uncertain

In this section we will discuss the portfolio positioning in anticipation of a change in interest rates, when the direction is uncertain

Example: Stephanie Joenk manages the emerging markets government bond portfolio for a major

German bank As per the investment mandate, portfolio’s effective duration must match that of benchmark, the Bloomberg Emerging Market Sovereign Bond Index Based on her bank’s internal economic forecasts and her own analysis, she expects that rates will move by 250 bps in the year ahead,

although the direction of change is not yet certain

To position the portfolio to profit from this view, Joenk plans to increase the portfolio’s convexity Joenk currently holds a Brazilian 10-year bond with a duration that, combined with the other positions in her portfolio, keeps the effective duration aligned with the benchmark Other securities that are readily available in the market include 6-month bills as well as 3-year notes and 30-year bonds Exhibit 18 shows the details of these securities

Joenk can add convexity by selling the 10-year Brazilian bonds and investing all of the proceeds into a duration-matched barbell position of shorter and longer bonds:

To maintain the effective duration match between the portfolio and the index, the weighted duration of the combined trade (buy 3-year notes and buy 30-year bonds) must equal the duration of the 10-year notes she is selling, that is,

7.109 = (Duration of 3year note × Weight of 3 year note)

+ (Duration of 30year bond × Weight of 30 year bond) 7.109 = 2.895x + 13.431(1 − x)

Solving for x, we find x = 0.60

The proceeds from the sale of the 10-year note should be allocated 60% to the 3-year note and 40% to the 30-year bond:

(60% × 2.895) + (40% × 13.431) = 7.109

The gain in convexity will be:

([(Weight of the 3 year) × (Convexity of the 3 year)] +[(Weight of the 30 year) × (Convexity of the 30 year)] − [(Weight of the 10 year) ×

(Convexity of the 10 year)] = 60% × 0.105) + (40% × 2.827) – (100% × 0.666) = 0.528

The give-up in yield will be:

(Weight of the 3 year) × (YTM of the 3 year) + (Weight of the 30 year) × (YTM of the 30 year)

− (Weight of the 10 year) × (YTM of the 10 year)

= (60% × 2.599%) + (40% × 6.332%) – (100% × 5.361%)

= – 0.127 or – 1.27%

4.3 Performance of Duration-Neutral Bullets, Barbells, and Butterflies Given a Change in the Yield Curve

4.3.1 Bullets and Barbells

Refer to the Exhibit 19 shown below, reflecting a parallel shift of the yield curve with three bonds

marked along the curve: A, B, and C The bulleted portfolio (Portfolio B) consists 100% of Bond B The barbelled portfolio (Portfolio AC) consists of Bonds A and C, with 50% of the market value allocated to each Portfolio AC has greater convexity than Portfolio B

Exhibit 19 shows how these portfolios perform when the curve experiences an instantaneous parallel downward yield curve shift, a curve flattening, or a curve steepening

 In an instantaneous downward parallel shift, the higher-convexity barbell portfolio AC will

outperform bullet portfolio B slightly because of AC’s greater sensitivity to declining yields and rising prices

Refer to Exhibit 20 below which displays the assumptions made regarding the portfolio characteristics

 If curve flattens (assume that the long end of the curve is unchanged but that short rates rise),

reflected in Exhibit 21 below In this scenario, Bond A (the risk-free overnight money market fund) does not decline in value given its duration of near zero Bond C (the 10-year notes) does not change

in value because its yield does not change Portfolio B loses money because the yield on position B (the five-year notes) rises In this flattening scenario, the barbell portfolio (AC) outperforms the bullet portfolio (B)

 If curve flattens via a rise in short rates and a decline in long rates, reflected in Exhibit 22 below The price of Bond B is unaffected because the bond’s yield is constant The price of Bond A is unchanged given its zero (cash-like) duration The price of Bond C increases as the bond’s yield declines In aggregate, the value of Portfolio AC rises while the value of Portfolio B remains unchanged Hence, the barbell portfolio (AC) outperforms the bullet portfolio (B)

 If the yield curve steepens (as shown in Exhibit 23), the bullet Portfolio B outperforms barbell Portfolio AC

This section addresses LO.e:

