Annualizing Information Ratios from Monthly Information Coefficients

Summary

The document asks how to convert information coefficients observed at a monthly frequency into an annualized information ratio. It presents a proposed scaling formula and raises a discrepancy with a sample calculation that applies an additional factor. The responses emphasize that the meaning of the frequency variable and the exact definition of the reported IC need to be established before interpreting the formula.

The key distinction is between an information coefficient, which measures association between a factor and subsequent stock returns under a chosen convention, and the conventional information ratio, defined as annualized excess return divided by annualized tracking error. Tracking error is the standard deviation of excess returns, with its own frequency adjustment. The replies do not settle a universal IC-to-IR conversion or validate the proposed expression; IC is not standardized enough for that without more context about the metric and sampling process.

Key ideas

• The conventional information ratio divides annualized excess return by annualized tracking error.
• Tracking error is the standard deviation of excess returns and must be annualized consistently.
• An information coefficient is distinct from an information ratio and lacks a single universal definition.
• A conversion formula depends on the IC definition, sampling frequency, and any scaling already applied.

Tags

# How to obtain annualized IR from t-monthly IC?


# How to obtain annualized IR from t-monthly IC?












When we checking the relation between some factors and Stock price, we could use Information Coefficient(IC) to meausre.

And then I already have t-monthly IC for each factor, and I need to calculate the annualized Information Ratio(IR).

I think the formula should be

```
Annual_IR = (AVG(IC) / t) / (STD(IC) * SQRT(12/t))
```

However, I read a sample code with a difference. What I am confused about is that he multiplies another 12 after the calculation above.

Thank you for any help!

## Answer by Chris (score 0)

https://quant.stackexchange.com/a/45044

What is 't'? Your definitions notwithstanding, it looks like a simple annualization--STD is annualized, average IC, unless done elsewhere, doesn't appear to be.

## Answer by Rehan (score 0)

https://quant.stackexchange.com/a/45046

The industry standard definition of IR is your excess return divided by your tracking error Tracking error is nothing but the standard deviation of your excess returns

$Information\ Ratio\ =\ \frac{Ann.\ Excess\ Returns}{Ann.\ Tracking\ Error}\\ \\ Ann.\ Tracking\ Error\ =Annualized\ \sigma ( Excess\ Returns)$

Information coefficient on the other hand is not a very standard metric. Could you elaborate on what metric you are using for IC?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.