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)

The Information Coefficient Information Ratio (ICIR) measures the consistency and stability of the IC across time periods:

\[ICIR = \frac{\text{mean}(IC)}{\text{std}(IC)}\]

Interpretation:

• ICIR > 0.5: Indicates good consistency in the factor’s predictive power.
• ICIR > 1.0: Indicates a very strong and stable factor.

These metrics are standard tools in quantitative finance for evaluating the quality and reliability of predictive factors.