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Understanding Volatility

Understanding Volatility​

Volatility measures the degree of variation in an asset's price over time, representing the uncertainty or risk of price changes. High volatility indicates larger price swings, while low volatility reflects steadier price movements. Traders use volatility to assess risk and identify potential rewards in trading.

The "Moneyball" Analogy​

Imagine two players: Billy and Mike.

  • Billy scores consistently between 19 and 23 runs in each game, while Mike’s scores fluctuate between 10 and 33 runs.
  • Despite similar averages, Billy’s lower volatility makes him a safer choice.

This principle applies to stock markets—low-volatility assets are less risky compared to highly volatile ones.

Measuring Volatility: Standard Deviation​

Volatility is quantified using standard deviation, which measures how much an asset’s price deviates from its average.

  • Example: If Nifty has a volatility of 16.5%, the index is expected to trade within ±16.5% of its current value over a given period.
    Volatility is typically represented as a percentage, showing the expected price range for the asset.

Historical Volatility​

Historical Volatility analyzes past price movements to gauge risk. Here's how it’s calculated:

  1. Daily Returns: Logarithmic returns account for compounding.
  2. Average Return: Calculate the mean daily return over a period.
  3. Standard Deviation: Measure the dispersion of returns to find daily volatility.
  4. Annualizing Volatility: Multiply the daily standard deviation by the square root of 252 (trading days in a year).

Example:

  • If the daily standard deviation is 1.47%, the annualized volatility is:
    [ 1.47% \times \sqrt252 \approx 23.33% ]
    This means the stock is expected to fluctuate by approximately 23.33% annually.

Historical volatility is vital for options trading, impacting option pricing models like Black-Scholes. However, it doesn’t predict future price movements and is often combined with implied volatility for better analysis.

Normal Distribution and Volatility​

In trading, price movements often follow a normal distribution, represented by a bell curve:

  • 68% of price changes fall within ±1 standard deviation (σ) of the mean.
  • 95% fall within ±2σ.
  • 99.7% fall within ±3σ.

Example:
If a stock is trading at ₹100 with an annual volatility of 20%, traders expect the price to stay within ₹80–₹120 for 68% of the time, assuming a normal distribution. This helps estimate potential risk and reward.

Volatility in Options Pricing​

Volatility is integral to options pricing:

  • Low Volatility: Leads to lower premiums, as price movements are expected to be small.
  • High Volatility: Results in higher premiums, as larger price swings increase the likelihood of options expiring in the money.

The Black-Scholes Model relies on normal distribution and standard deviation (volatility) to calculate option prices accurately.

Conclusion​

Volatility is central to understanding market risk and pricing options. Whether through historical analysis or normal distribution, volatility helps traders predict price ranges, manage risk, and refine their strategies. Using tools like AlgoTest’s Strategy Builder and Simulator, traders can incorporate volatility into their trading decisions to enhance performance.