1. Standard Deviation

Standard deviation measures the volatility or risk associated with the returns of an investment. It indicates how much a security’s returns deviate from its average return over a specific period. A higher standard deviation suggests greater fluctuations in returns, implying higher risk.

Standard deviation, also denoted as sigma (σ), is calculated as:

Where:

• Rt is the return of the security at time t
• R(avg) is the average return over the period
• T is the total number of return observations

For instance, if we calculate standard deviation using monthly returns over 5 years, T=60 (as there are 60 monthly return observations). Each R(t) represents the stock’s return in a given month, and R(avg) is the average monthly return over the 60 months.

A standard deviation of 4% for a stock with an average return of 10% means that, on average, the stock’s returns fluctuate about 4% above or below the mean return of 10%. This measure helps investors assess risk by understanding the variability of returns over time.

Source: CMIE, NJ’s Smart Beta Platform. Data is for the period 30th September 2006 to 31st December 2024. “Low 36-Month Daily Standard Deviation” is the portfolio of the top 100 stocks from the Nifty 500 universe based on lowest 36-Month standard deviation of daily returns. “High 36-Month Daily Standard Deviation” is the portfolio of the bottom 100 stocks from the Nifty 500 universe based on highest 36-Month standard deviation of daily returns. Companies with less than 36-month price history are not considered. Past performance may or may not be sustained in future and is not indication of future return.

2. Beta

Beta is a measure of a security's sensitivity to market movements. It compares the volatility of a stock or portfolio to the broader market, typically represented by a benchmark index.

• A beta of 1 implies the stock moves in line with the market.
• A beta greater than 1 indicates higher sensitivity (more volatile than the market).
• A beta less than 1 suggests lower sensitivity (less volatile than the market).

Example:
Suppose Stock A has a beta of 1.2.

• If the market rises by 10%, Stock A is expected to rise by 12% (1.2 × 10%).
• Conversely, if the market falls by 10%, Stock A is expected to fall by 12%.

Beta helps investors assess the risk of a stock relative to market movements and its suitability in a diversified portfolio.

Source: CMIE, NJ’s Smart Beta Platform. Data is for the period 30th September 2006 to 31st December 2024. “Low 36-Month Beta” is the portfolio of the top 100 stocks from the Nifty 500 universe based on lowest 36-Month Beta relative to Nifty 500 index. “High 36-Month Beta” is the portfolio of the bottom 100 stocks from the Nifty 500 universe based on the highest 36-Month Beta relative to Nifty 500 index. Companies with less than 36-month price history are not considered. Past performance may or may not be sustained in future and is not indication of future return.

3. Semi Deviation

Semi-deviation measures the volatility or risk of an investment but focuses only on the negative deviations below the mean return. It is often used by risk-averse investors to assess downside risk while ignoring positive fluctuations. A higher semi-deviation indicates greater downside volatility, implying higher risk.

Semi-deviation is calculated as:

Where:

• R(t) = Return of the security at time t
• R(avg) = Average return over the period
• T− = Number of return observations below R(avg)
• T = Total number of return observations

For instance, if we calculate semi-deviation using monthly returns over 5 years (T=60), we only consider the months where returns were below the average return. If semi-deviation is 3% for a stock with an average return of 10%, it means that, on average, the negative returns deviate by 3% from the mean.

While the most common approach is to consider returns below the average return, there are other ways to compute semi-deviation based on specific risk preferences:

• Using Only Negative Returns: Instead of measuring deviations from the mean, this method considers only those return observations that are negative (i.e., losses). This is useful for investors who are concerned only with periods of absolute loss rather than relative underperformance.
• Using a Fixed Threshold: Investors may define a specific benchmark return (e.g., S&P 500 or Nifty 500) or a required minimum return (e.g., 5%). Semi-deviation is then calculated considering only the returns below this threshold, making it a more tailored measure of downside risk.

Each of these variations helps investors quantify risk in a way that aligns with their risk tolerance and investment objectives. By focusing solely on downside fluctuations, semi-deviation provides a more refined view of risk compared to standard deviation, especially for those prioritizing capital preservation.

Source: CMIE, NJ’s Smart Beta Platform. Data is for the period 30th September 2006 to 31st December 2024. "Low 36-Month Semi-Deviation" is the portfolio of the top 100 stocks from the Nifty 500 universe based on lowest 36-Month semi-deviation. "High 36-Month Semi-Deviation" is the portfolio of the bottom 100 stocks from the Nifty 500 universe based on the highest semi-deviation. Companies with less than 36-month price history are not considered. Past performance may or may not be sustained in future and is not indication of future return.