Chapter 14: Understanding Fixed-Income Risk and Return

1

Sources of Return in Fixed-Income Investing

Fixed-income returns are generated from multiple sources, each with distinct risk characteristics and time horizons. Understanding these components is essential for effective portfolio management and risk assessment.

Primary Return Components

Return Source	Description	Time Sensitivity	Risk Factors
Coupon Income	Periodic interest payments	Predictable timing	Credit risk, default risk
Rolldown Return	Price appreciation as bond approaches maturity	Time-dependent	Yield curve shape changes
Capital Gains/Losses	Price changes due to spread/rate movements	Market-dependent	Interest rate, credit, liquidity
Currency Effects	Foreign exchange gains/losses (if applicable)	Continuous	Currency volatility

Total Return = Coupon Income + Rolldown Return + Capital Gains/Losses + Currency Effects

Rolldown Return

Rolldown return occurs when the yield curve is not flat. As a bond approaches maturity, it "rolls down" the yield curve. In a normal upward-sloping curve, this generates positive returns even if yields don't change.

2

Interest Rate Risk Decomposition

Interest rate risk in fixed-income portfolios can be decomposed into various components, each requiring different management approaches and hedging strategies.

Level, Slope, and Curvature Risk

Yield Curve Risk Factors

Level Risk: Parallel shifts in the yield curve

Affects all maturities equally
Measured by portfolio duration
Most significant risk factor (typically 80-90% of total risk)

Slope Risk: Changes in yield curve steepness

Short vs. long-term rate differential changes
Measured by key rate durations
Important for bullet vs. barbell portfolios

Curvature Risk: Changes in yield curve convexity

Non-parallel, non-slope changes
Butterfly spread movements
Affects intermediate maturity bonds most

Key Rate Duration

Key rate duration measures sensitivity to changes in specific points on the yield curve, providing more granular risk measurement than modified duration.

Maturity Point	Key Rate Duration	Interpretation
2-year	0.5	0.5% price change for 1% change in 2-year rate
5-year	2.1	2.1% price change for 1% change in 5-year rate
10-year	1.8	1.8% price change for 1% change in 10-year rate
30-year	0.3	0.3% price change for 1% change in 30-year rate

Portfolio Key Rate Duration = Σ(Weight_i × Key Rate Duration_i)

3

Credit Risk Analysis and Measurement

Credit risk represents the possibility of loss due to deterioration in issuer creditworthiness or outright default. This risk has multiple dimensions that require comprehensive analysis.

Components of Credit Risk

Credit Risk Breakdown

Default Risk: Probability of issuer failing to meet obligations
Credit Migration Risk: Loss due to rating downgrades
Credit Spread Risk: Changes in risk premiums demanded by market
Recovery Risk: Uncertainty about recovery rates in default

Credit Risk Metrics

Metric	Formula	Application
Credit Spread Duration	Modified Duration × Spread Beta	Sensitivity to credit spread changes
Expected Loss	PD × LGD × EAD	Expected credit loss over time horizon
Credit VaR	Statistical model output	Potential credit loss at confidence level

Credit Spread Duration Example

A corporate bond has:

Modified Duration: 6.5 years
Credit spread: 150 basis points
Spread beta to index: 1.2

Credit Spread Duration = 6.5 × 1.2 = 7.8

If credit spreads widen by 50 basis points:
Price Impact = -7.8 × 0.50% = -3.9%

PD, LGD, and EAD Definitions

PD (Probability of Default): Likelihood of default within specified timeframe
LGD (Loss Given Default): Percentage of exposure lost if default occurs
EAD (Exposure at Default): Amount exposed to loss at time of default

4

Liquidity Risk and Market Microstructure

Liquidity risk in fixed-income markets can significantly impact portfolio performance, especially during periods of market stress. Understanding market microstructure helps in managing this risk.

