What is the Information Ratio Formula?
“Information ratio” (IR) refers to the measure of an active investment manager’s success strategy which is derived by comparing the excess returns generated by the investment portfolio to the volatility of those excess returns.
The formula for information ratio is derived by dividing the excess rate of return of the portfolio over and above the benchmark rate of return by the standard deviation of the excess return with respect to the same benchmark rate of return.
Mathematically, the information ratio formula is represented as below,
where,
 R_{p} = Rate of return of the investment portfolio
 R_{b} = Benchmark rate of return
 Tracking error = Standard deviation of the excess return with respect to the benchmark rate of return
In case this ratio has been calculated based on daily returns, it can be annualized by multiplying the ratio by the square root of 252 i.e. number of trading days in a year.
Explanation of the Information Ratio Formula
The formula for the calculation of information ratio can be obtained by using the following steps:
Step 1: Firstly, gather the daily return of a particular investment portfolio over the course of a significant period of time, which may be monthly, annually etc. The return is computed based on the net asset value of the portfolio at the beginning of the period and at the end of the period. Then the average of all the daily returns is determined which is denoted as R_{p}.
Step 2: Now, determine the daily return of the benchmark index is gathered to compute the benchmark rate of return which is denoted by R_{b}. S&P 500 is an example of such a benchmark index.
Step 3: Now, the excess rate of return of the investment portfolio is calculated by deducting the benchmark rate of return (step 2) from the rate of return of the investment portfolio (step 1) as shown below.
Excess rate of return = R_{p} – R_{b}
Step 4: Now, the determine the tracking error which is the standard deviation of the excess calculate return of the portfolio.
Step 5: Finally, the calculation of information ratio is done by dividing the excess rate of return of the investment portfolio (step 3) by the standard deviation of the excess return (step 4).
Step 6: Further, this ratio can be annualized by multiplying the above ratio by the square root of 252 as shown above.
Examples of Information Ratio Formula (with Excel Template)
Let’s see some simple to advanced examples of Information Ratio Formula to understand it better.
Example #1
Let us take an example of an investment portfolio with a rate of return of 12% while the benchmark rate of return is 5%. The tracking error of the portfolio’s return is 6%.
Let’s use the belowgiven information for the calculation of the Information Ratio Formula.
Therefore, the calculation of Information ratio will be as follows,
 IR Formula = (12% – 5%) / 6%
IR will be –
 IR = 116.7%
This means that the investment portfolio generates a riskadjusted return of 116.7% for every unit of additional risk with respect to the benchmark index.
Example #2
Let us take an example of two investment portfolio P and S with the rate of return of 13% and 19%, while during the same period the benchmark rate of return is 6%. On the other hand, the tracking error for portfolio P and S are 5% and 14%. Determine which portfolio is the better investment given the risk associated.
Given below is the data used for the calculation of Information Ratio for Portfolio P and S.
For Portfolio P
The calculation of Information Ratio for Portfolio P is as follows,
 IR_{P} = (13% – 6%) / 5%
IR for Portfolio P will be –
 IR_{P }= 140.0%
For Portfolio S
The calculation of Information Ratio for Portfolio S is as follows,
 IR_{S }= (19% – 6%) / 14%
IR for Portfolio S will be –
 IR _{S }= 92.9%
From the above example, it can be seen that although portfolio S has a higher return compared to portfolio P, portfolio P is a better investment portfolio because it offers higher riskadjusted return indicated by the ratio of 140.0% as compared to 92.9% of portfolio S.
Information Ratio Formula Calculator
You can use the following Calculator.
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R_{b}  
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Information Ratio Formula =  
Information Ratio Formula = 


Relevance and Uses
From the perspective of an investor, it is important to understand the concept of information ratio because it is used as a performance metric by fund managers. Further, the ratio is also utilized to compare the abilities and skills of the fund managers dealing with investment strategies. The ratio throws light on the fund manager’s ability to generate sustainable excess returns or abnormally high returns over a period of time. Accordingly, a higher value of this ratio indicates the better riskadjusted performance of the investment portfolio.
Most of the investors use this ratio while making decisions pertaining to investments in exchangetraded funds or mutual funds based on their risk appetite. Although it can be argued that past performance may not be the right indicator of the future profits, the information ratio still finds its use in the determination of the portfolio performance visàvis the benchmark index fund.
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