Learning Module 5: Yield Curve Strategies

Learning Outcome Statements (LOS)

1. Factors affecting fixed-income portfolio returns due to a change in benchmark yields

Decomposition of Expected Return

Total expected return (\(E[R]\)) for a fixed-income portfolio can be decomposed into five components:

1. Yield Income
   • Coupon income + Reinvestment income
2. Rolldown Return
   • Price change as a bond moves closer to maturity (assuming a stable yield curve)
   • Rolling Yield = Yield Income + Rolldown Return
3. Expected Price Change (View of Yields)
   • Gain/loss based on the manager’s forecast of yield curve level changes
   • Includes duration & convexity effects
4. Expected Price Change (View of Spreads)
   • Gain/loss based on changes in credit spreads
5. Expected Currency Gains/Losses
   • For foreign bond holdings

Price-Yield Formula

\[\%\Delta P \approx -(\text{ModDur} \times \Delta Y) + \frac{1}{2} \times \text{Convexity} \times (\Delta Y)^2\]

2. Portfolio positioning strategy: Interest rate view coincides with market (Static)

Static Yield Curve Strategies

When the manager expects the yield curve to remain stable (unchanged), they can generate excess returns through:

1. Buy and Hold
   • Aim for higher yield by holding longer-duration or higher-yielding bonds
2. Riding the Yield Curve (Rolldown)
   • Buying bonds with a maturity longer than the investment horizon
   • As time passes, the bond “rolls down” a steep upward-sloping yield curve
   • Bond price rises as yield drops
   • Condition: Yield curve must be upward sloping and stable
   • Risk: Yields rise (capital loss)
3. Carry Trade
   • Borrowing at a low short-term rate (funding cost) to invest in a higher-yielding long-term bond
   • Profit: Yield spread (Carry) + Price appreciation (Rolldown)
   • Risk: Funding costs rise or long-term yields rise
4. Derivatives Implementation
   • Long Futures: Synthetically extend duration (leverage)
   • Receive-Fixed Swap: Receive long-term fixed rate (high), pay short-term floating rate (low)
     • Functions like a carry trade

3. Portfolio positioning strategy: Interest rate view diverges from market (Dynamic)

A. Divergent View on Rate Level (Duration Management)

• View: Rates will Fall (Bullish)
  • Action: Increase portfolio duration > Benchmark
  • Mechanics: Buy long-term bonds, sell short-term bonds
  • Use futures/swaps to extend duration
• View: Rates will Rise (Bearish)
  • Action: Decrease portfolio duration < Benchmark
  • Mechanics: Hold cash/short-term bonds, short futures
  • Pay-fixed on swaps

B. Divergent View on Yield Curve Slope

• Steepener: Expect spread between long and short rates to widen

  • Bull Steepener: Short-term rates fall faster than long-term rates
    • Action: Long Short-Term / Short Long-Term (Net positive duration)
  • Bear Steepener: Long-term rates rise faster than short-term rates
    • Action: Short Long-Term / Long Short-Term (Net negative duration)

• Flattener: Expect spread between long and short rates to narrow

  • Bull Flattener: Long-term rates fall faster than short-term rates
    • Action: Long Long-Term / Short Short-Term (Net positive duration)
  • Bear Flattener: Short-term rates rise faster than long-term rates
    • Action: Short Short-Term / Long Long-Term (Net negative duration)

C. Divergent View on Yield Curve Shape (Curvature)

• Butterfly Trades: Capitalize on changes in the curvature (hump) of the curve

  • Long Butterfly (Bet on Curvature Increasing/Stable)
    • Long the “Wings” (Short & Long maturities)
    • Short the “Body” (Intermediate maturity)
    • Benefits: Positive convexity
    • Profits if intermediate yields rise relative to wings
  • Short Butterfly (Bet on Curvature Decreasing)
    • Short the “Wings”
    • Long the “Body”
    • Benefits: Profits if the curve flattens/straightens out

4. Portfolio positioning based on expected interest rate volatility

Strategies depend on whether implied volatility (priced in options) is higher or lower than the manager’s expected volatility.

Long Volatility (Expect Volatility to Rise)

• Buy Straddle/Strangle
  • Buy Call + Buy Put
  • Profits from large moves in either direction
• Buy Bonds with Positive Convexity
  • Long option-free bonds perform better in volatile environments
  • Better than those with negative convexity (callable bonds/MBS)

Short Volatility (Expect Volatility to Fall/Stable)

• Sell Straddle/Strangle
  • Sell Call + Sell Put
  • Profits from stable rates (collect premiums)
• Buy Callable Bonds
  • High yield, but negative convexity
  • Performs well if rates are stable
• Sell Options on Futures
  • Sell puts or calls to earn income

Increasing Convexity

• Buy calls, puts, or putable bonds

• Reduce exposure to MBS and callable bonds ### 5. Evaluate sensitivity using Key Rate Durations (KRD)

• Effective Duration

  • Measures sensitivity to a parallel shift in the yield curve

• Key Rate Duration

  • Measures sensitivity to a shift in the yield curve at a specific maturity point
  • Measures shaping risk, holding other rates constant

Application

• A portfolio might match the benchmark’s Effective Duration but have different KRDs

• Example: Barbell portfolio (Long 2Y and 30Y) vs. Bullet portfolio (Long 10Y)

  • May have the same duration
  • If the curve steepens: Barbell outperforms
    • 2Y yield drops more or rises less than 10Y
  • If intermediate rates rise (curvature increases): Bullet underperforms

• Managers use KRD to identify and manage Shaping Risk

6. Yield curve strategies across currencies

Cross-Currency Carry Trade

Strategy

• Borrow in a low-yield currency (funding currency)
• Invest in a high-yield currency (target currency)

Return Sources

1. Yield Spread (Interest rate differential)
2. Currency movement (Spot FX change)

Unhedged

• Exposed to FX risk
• If funding currency appreciates > yield spread, trade loses money

Hedged

• Using forward contracts to hedge FX risk
• Eliminates the yield spread advantage (due to Covered Interest Parity)
• Carry trades are typically unhedged or selectively hedged

Breakeven Rate

• The amount the high-yield currency can depreciate before the trade loses money

7. Evaluate the expected return and risks of a yield curve strategy

Risk Assessment Framework

1. Duration Risk
   • Is the portfolio exposed to parallel shifts?
   • Measure: Effective Duration
2. Yield Curve Risk
   • Is the portfolio exposed to twists/turns?
   • Measure: Key Rate Durations
3. Convexity Risk
   • Is the portfolio exposed to large rate moves?
   • Measure: Convexity
4. Spread Risk
   • Exposure to credit/swap spreads
5. Currency Risk
   • For international trades

Scenario Analysis

• Projecting portfolio value under different yield curve scenarios

  • Parallel Shift
  • Steepening
  • Flattening

• Active Return = Portfolio Return - Benchmark Return

• Managers must verify if the potential alpha justifies the active risk

  • Tracking error introduced by the strategy