Information Ratio (IR): Definition, Formula, vs. Sharpe Ratio

What Is the Information Ratio (IR)?

The information ratio (IR) measures portfolio returns beyond the returns of a benchmark, usually an index, compared to the volatility of those returns. The benchmark is typically an index representing the market or a particular sector or industry.

The IR is often used to measure a portfolio manager's level of skill and ability to generate excess returns relative to a benchmark, but it also attempts to identify consistency of performance by incorporating a tracking error or standard deviation component into the calculation.

The tracking error identifies the level of consistency in which a portfolio "tracks" the performance of an index. A lower tracking error indicates more consistent performance and less volatility relative to the benchmark, while a higher tracking error suggests greater variability and potential costs due to performance fluctuations.

The IR goes beyond simple return metrics, offering a nuanced view of how consistently a portfolio outperforms its benchmark while accounting for how much risk is taken. This makes it a key tool for evaluating active investment strategies.

Formula and Calculation of the Information Ratio (IR)

Although compared funds may be different in nature, the IR standardizes the returns by dividing the difference in their performances, known as their expected active return, by their tracking error:

$\begin{aligned} &\text{IR} = \frac{ \text{Portfolio Return} - \text{Benchmark Return} }{ \text{Tracking Error} } \\ &\textbf{where:}\\ &\text{IR} = \text{Information ratio} \\ &\text{Portfolio Return} = \text{Portfolio return for period} \\ &\text{Benchmark Return} = \text{Return on fund used as benchmark} \\ &\text{Tracking Error} = \text{Standard deviation of difference} \\ &\text{between portfolio and benchmark returns} \\ \end{aligned}$​IR=Tracking ErrorPortfolio Return−Benchmark Return​where:IR=Information ratioPortfolio Return=Portfolio return for periodBenchmark Return=Return on fund used as benchmarkTracking Error=Standard deviation of differencebetween portfolio and benchmark returns​

To calculate IR, subtract the total of the portfolio return for a given period from the total return of the tracked benchmark index. Divide the result by the tracking error.

Tracking errors can be calculated by taking the standard deviation of the difference between portfolio returns and index returns. For ease, calculate the standard deviation using a financial calculator or Excel.

What the IR Can Tell You

The information ratio identifies how much a fund has outperformed a benchmark. Higher information ratios indicate a desired level of consistency, whereas low information ratios indicate the opposite. Many investors use the information ratio when selecting exchange-traded funds (ETFs) or mutual funds based on their preferred risk profiles. While past performance doesn’t guarantee future returns, the IR helps assess if a portfolio consistently beats its benchmark.

Tracking errors are often calculated using the standard deviation of the difference in returns between a portfolio and the benchmark index. Standard deviation helps measure the risk or volatility level associated with an investment. A high standard deviation means more volatility and less consistency or predictability. The information ratio helps determine how much and how often a portfolio trades over its benchmark but factors in the risk of achieving excess returns.

As fees for actively managed funds range from 0.5% to 2% annually, more investors are shifting to passively managed funds that track benchmarks like the S&P 500. In 2023, the average expense ratio for equity mutual funds fell to 0.42%. It's important to evaluate whether an active fund consistently outperforms a comparable benchmark, and the information ratio (IR) offers a quantitative measure of a fund's performance relative to its benchmark.

The Difference Between the IR and the Sharpe Ratio

Like the information ratio, the Sharpe ratio assesses risk-adjusted returns. However, the Sharpe ratio compares an asset's return to a risk-free rate, such as a U.S. Treasury yield. It doesn't account for correlations with other assets, which may affect overall portfolio risk. 

The IR measures the risk-adjusted return related to a benchmark, such as the Standard & Poor's 500 Index (S&P 500), instead of a risk-free asset. The IR also measures the consistency of an investment's performance. However, the Sharpe ratio measures how much an investment portfolio outperformed the risk-free rate of return on a risk-adjusted basis.

Both financial metrics are useful, but the IR's use of an index benchmark often makes it more relevant for investors evaluating active fund management against the broader market. Also, the index comparison makes the IR more appealing since index funds are typically the benchmark for comparing investment performance, and the market return is usually higher than the risk-free return.

Limitations of Using the IR

Any ratio measuring risk-adjusted returns can have different interpretations depending on the investor. Each investor has different risk tolerance levels and, depending on factors such as age, financial situation, and income, might have different investment goals. Therefore, each investor interprets the IR differently depending on their needs, goals, and risk tolerance levels.

Also, comparing multiple funds to a benchmark can be complicated due to differences in securities, asset allocations, and entry points. Investors should consider various financial metrics alongside the IR to make a well-rounded investment decision.

Example of How to Use the IR

A high IR can be achieved by having a high rate of return in the portfolio compared to a lower return in the index and a low tracking error. A high ratio means that, on a risk-adjusted basis, a manager has consistently produced better returns than the benchmark index.

For example, say you're comparing two different fund managers:

• Fund Manager A has an annualized return of 13% and a tracking error of 8%
• Fund Manager B has an annualized return of 8% and a tracking error of 4.5% 
• Also, assume the index has an annualized return of -1.5%

Fund Manager A's IR equals 1.81 or (13 - (-1.5) / 8). Fund Manager B's IR equals 2.11 or (8 - (-1.5) / 4.5). Although Manager B had lower returns than Manager A, their portfolio had a better IR because, in part, it has a lower standard deviation or tracking error, which means less risk and more consistency of the portfolio's performance relative to the benchmark index.

The Bottom Line

The information ratio can be used to determine the effectiveness of a portfolio manager and whether the manager can continuously outperform a specific benchmark. This can help investors choose where to allocate their capital, specifically in deciding whether it is better to invest in a certain actively managed fund or if a passively managed fund would be a better option, particularly since passively managed funds have lower expense ratios.