The information ratio is a statistical measure used to evaluate the performance of an investment strategy. It is calculated by dividing the excess return of the strategy by the tracking error, which is a measure of the strategy’s risk. The formula for the information ratio is as follows:
Information Ratio = (Return of Strategy – Benchmark Return) / Tracking Error
Formula for Information Ratio
The information ratio is a measure of the risk-adjusted performance of an investment or a portfolio. It is calculated by dividing the excess return of the investment or portfolio by its tracking error. The excess return is the return of the investment or portfolio minus the return of a benchmark. The tracking error is the standard deviation of the difference between the return of the investment or portfolio and the return of the benchmark.
The higher the information ratio, the better the risk-adjusted performance of the investment or portfolio. A high information ratio indicates that the investment or portfolio is generating excess return with relatively low risk.
The formula for the information ratio is:
Information Ratio = Excess Return / Tracking Error
Steps to calculate the information ratio:
- Calculate the excess return of the investment or portfolio.
- Calculate the tracking error of the investment or portfolio.
- Divide the excess return by the tracking error.
The following table shows an example of how to calculate the information ratio:
| Investment or Portfolio | Excess Return | Tracking Error | Information Ratio |
|---|---|---|---|
| Portfolio A | 5% | 2% | 2.5 |
| Portfolio B | 8% | 4% | 2 |
As you can see from the table, Portfolio A has a higher information ratio than Portfolio B. This indicates that Portfolio A is generating excess return with relatively low risk compared to Portfolio B.
Factors that affect the information ratio:
- The risk-free rate: The risk-free rate is the return of a risk-free investment, such as a Treasury bill. The information ratio is calculated using the excess return, which is the return of the investment or portfolio minus the risk-free rate. Therefore, the risk-free rate can affect the information ratio.
- The correlation between the investment or portfolio and the benchmark: The correlation between the investment or portfolio and the benchmark measures how closely the two move together. A high correlation indicates that the investment or portfolio is following the benchmark closely, while a low correlation indicates that the investment or portfolio is moving independently of the benchmark. The correlation between the investment or portfolio and the benchmark can affect the information ratio.
- The volatility of the investment or portfolio: The volatility of the investment or portfolio measures how much the return of the investment or portfolio fluctuates. A high volatility indicates that the investment or portfolio is risky, while a low volatility indicates that the investment or portfolio is stable. The volatility of the investment or portfolio can affect the information ratio.
Use of the information ratio:
The information ratio can be used to:
- Compare the risk-adjusted performance of different investments or portfolios.
- Evaluate the performance of an investment or portfolio over time.
- Make investment decisions.
Question: How is the formula for information ratio calculated?
Answer: The formula for information ratio (IR) is:
IR = (Expected Return - Risk-Free Rate) / Tracking Error
Subject: IR
Predicate: is calculated by
Object: (Expected Return – Risk-Free Rate) / Tracking Error
Question: What is the purpose of the information ratio?
Answer: The information ratio measures the excess return (above the risk-free rate) per unit of tracking error.
Subject: Information ratio
Predicate: has the purpose of measuring
Object: Excess return per unit of tracking error
Question: How is tracking error related to the information ratio?
Answer: Tracking error is the standard deviation of the difference between the returns of a portfolio and its benchmark. The lower the tracking error, the more closely the portfolio follows the benchmark.
Subject: Tracking error
Predicate: is related to
Object: Information ratio
Well, there you have it folks! The not-so-secret formula for calculating the information ratio. I know this topic can be a bit of a brain teaser, but hey, at least now you have a cheat sheet to refer to. Thanks for sticking with me through all those numbers. If you’re feeling a bit overwhelmed, don’t worry, this stuff takes time to sink in. Just come back and visit again if you need a refresher. In the meantime, keep on investing wisely and may all your portfolio dreams come true!