Information Ratio Formula

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,

Information ratio Formula = (Rp – Rb) / Tracking error

where,

  • Rp = rate of return of the investment portfolio
  • Rb = 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., the number of trading days in a year.

Information Ratio Annualized = (Rp – Rb) / Tracking error * 252

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Explanation of the Information Ratio Formula

The formula for the calculation of information ratio can be obtained by using the following steps:

Below are the steps for calculation of information ratio –

  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 Rp.

  2. Now, determine the daily return of the benchmark index is gathered to compute the benchmark rate of return, which is denoted by Rb. Su0026P 500 is an example of such a benchmark index.

  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 = Rp u2013 Rb

  4. Now, they determine the tracking error, which is the standard deviation of the excess calculate the return of the portfolioCalculate The Return Of The PortfolioThe portfolio return formula calculates the return of the total portfolio consisting of the different individual assets. The formula is computed by calculating the return on investment on individual asset multiplied with respective weight class in the total portfolio and adding all the resultants together. Rp = ∑ni=1 wi riread more.

  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).

  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.

You can download this Information Ratio Formula Excel Template here – Information Ratio Formula Excel Template

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 below-given information for the calculation of the Information Ratio Formula.

Portfolio Rate of Return, Rp12%
Benchmark Rate of Return, Rb5%
Tracking Error6%

Therefore, the calculation of Information ratio will be as follows,

information ratio formula example 1.3
  • IR Formula = (12% – 5%) / 6%

IR will be –

information ratio formula example 1.3
  • IR = 116.7%

This means that the investment portfolio generates a risk-adjusted 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 portfolios 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 errorTracking ErrorTracking Error Formula measures the divergence arising between the price behaviour of the portfolio and the price behaviour of the respective benchmark. Tracking error = Rp-Ri (Rp = return from the portfolio, Ri = return from the index)read more for portfolio P and S is 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.

ParticularsPortfolio PPortfolio S
Portfolio Rate of Return13%12%
Tracking Error5%5%
Benchmark Rate of Return6%6%

For Portfolio P

The calculation of Information Ratio for Portfolio P is as follows,

information ratio formula example 2.2
  • IRP = (13% – 6%) / 5%

IR for Portfolio P will be –

IR formula example 2.3
  • IR= 140.0%

For Portfolio S

The calculation of Information Ratio for Portfolio S is as follows,

IR formula example 2.4
  • IR= (19% – 6%) / 14%

IR for Portfolio S will be –

IR formula example 2.5
  • IR = 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 a higher risk-adjusted 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.

Rp
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Information Ratio Formula =
 

Information Ratio Formula =
RpRb
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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 risk-adjusted performance of the investment portfolio.

Most of the investors use this ratio while making decisions pertaining to investments in exchange-traded funds or mutual funds based on their risk appetiteTheir Risk AppetiteRisk appetite refers to the amount, rate, or percentage of risk that an individual or organization (as determined by the Board of Directors or management) is willing to accept in exchange for its plan, objectives, and innovation.read more. 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 vis-à-vis the benchmark index fundIndex FundIndex Funds is a form of mutual fund constructed to replicate and match the performance of a particular country's index like S&P, NASDAQ, etc., and helps investors take broad market exposure due to the amount invested in various stocks of the different sectors of the economy.read more.

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