Volatility is a statistical measure of the dispersion of returns for a given security or market index. Typically, higher volatility indicates a riskier security. Volatility is often quantified using the standard deviation or variance between returns.
In securities markets, volatility implies significant swings in either direction. For example, a stock market with sustained rises and falls of more than one percent is considered volatile. Volatility is crucial in options pricing.
Key Takeaways
- Volatility reflects how much an asset’s prices fluctuate around the mean price.
- Several methods measure volatility, including beta coefficients, option pricing models, and standard deviations of returns.
- Volatile assets are considered riskier due to unpredictable price movements.
- Implied volatility predicts future market volatility, while historical volatility examines past price changes over set periods.
- Volatility is essential for calculating options prices.
Understanding Volatility
Volatility often signifies the uncertainty or risk related to the magnitude of changes in a security’s value. Higher volatility indicates a security’s value could be spread over a larger range, leading to dramatic price changes over short periods. In contrast, lower volatility means steadier asset value.
One way to measure an asset’s variation is by quantifying its daily returns. Historical volatility uses past prices to show the return variability. While variance captures return dispersion around an asset’s mean, volatility measures this variance over a specific time frame. Hence, volatility can be reported daily, weekly, monthly, or annually.
How to Calculate Volatility
Volatility is calculated using variance and standard deviation. The standard deviation, when multiplied by the square root of the period number, gives volatility:
Volatility = σ√T
Where:
- σ = standard deviation of returns
- T = number of time periods
For instance, consider monthly stock closing prices from $1 to $10. Here’s how to calculate variance and standard deviation:
- Find the mean: Sum of values ($55) divided by number of values (10) = $5.50.
- Calculate each value’s deviation from the mean. For example, $10 - $5.50 = $4.50.
- Square the deviations to remove negatives.
- Sum the squared deviations: 82.5.
- Divide by number of values: 8.25.
The resulting variance is $8.25. The square root gives the standard deviation: $2.87. This measure helps traders gauge potential price deviations from the average.
Types of Volatility
Implied Volatility
Implied volatility (IV) estimates future market volatility from an option’s price. It’s crucial for options traders because it reflects market predictions. Note that implied volatility shouldn’t be considered predictive science but a way to gauge probability.
Historical Volatility
Historical volatility (HV) measures past price fluctuations over predetermined periods. It is less commonly used than implied volatility, as it looks backward. A rise in HV indicates more movement than usual, suggesting a significant change. Conversely, a drop signifies stability.
Volatility and Options Pricing
Volatility is vital in options pricing models, estimating the underlying asset’s return fluctuation until the option expires. Higher volatility increases option premiums as the chance of the option ending in-the-money rises. Traders aim to predict future volatility to reflect the market price’s implied volatility.
Other Measures of Volatility
Beta
A stock’s beta (β) measures its relative volatility to the market. A beta of 1.1 indicates the stock moves 110% for every 100% market move.
The VIX
The Volatility Index (VIX) measures broad market volatility, gauging the 30-day expected volatility of the U.S. stock market from S&P 500 options. A higher VIX reading implies a riskier market.
Tips on Managing Volatility
Long-term investors should ignore short-term volatility and stay the course, as markets tend to rise long-term. Emotions like fear and greed can undermine strategies, but some investors use volatility to buy dips. Hedging strategies, like protective puts, are also helpful but become pricier with higher volatility.
Example of Volatility
Imagine an investor builds a retirement portfolio. Seeking low volatility, they consider two stocks:
- ABC Corp.: Beta of 0.78 (less volatile).
- XYZ, Inc.: Beta of 1.45 (more volatile).
A conservative investor might choose ABC Corp. for steadier short-term value.
What Is Volatility, Mathematically?
Volatility measures data dispersion around its mean over time, calculated as the standard deviation squared by the time periods. In finance, it refers to annualized market price dispersion.
Is Volatility the Same As Risk?
Volatility often indicates risk but isn’t the same. Risk involves potential losses, while volatility describes price magnitude and speed. High volatility can imply higher risk if it means more chances of loss.
Is Volatility a Good Thing?
Volatility’s value depends on one’s trading style and risk appetite. It can mean trouble for long-term investors but opportunities for day traders and options traders.
What Does a High Volatility Mean?
High volatility means rapid and steep price movements in both directions.
What Is the VIX?
The VIX is the CBOE’s short-term volatility measure derived from S&P 500 options. Also known as the “fear index,” it rises with falling stocks and indicates market sentiment.
The Bottom Line
Volatility measures price movements over time, often signaling fear and uncertainty. While increased volatility can create trading opportunities, it’s also crucial in options pricing.
Related Terms: risk, options, standard deviation, beta, variability, variance.
References
- Bhowmik, Roni and Wang, Shouyang. “Stock Market Volatility and Return Analysis: A Systematic Literature Review”. Entropy (Basel), vol. 22, no. 5, May 2020.
- P. J. Kaufman. “Trading Systems and Methods”, Pages 43-55, 849-867. John Wiley & Sons, 2019, sixth edition.
- Lee, Roger W. “Implied Volatility: Statics, Dynamics, and Probabilistic Interpretation”. Recent Advances in Applied Probability, Springer 2004, pp. 241–268.
- P. J. Kaufman. “Trading Systems and Methods”, Pages 855-856. John Wiley & Sons, 2019, sixth edition.
- JoVE. “JoVE Core Statistics; Chapter 4, Measures of Variation; 4.7: Coefficient of Variation”.
- Prof. C. J. Foot, Physics Department, University of Oxford. “SO9: Financial Physics; The Binomial Tree Model: A Simple Example of Pricing Financial Derivatives”.
- P. J. Kaufman. “Trading Systems and Methods”, Pages 44, 809. John Wiley & Sons, 2019, sixth edition.
- Cboe. “Cboe Volatility Index”.
- TradingView. “VIX”.
