How can volatility in CAD and oil be measured?

Direct answer

Volatility in CAD and oil (and the way they move together) can be measured by quantifying how much recent price changes vary over time. Instead of treating “volatility” as one number, use a small set of measures: (1) variability of returns for each series, and (2) co-movement stability (for example, rolling correlation) to describe whether CAD and oil tend to fluctuate together.

The key idea is to separate what the calculation captures (historical variability under explicit assumptions) from what it cannot guarantee (future movement, a stable relationship, or any predictive accuracy).

Mechanism or definition

Volatility is commonly operationalized as the variability of price changes. A practical approach starts with returns—the normalized change in price over a time interval—because returns are easier to compare across different price levels.

1. Single-series volatility (CAD or oil individually)

• Choose a data frequency (for example, daily closes) and a return definition (such as simple return or log return).
• Compute returns for each consecutive interval.
• Measure variability in a rolling window, for example:
  • Rolling standard deviation of returns over the last N intervals.
  • Optionally, a range-based measure (if you use high/low data), such as average true range, which reflects how wide price ranges get.

2. Relationship volatility (CAD versus oil together)

• Compute how strongly CAD and oil returns move together using correlation.
• Use a rolling window so you can observe whether the relationship is stable or changes.
• Complement correlation with a scenario range: for example, estimate what CAD return variability looks like during periods when oil returns were unusually large (top decile moves). This is still historical, but it ties “CAD volatility” to “oil volatility” conditions.

Worked example (assumptions stated)

Assume you have a time series of daily CAD returns and daily oil returns.

• Let r^CAD_t be the chosen daily return for CAD at day t.
• Pick a window length N (for instance, 20 trading days).
• Compute volatility as the rolling standard deviation:
  • σ^CAD_t = stdev(r^CAD_{t-N+1} … r^CAD_t)
• Repeat for oil to get σ^oil_t.
• For co-movement stability, compute rolling correlation over the same window:
  • corr_t = corr(r^CAD_{t-N+1} … r^CAD_t, r^oil_{t-N+1} … r^oil_t)

This yields time-varying volatility estimates that you can plot and compare.

Evidence or example in realistic situations

Realistic situation 1: “Volatility spikes”

• In many markets, variability clusters: when price changes become larger, they often stay large for a while.
• Measuring rolling standard deviation lets you see whether CAD volatility and oil volatility rise together, even if the average level differs.

Possible consequence

• If CAD volatility spikes mainly during high oil-volatility periods, your co-movement summary will show more frequent times when correlation or co-movement strength is elevated.

Realistic situation 2: “Correlation breaks”

• A rolling correlation can be high for a period and then weaken when economic conditions, policy expectations, or market structure changes.

Possible consequence

• A method that reports “CAD and oil move together” based on the full history may mislead; a rolling method helps you check whether the relationship persisted.

Control point

• Always compare multiple window lengths (short and medium) to see whether your volatility conclusions are robust or only true under one choice.

Limitations and risks

1. Measurement is method-dependent Changing the return formula, the window size N, or the time frequency (daily versus hourly) can change the volatility numbers. Two measures can disagree (for example, a range-based metric versus return standard deviation), especially when data quality differs.

2. Historical relationships do not establish future results Even if CAD volatility historically increased during oil volatility, that does not mean it will do so after a regime change.

3. Data and alignment problems CAD and oil series may be sampled at different times, and time zones or trading calendars can cause misalignment. Small alignment differences can alter correlation estimates.

4. Failure mode: structural breaks When relationships change abruptly, rolling estimates may lag. A volatility measure may show “elevated” variability, but it cannot tell you why the break happened without additional context.

Verification or next question

To independently verify your volatility measurements:

• Replicate the calculation using your own data source.