---
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.