Predictability Measure - IC, ICIR
For a factor model, we can measure the predictability of a factor by calculating the Information Coefficient (IC) and the Information Coefficient Information Ratio (ICIR).
Information Coefficient (IC)
Information Coefficient (IC) measures the cross-sectional correlation between factor scores at time t and realized returns at time t+1:
\[IC_t = \text{corr}(f_t, r_{t+1})\]where:
- $f_t$ is the factor score(factor loading) at time t.
- $r_{t+1}$ is the realized return at time t+1.
Interpretation:
- IC > 0.15: strong predictive power
- IC ≈ 0: no predictive power
- IC < 0: inverse predictor (potentially shortable)
Spearman rank IC and Pearson IC
IC can be calculated using either Spearman rank correlation or Pearson correlation:
Pearson vs Spearman Information Coefficient (IC)
| Feature | Pearson IC | Spearman IC |
|---|---|---|
| Definition | Correlation of raw values | Correlation of ranked values |
| Measures | Linear relationship | Monotonic relationship |
| Sensitivity to outliers | High (can be distorted by outliers) | Low (robust to extreme values) |
| Suitable when | Factor scores and returns are linearly related | Factor and returns follow any consistent ordering |
| Common in finance? | Sometimes used, but less robust | Widely used in quant research |
| Interpretation | Can be misleading if extreme values dominate | Better reflects true rank predictability |
| Preferred for factor IC? | No (unless assumptions clearly hold) | Yes (default choice in empirical analysis) |
Information Coefficient Information Ratio (ICIR)
Information Coefficient Information Ratio (ICIR) measures the stability of IC across time periods:
\[ICIR = \frac{\text{mean}(IC)}{\text{std}(IC)}\]Interpretation:
- ICIR > 0.5: good consistency
- ICIR > 1.0: very strong and stable factor
These metrics are standard in quantitative finance for assessing factor quality.
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