Types of Liquidity Risk

Liquidity Risk Type	Description	Key Indicators	Mitigation Strategies
Market Liquidity	Ability to trade without price impact	Bid-ask spreads, trading volume	Focus on liquid sectors
Funding Liquidity	Access to cash for margin calls	Repo rates, cash reserves	Maintain cash buffers
Redemption Risk	Investor withdrawals forcing sales	Fund flow patterns	Liquidity tiering

Liquidity Measurement

Several metrics help quantify liquidity risk in fixed-income portfolios:

Common Liquidity Metrics

Average Daily Trading Volume: Historical trading activity measure
Bid-Ask Spread: Transaction cost indicator
Days to Liquidate (DTL): Time to liquidate position without excessive market impact
Market Impact Cost: Expected price impact of trading
Liquidity-Adjusted VaR: VaR including liquidity risk premium

Days to Liquidate = Position Size / (Daily Volume × Participation Rate)

Liquidity Risk in Stress Periods

During market stress, liquidity can evaporate quickly:

Bid-ask spreads widen dramatically
Trading volumes decline sharply
Correlations increase toward 1.0
Funding liquidity becomes constrained

5

Portfolio Risk Attribution and Decomposition

Understanding how different risk factors contribute to portfolio volatility enables more effective risk management and helps explain performance attribution.

Risk Factor Models

Multi-factor models decompose portfolio risk into systematic risk factors:

Risk Factor	Description	Typical Contribution
Duration Risk	Interest rate level sensitivity	60-80% of total risk
Curve Risk	Yield curve shape changes	10-20% of total risk
Credit Spread Risk	Credit risk premium changes	15-25% of total risk
Sector/Security Risk	Idiosyncratic factors	5-15% of total risk

Risk Attribution Calculation

Portfolio Variance = Σᵢ Σⱼ wᵢ wⱼ σᵢⱼ

where: wᵢ, wⱼ = portfolio weights, σᵢⱼ = covariance between assets i and j

Risk Decomposition Example

A portfolio with 4% annual volatility might decompose as:

Duration Risk: 3.2% (80% of total)
Credit Spread Risk: 0.8% (20% of total)
Curve Risk: 0.4% (10% of total)
Idiosyncratic Risk: 0.2% (5% of total)

Note: Components don't sum to total due to correlation effects.

Marginal vs. Component Risk

Marginal Risk: Additional risk from small position increase
Component Risk: Portion of total risk attributable to each position

Component risks sum to total portfolio risk, while marginal risks indicate optimal position sizing.

6

Risk Management Techniques and Hedging

Effective fixed-income risk management requires a combination of portfolio construction techniques, derivatives usage, and systematic monitoring processes.

Hedging Strategies

Strategy	Instrument	Risk Hedged	Considerations
Duration Hedging	Interest rate futures	Parallel yield curve shifts	Basis risk, rebalancing needs
Credit Hedging	CDS, credit indices	Credit spread widening	Counterparty risk, liquidity
Curve Hedging	Multiple futures maturities	Yield curve shape changes	Complex implementation
Currency Hedging	FX forwards, swaps	Foreign exchange risk	Hedging costs, timing

Portfolio Construction Techniques

Risk Budgeting Approach

Allocate risk rather than capital:

Total Risk Budget: Maximum acceptable portfolio volatility
Factor Risk Limits: Maximum exposure to each risk factor
Concentration Limits: Single issuer/sector exposure limits
Liquidity Requirements: Minimum liquidity buffer maintenance

Hedge Ratio Calculation

To hedge duration risk using Treasury futures:

Hedge Ratio = (Portfolio Duration × Portfolio Value) / (Future Duration × Future Value × Conversion Factor)

Example:

Portfolio: $100M, Duration = 5.5
Future: Duration = 6.2, Price = $125,000
Conversion Factor = 0.95

Hedge Ratio = (5.5 × $100M) / (6.2 × $125,000 × 0.95) = 745 contracts

Dynamic Risk Management

Risk management requires continuous monitoring and adjustment:

Daily Risk Monitoring: Track key risk metrics
Stress Testing: Evaluate performance under adverse scenarios
Rebalancing Rules: Systematic approach to maintaining target risk
Performance Attribution: Understand sources of returns and risks