Volatility: measuring how much a price moves

For the members of the Financial Market Club, FSJES

Volatility measures the dispersion of an asset's returns around its average over time. In financial economics, it is computed as the standard deviation of logarithmic returns:

$$\sigma = \sqrt{\frac{1}{N - 1} \sum_{t=1}^{N} (r_t - \bar{r})^2}$$

Volatility does not measure whether an investment will make or lose money. It measures how violently price fluctuates along the path. A stock can exhibit high volatility and deliver outstanding multi-year returns, or display low volatility while slowly decaying in value.

Annualizing volatility#

Daily volatility is scaled to an annual benchmark by multiplying by the square root of the number of trading sessions in a year (typically 252 trading days on the Bourse de Casablanca):

$$\sigma_{\text{annuel}} = \sigma_{\text{quotidien}} \times \sqrt{252}$$

The square root scaling relies on the classical random walk assumption that daily returns are independent and identically distributed (i.i.d.).

In real markets, this independence assumption fails:

  • Volatility clustering: Periods of high volatility are followed by high volatility, and calm days cluster together (a phenomenon formalized by Robert Engle in ARCH/GARCH modeling).
  • Fat tails (leptokurtose): Extreme return events occur far more frequently in financial markets than predicted by a standard Gaussian bell curve. Stress tests assuming three standard deviations routinely underestimate crash frequency.

Volatility across Moroccan sectors#

The Moroccan equity market offers a compelling study in sectoral volatility divergence.

On the Bourse de Casablanca:

  1. Low-volatility defensive stalwarts: Companies with stable, regulated, or domestic cash flows (such as Maroc Telecom, Cosumar, and established retail banks like BCP) traditionally demonstrate annualized volatilities between 10% and 15%.
  2. Medium-volatility cyclical stocks: Industrial manufacturers, building materials (LafargeHolcim Maroc, Ciments du Maroc), and port operators (Marsa Maroc) fluctuate between 15% and 25% annualized volatility as construction and trade cycles wax and wane.
  3. High-volatility speculative assets: Mining firms tied to global metal commodity prices (Managem, SMI) and real estate development companies (Addoha, Alliances) have historically posted annualized volatilities exceeding 35% to 50%, reflecting high financial leverage and sensitivity to macro sentiment.

Because MASI is heavily weighted toward low-volatility banks and telecom, the headline Moroccan index frequently appears calm (annualized volatility around 8% to 12%), masking large volatility swings occurring within individual constituent stocks.

Historical volatility versus implied volatility#

Analysts distinguish between two distinct perspectives on volatility:

  • Historical (realized) volatility: Calculated retrospectively from past closing prices over a specified window (such as 30, 90, or 252 trading days). It records how turbulent price action was over historical intervals.
  • Implied volatility: Derived prospectively from options premiums using mathematical models like Black-Scholes. It reflects the market consensus forecast of future uncertainty over the contract lifespan.

Because Morocco does not currently feature an active exchange-traded equity derivatives market, participants on the Bourse de Casablanca rely primarily on realized volatility metrics and Parkinson high-low estimators to assess ongoing regime shifts.

Volatility is a proxy for risk, not risk itself#

A common mistake is treating volatility as identical to risk. Volatility treats upside rallies and downside crashes equally: a 5% surge and a 5% drop generate the exact same variance.

For a student investor, permanent capital destruction (such as corporate bankruptcy or terminal dilution) is the true risk, not temporary price fluctuation. To assess true downside exposure, investors pair volatility with path-dependent measures like Maximum Drawdown.

For discussion#

  1. If Attijariwafa Bank shares have a daily return standard deviation of 0.8%, calculate its annualized volatility assuming 252 trading days.
  2. Why does computing volatility over a quiet summer period on the Casablanca exchange give an artificially low risk forecast for the autumn trading months?
  3. If an investor holds a portfolio of five stocks, can the portfolio's total volatility be lower than the volatility of every individual stock it contains? Under what mathematical condition?

For the members of the Financial Market Club, FSJES.

Sources: Bodie, Kane, and Marcus, Investments, chapter 5 (risk and return). Hull, Options, Futures, and Other Derivatives, chapter 15 (volatility and historical estimation). Bank Al-Maghrib, Rapport annuel sur la stabilite financiere. Bourse de Casablanca market statistics.