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gateway/knowledge/trading/strategies/fixed-income/value-factor.md

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+---
+description: "The value factor strategy for bonds selects bonds with the highest actual credit spread relative to a theoretically predicted spread from a cross-sectional regression, going long undervalued bonds in the top decile."
+tags: [fixed-income, factor, value, credit-spread, regression]
+---
+
+# Value Factor
+
+**Section**: 5.10 | **Asset Class**: Fixed Income | **Type**: Factor / Value
+
+## Overview
+"Value" in fixed income is defined by comparing a bond's observed credit spread to a theoretically predicted (fair value) credit spread. Bonds trading with a spread significantly above their predicted fair value are cheap (high value); those below are expensive. The strategy buys the top-decile bonds by value score.
+
+## Construction / Mechanics
+
+**Step 1: Estimate fair value spreads** via a cross-sectional linear regression across N bonds (i = 1,...,N):
+
+```
+S_i = Σ_{r=1}^K β_r · I_{ir} + γ · T_i + ε_i                      (410)
+```
+
+where:
+- S_i: observed credit spread of bond i (bond yield minus risk-free rate)
+- I_{ir}: dummy variable = 1 if bond i has credit rating r, 0 otherwise (K ≤ 21 ratings)
+- T_i: maturity of bond i
+- β_r, γ: regression coefficients (note: no separate intercept since Σ_r I_{ir} = 1 for each bond)
+- ε_i: regression residual
+
+The constraint:
+```
+Σ_{r=1}^K I_{ir} = 1   for all i                                    (412)
+```
+(each bond has exactly one credit rating, so the intercept is absorbed into the rating dummies)
+
+**Step 2: Compute fair value spread**:
+```
+S_i* = S_i - ε_i                                                     (411)
+```
+(the fitted value from the regression)
+
+**Step 3: Compute value score** — either:
+- V_i = ln(S_i / S_i*), or
+- V_i = ε_i / S_i* = S_i / S_i* - 1
+
+**Step 4: Select portfolio** — long bonds in the top decile by V_i (most undervalued).
+
+## Payoff / Return Profile
+- Profits when cheap bonds (high V_i) revert toward fair value, compressing their spreads.
+- Returns driven by credit spread compression and coupon income.
+- The strategy assumes mean-reversion in credit spreads around their rating- and maturity-implied fair value.
+
+## Key Parameters / Signals
+- S_i: observed credit spread (bond yield minus risk-free rate)
+- S_i*: fair value credit spread from cross-sectional regression
+- V_i = ln(S_i/S_i*) or V_i = S_i/S_i* - 1: value score
+- Top decile by V_i: the portfolio selection criterion
+
+## Variations
+- Long-short: long top decile (cheap bonds), short bottom decile (expensive bonds).
+- Separate regressions for Investment Grade and High Yield universes.
+- Additional cross-sectional controls (e.g., industry, liquidity) can be added as regressors.
+
+## Notes
+- "Value" in fixed income is harder to define than in equities because bonds have finite lifetimes and their spreads are heavily influenced by credit ratings and maturity.
+- The cross-sectional regression should be run on bonds within a comparable universe (e.g., only IG or only HY) to ensure meaningful comparisons.
+- Credit spread data may be noisy; outliers from bonds near distress can distort the regression.
+- Shorting corporate bonds is operationally challenging; the strategy is often implemented long-only.