LO.e: evaluate a portfolio’s sensitivity to a change in curve slope using key rate durations of the portfolio and its benchmark;

Example: Haskell Capital Management needs to manage a $60 million portfolio It anticipates that

short-term yields will go up and long-short-term yields will go down (refer to Exhibit 30, second column named “Key rate curve shift” We need to evaluate which of the two portfolios (Portfolio 1 and Portfolio 2) will perform better Portfolio 2 is more barbelled, evidenced by its PVBPs which is higher at shorter end and longer end of the curve

The impact of shift in the curve on the portfolio value is calculated as follows:

Predicted change = Portfolio par amount × Partial PVBP × (–Curve shift)

 For the original portfolio, the predicted change is of $43,500

 For the modified portfolio, the predicted change is of $119,200

 Hence, it is evident that in flattening yield curve scenario, Portfolio 2, which is a more barbelled portfolio, will outperform the less barbelled portfolio (Portfolio 1)

Refer to Example 2 from the curriculum

This section addresses LO.f:

LO.f: construct a duration-neutral government bond portfolio to profit from a change in yield curve curvature;

4.3.2 Butterflies

A butterfly trade is a combination of a barbell (wings of the butterfly) and a bullet (body of the

butterfly) The butterfly trade involves taking positions in three securities with varying maturities: short term, intermediate term, and long term Refer to the table below

There can be two types of butterfly structure:

1) Long barbell and a short bullet: Long barbell implies long on 2’s and long on 10’s while short bullet

means short on 5’s

 This structure benefit from flattening yield curve;

 This structure has positive convexity;

 This structure is more valuable when interest rate volatility is high

2) Short barbell and a long bullet: Short barbell implies short on 2’s and 10’s while long bullet means

long on 5’s

 This structure benefit from steepening yield curve;

 In this structure, we effectively sell convexity;

 This structure is more valuable when interest rates are stable

Ways to structure the wings of a butterfly portfolio: Following are three commonly used ways to

structure (i.e., weight) the wings of a butterfly portfolio:

1) Duration neutral weighting: In duration-neutral weighting, the weights are selected so that the duration of the wings equals the duration of the body and the market values are also the same Thus, the positions are also money duration neutral

1) 50/50 weighting: In a 50/50 weighting, we short the body and allocate the proceeds of the short sale

to the wings such that half the duration value (market value multiplied by modified duration) is allocated to each wing of the barbell portfolio

2) Regression weighting: A regression weighting butterfly uses historical data to estimate how much more volatile short-term rates are than long-term rates In this method, we would regress the spread between the long wing and the body against the spread between the body and the short wing

Condor: This strategy is a four-position trade For example,

 Long 2s Short 5s and Short 10s Long 30s

 Short 2s Long 5s and Long 10s Short 30s

Each pair will produce profits if the yield curve adds curvature

Refer to Example 3 from the curriculum

4.4 Using Options

The convexity of shorter maturities is relatively small Hence, it is quite difficult to add convexity to a portfolio without buying longer-maturity securities In such cases, we can extend duration and add convexity with options For example, we can easily increase the convexity of the portfolio by buying a call option (on Futures contract) Refer to the table below

We need to estimate how much par value worth of call option to buy Currently, the par value of 30-year bond in a portfolio is 10,000 as shown in the Exhibit 34 below If we want to reduce the par value to 3,200 This means we want to sell 6,800 par value worth of 30-year bond

We can estimate the par value of call option as follows:

6,800 × (PVBP of 30 year bond

PVBP of call option ) = 6,800 × (

0.21130.149) = 9,640

The original portfolio had effective convexity of 1.276 (Exhibit 34) whereas, the modified portfolio (Exhibit 35) has an effective convexity of 5.952 Now let us evaluate the impact of change in interest

30-4.4.1 Changing Convexity Using Securities with Embedded Options

In order to reduce convexity (or in other words, to buy negative convexity), we can either sell options or buy MBS

Example: A manager anticipates that yields will be relatively stable for the duration of the trade Hence,

he wants to sell convexity The manager has a starting position of $10 million US Treasury Note 1.375% maturing 31 January 2021; effective duration is 4.72

The manager can sell convexity by selling the Treasury and buying the 30-year Federal National