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What Is Volatility?

Volatility measures how much an asset’s price or returns move up and down over time. It’s the most commonly used measure of risk in investing.

Definition

Volatility measures how much an asset’s price or returns move over time. High volatility means big swings and more uncertainty; low volatility means smaller movements and more stability. Volatility does not predict direction — only the magnitude of moves.

Why Volatility Matters

1. How risky it feels: Two assets with the same return can feel very different if one is much more volatile.
2. Long-term growth: High volatility can reduce compounded returns through drawdowns.
3. Portfolio behavior: The optimizer uses volatility to build the efficient frontier, compute risk scores, and calculate Sharpe ratio.
4. Emotional decisions: High volatility can cause investors to sell at the worst times.

How Volatility Is Measured

Volatility is usually measured as the standard deviation of returns:

Where r_i are individual period returns, r̄ is the mean return, and n is the number of periods. This formula captures how spread out returns are around their average.

Types of Volatility

• Historical volatility — based on past returns (commonly used by optimizers).
• Implied volatility — derived from option prices and reflects market expectations.
• Realized volatility — the actual volatility observed over a period.
• Annualized volatility — short-period volatility scaled to a yearly number.

Simple Examples

Example 1 — Low volatility asset: A bond fund that moves ±1% per month — stable and predictable.

Example 2 — High volatility asset: A crypto asset that moves ±15% per month — unstable with dramatic swings.

Example 3 — Same return, different volatility: Both portfolios return 8% per year: Portfolio A volatility 5%, Portfolio B volatility 20% — Portfolio A is far more stable and efficient.

Volatility and Compounding

Volatility reduces compounded returns via drawdowns (volatility drag). For example, +20% followed by −20% does not bring you back to the starting point — you end down about −4%:

Lower volatility leads to smoother compounding over time.

Why Crypto Has High Volatility

Crypto often displays large swings due to sentiment-driven moves, lower liquidity, regime shifts, and fat-tailed return distributions. Optimizers therefore apply robust techniques (MAD clipping, robust covariance estimation) and often limit crypto weights.

How Diversification Reduces Volatility

Volatility is reduced when assets do not move together (low correlation). Combining assets with low or negative correlation can significantly lower portfolio volatility even if individual assets are volatile.

How Your Optimizer Uses Volatility

• Builds the covariance matrix used for portfolio risk calculations.
• Computes portfolio standard deviation and risk scores.
• Calculates risk‑adjusted measures like the Sharpe ratio.
• Applies MAD clipping and other robust methods to limit outlier influence.
• Generates diagnostics for data quality and stability.

How to Interpret Volatility Levels

• Low (0–10%) — very stable, often bond-heavy.
• Moderate (10–20%) — balanced, typical for diversified portfolios.
• High (20%+) — large swings, higher emotional stress; common with crypto or concentrated equities.