CFA 2018 r23 yield curve strategies

Yield Curve Movements and Slope • Yield levels have fallen to all time lows • Yield curve movements can be represented as changes in 1 level 2 slope and 3 curvature • Yield curve slope

Level III

Yield Curve Strategies

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Reproduced and republished with permission from CFA Institute All rights reserved

Contents and Introduction

1 Introduction

2 Foundational Concepts for Active Management of Yield Curve Strategies

3 Major Types of Yield Curve Strategies

4 Formulating a Portfolio Positioning Strategy Given a Market View

5 Comparing the Performance of Various Duration-Neutral Portfolios in Multiple

Curve Environments

6 A Framework for Evaluating Yield Curve Trades

2 Foundational Concepts for Active Management of Yield Curve Strategies

Multiple forms of the yield curve

Some assumptions are made to construct

the yield curve

Challenges:

• Gaps in maturities that require

interpolation and/or smoothing

• Observations that seem inconsistent

with neighboring values

• Differences in accounting or regulatory

treatment of certain bonds

Yield Curve Movements and Slope

• Yield levels have fallen to all time lows

• Yield curve movements can be represented as changes in 1) level 2) slope and 3) curvature

• Yield curve slope = spread between yield on long maturity bonds and short maturity bonds

• Yield curve curvature is measured using the butterfly spread

• Butterfly spread = – short-term yield + 2 medium-term yield – long-term yield

Duration and Convexity

3 Major Types of Yield Curve Strategies

1 Active strategies under assumption of a stable yield curve

• Buy and hold

• Roll down/ride the yield curve

• Sell convexity

• The carry trade

2 Active strategies for yield curve movement of level, slope, and curvature

• Duration management

• Buy convexity

• Bullet and barbell structures

The application of these strategies depends on:

• The investment mandate

• The investment guidelines

• The investment manager’s expectations

• The costs of being wrong

3.1 Strategies under Assumptions of a Stable Yield Curve

• Buy and Hold

• Riding the Yield Curve

• Sell Convexity

• Carry Trade

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

• Duration Management

• Buy Convexity

• Bullet and Barbell Structures

Duration Management (1/2)

% P change ≈ –D × ∆Y (in percentage points)

How duration is changed impacts final result

Duration Management (2/2)

Futures contracts

Nf = Required additional PVBP / PVBP of the futures contract

Leverage

MV of bonds to be purchased = (Additional PVBP / Duration of bonds to be purchased ) x 10,000

Effective portfolio duration ≈ (Notional portfolio value / portfolio equity ) x duration

Swaps

Maturity

Effective PVBP Receive Fixed

Effective PVBP Pay Floating

Net Effective PVBP

PVBP per Million

Buy Convexity

When yield changes, convexity is good for a bondholder

If yield is expected to change  add convexity

• Higher convexity bonds are more expensive (lower yield)

• Anticipated decline must happen quickly

How can we ‘buy convexity’?

• Alter portfolio structure

• Add instrument with curvature (call option)

Bullet and Barbell Structures

Bullet Portfolios

• Securities targeting a single segment of the yield curve

• Take advantage of a steepening yield curve

Barbell Portfolios

• Securities concentrated in short and long maturities

• Take advantage of a flattening yield curve

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

Embedded Example

• Portfolios 1 and 2 have the same effective duration but different KRDs and convexity

• Portfolio 1 is more ‘bulleted’ and Portfolio 2 is more ‘barbelled’

• Portfolio 1 outperforms if yield curve steepens; Portfolio 2 outperforms if yield curve flattens

Example 1: 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

• Roll down/ride the yield curve

4 Formulating a Portfolio Positioning Strategy Given a

Market View

Sections:

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

• the benchmark

• the role the portfolio is intended to fill in the client’s portfolio

• any client-imposed constraints

• current portfolio characteristics

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

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

bonds)

Next 12-Month Price and Return Expectations under Assumption of Stable Yield Curve

Implied Forward Yield and Implied Yield Change

Next 12-Month Yield Forecast and Holding Period Return Estimation under Forecast Interest Rate Change (+60 bps)

Maturity Coupon

Current price

New Price

with Rolldown a

Holding Period Return

Forward Yield b

Implied Yield Change

Yield Curve Forecast

Holding Period Return c

4.2 Portfolio Positioning in Anticipation of a Change in

Interest Rates, Direction Uncertain

Maintain duration but add convexity  Create more of a barbelled portfolio

Security Coupon Maturity Date Price

Yield to Maturity

Effective Duration

Effective Convexity Brazil 6 month 6.000 17 Jan 2017 102.70 1.110 0.538 0.006

Brazil 3 year 8.875 14 Oct 2019 119.75 2.599 2.895 0.105

Brazil 10 year 6.000 7 April 2026 104.80 5.361 7.109 0.666

Brazil 30 year 5.000 27 Jan 2045 82.50 6.332 13.431 2.827

4.3 Performance of Duration-Neutral Bullets, Barbells,

and Butterflies Given a Change in the Yield Curve

Haskell Capital Management

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

Example 2: 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 10-year

maturities each decline by 5 bps, and the yield for the 30-year maturity increases by 23 bps

Which portfolio would Haskell prefer to own under this scenario?

