Which are the common statistical terms used in Investing?
This article gives a brief overview of basic statistical terms used in investing in stocks and mutual funds.
Which are the common statistical terms used in Investing?
Posted on 08 Jul 2024
Author: Sayan Sircar
Tags: 
Choosing Investments
4 mins read
Choosing Investments
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This article gives a brief overview of basic statistical terms used in investing in stocks and mutual funds.
📚 Topics covered:
- What is Average?
- What is Median?
- What is Standard Deviation?
- What is Sharpe Ratio?
- What is Treynor Ratio?
- What is Alpha?
- What is Information Ratio?
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What is Average?
Average = (Sum of all values) / (Number of values)
The average, or mean, is a measure of central tendency that gives an idea of the central value of a dataset. In investing, it helps to understand the typical return over a period.
If the monthly returns of a mutual fund over three months are 2%, 3%, and 5%, the average return is (2% + 3% + 5%) / 3 = 3.33%.
What is Median?
Median = Middle value of a dataset when arranged in ascending or descending order
The median is the middle value of a dataset and is used to understand the central tendency without being affected by outliers. In investing, it can show the typical return in a way that is not skewed by extreme values. Median is best suited in data sets where mean is not sutiable.
For the returns 1%, 3%, 5%, 7%, and 9%, the median is 5%, as it is the middle value.
What is Standard Deviation?
Standard Deviation = sqrt[(Σ(xi - μ)²) / N]
Standard deviation measures the dispersion or variability of a dataset relative to its mean. In investing, it is used to gauge the risk or volatility of a stock or mutual fund.
If a mutual fund has monthly returns of 1%, 3%, 5%, 7%, and 9%, the standard deviation can show how much these returns deviate from the average, indicating the risk.
What is Sharpe Ratio?
Sharpe Ratio = (Rp - Rf) / σp
The Sharpe Ratio measures the performance of an investment compared to a risk-free asset, after adjusting for its risk (measured by standard deviation). It helps to understand the return of an investment relative to its risk.
If a mutual fund has a return of 10%, a risk-free rate of 4%, and a standard deviation of 5%, the Sharpe Ratio is (10% - 4%) / 5% = 1.2.
What is Treynor Ratio?
Treynor Ratio = (Rp - Rf) / βp
The Treynor Ratio measures returns earned in excess of that which could have been earned on a risk-free investment, per each unit of market risk. It is similar to the Sharpe Ratio but uses beta as the risk measure.
If a mutual fund has a return of 12%, a risk-free rate of 5%, and a beta of 1.5, the Treynor Ratio is (12% - 5%) / 1.5 = 4.67.
What is Alpha?
Alpha = Rp - [Rf + βp (Rm - Rf)]
Alpha measures the performance of an investment relative to a market index. A positive alpha indicates that the investment has outperformed the market after adjusting for risk.
If a mutual fund has a return of 15%, the market return is 10%, the risk-free rate is 4%, and the beta is 1.2, the alpha is 15% - [4% + 1.2*(10% - 4%)] = 3.8%.
What is Information Ratio?
Information Ratio = (Rp - Rb) / σ(Rp - Rb)
The Information Ratio measures the returns of an investment above the returns of a benchmark, relative to the volatility of those returns. It helps to assess the consistency of an investment’s performance.
If a mutual fund has a return of 14%, the benchmark return is 10%, and the tracking error (standard deviation of the difference) is 2%, the Information Ratio is (14% - 10%) / 2% = 2.
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