Key Rate PVBPs Total 1 Year 2 Year 3 Year 5 Year 10 Year 20 Year 30 Year

Pro forma portfolio (1) 0.0587 0 0.0056 0.0073 0.0126 0.0127 0.0014 0.0191

More barbelled portfolio (2) 0.0585 0 0.0096 0.0040 0.0074 0.0119 0.0018 0.0238

Butterflies

Long barbell and a short bullet

 Benefit from flattening yield curve

 Positive convexity

 More valuable when interest rate volatility is high

Short barbell and a long bullet

 Benefit from steepening yield curve

 Effectively selling convexity

 More valuable when interest rates are stable

Ways to structure wings of a butterfly portfolio:

1 Duration neutral

2 50/50 weighting

3 Regression weighting

Condor: 4 positions Examples:

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

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

Example 3: Bullets and Barbells

Yield to Maturity

Effective Duration Effective Convexity

Effective Duration

Effective Convexity

4.4 Using Options

Convexity can be added using options

Effective Convexity

Yield to Maturity Price

Accrued Interest Nominal Effective Par Value

Market Value

Effective Duration

Yield to Maturity

Price

Accrued Interest Par Value Market Value

Adding Convexity with Options

Changing Convexity Using Securities with Embedded Options

To reduce convexity sell options or buy MBS

Starting position = $10 million US Treasury Note 1.375% maturing 31 January 2021; effective duration = 4.72

Manager’s expectation: low yield volatility over a short horizon

Strategy: Sell convexity by selling the Treasury and buying the 30-year Federal National Mortgage Association

(FNMA) 3% MBS, which has a slightly shorter effective duration of 4.60

FNMA 30-year 3% 2.647 2.204 1.458 0.432 –0.855 –2.340 –3.941

US 1.375% 31 Jan 2021 3.774 2.588 1.417 0.262 –0.879 –2.005 –3.117

Difference –1.127 –0.384 0.041 0.17 0.024 –0.335 –0.824

5 Comparing the Performance of Various

Duration-Neutral Portfolios in Multiple Curve Environments

1 The Baseline Portfolio

2 The Yield Curve Scenarios

3 Extreme Barbell vs Laddered Portfolio

4 Extreme Bullet

5 A Less Extreme Barbell Portfolio vs Laddered Portfolio

6 Comparing the Extreme and Less Extreme Barbell Portfolios

5.1 The Baseline Portfolio

Laddered Portfolio

Market Value (millions) Coupon Maturity Price

Yield to Maturity

Effective Duration

5.2 The Yield Curve Scenarios

Maturity(years) Starting Yield Parallel –100 Parallel +100 Flatter Steeper Less Curvature More Curvature

Starting yield curve 0.964 2.266 2.991 0.577

5.3 Extreme Barbell vs Laddered Portfolio

Market Value (millions) Coupon Maturity Price

Yield to Maturity

Effective Duration

5.4 Extreme Bullet

Market Value (millions) Coupon Maturity Price

Yield to Maturity

Effective Duration

5.5 A Less Extreme Barbell Portfolio vs Laddered Portfolio

Market Value (millions) Coupon Maturity Price

Yield to Maturity

Effective Duration

5.6 Comparing the Extreme and Less Extreme Barbell

Exhibit 53 Relative Performance of Bullets and Barbells

under Different Yield Curve Scenarios

Slope change

Curvature change

Rate volatility change

Decreased rate volatility Underperforms Outperforms Increased rate volatility Outperforms Underperforms

Example 4: Positioning for Changes in Curvature and Slope

Heather Wilson, CFA, works for a New York hedge fund managing its US Treasury portfolio Her role is to take

positions that profit from changes in the curvature of the yield curve Wilson’s positions must be duration neutral, and the maximum position that she can take in 30-year bonds is $100 million On-the-run Treasuries have the

characteristics shown in the following table:

Maturity Coupon Price

Yield to Maturity Duration PVBP/$ Million

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?

6 A Framework for Evaluating Yield Curve Trades

+ Rolldown return + E(Change in price based on investor’s views of yields and spreads)

- E(Credit losses) + E(Currency gains or losses)

Expected gain/loss from change in yield ≈ [-MD × ∆Yield] + [½ × Convexity × (∆Yield)2]

Calculation of forward rates

Victoria Lim

Buy-and-Hold Portfolio Ride the Yield Curve Portfolio

If forecasted ending yield < forward rate  expected return > one-period rate

If forecasted ending yield > forward rate  expected return < one-period rate

Lamont Cranston

Average bond price for portfolio in one year (assuming

stable yield curve)

Example 5: Components of Expected Returns

Average ending bond price for portfolio (assuming rolldown and stable

yield curve)

Using Structured Notes in Active Fixed-Income Management

There is a class of fixed-income securities that can provide highly customized exposures to alter a portfolio’s

sensitivity to yield curve changes These securities fall under the broad heading of structured notes Among the many types of structured notes used in fixed-income portfolio management are the following:

• Inverse floaters

• Deleveraged floaters

• Range accrual notes

• Extinguishing accrual notes

• Interest rate differential notes

• Ratchet floaters

Structured notes can offer significantly lower all-in costs compared with traditional financing When used by

sophisticated investors, structured notes allow the packaging of certain risks or bets Some structured notes can be extremely complicated, with complex formulas for coupon payments and redemption values

Structured notes can be complicated and often lack liquidity Thorough due diligence and a high level of

investment expertise are essential to effectively invest in these securities Many unsophisticated investors have purchased these securities without truly understanding their idiosyncratic characteristics and risks The Orange County debacle of 1994 is one notable example