Direct answer
Volatility between AUD USD and NZD USD can be measured by quantifying how much their prices (or their changes) vary over a chosen time window. The key is to define what “variation” means (range, percentage change, or return dispersion) and then apply the same method consistently to both pairs. This gives a self-contained numeric description that you can verify with your own historical price data.
A practical way to compare the pairs is to compute volatility on comparable inputs—typically time-based returns (for example, hourly or daily percentage returns) and then summarize variation with one metric per window. If your goal is to compare the two pairs’ volatility, use the same sampling frequency and the same window length for both.
Mechanism or definition
Volatility is usually defined as variability in returns over time. A return is the change in price over a period, often expressed as a percentage. For a time step from t−1 to t, one simple choice is the log return:
- r_t = ln(P_t / P_{t−1})
Where P_t is the AUD USD (or NZD USD) price at time t.
From that, you can measure volatility in several common ways:
- Standard deviation of returns (time-window volatility)
- Pick a window length (for example, 20, 60, or 120 trading days) and compute the standard deviation of r_t within that window.
- This produces a volatility number with a clear statistical meaning: how dispersed returns are.
- High–low range volatility (range-based)
- For each period, measure the range between the period’s high and low, such as (High − Low) relative to price.
- Then average these ranges over a window.
- This can work even if you only trust intraperiod extremes, but it depends on what “high” and “low” timestamps mean in your dataset.
- Average true-range style measures (movement-based)
- These use candle-to-candle movement that accounts for gaps between periods.
- They depend on price history at multiple time steps, and choices like “true range” definition matter.
Evidence or example (with explicit assumptions)
Assume you have historical daily AUD USD and NZD USD prices for 60 trading days, with consistent timestamps, and you want one volatility estimate per day.
Example using return standard deviation:
- For each day t, compute daily log returns r_t for AUD USD and for NZD USD.
- For day t, compute the standard deviation of the last 20 daily returns for each pair: σ_AUD(t) and σ_NZD(t).
- Compare σ_AUD(t) and σ_NZD(t).
Assumptions that must match for both pairs:
- The same trading calendar or same “number of observations” per window.
- The same price source and method of handling non-trading days.
- The same return formula (log returns vs percentage returns).
What you can learn from this comparison:
- If σ_AUD consistently exceeds σ_NZD across many windows, AUD USD’s daily returns have been more dispersed.
- If the difference flips, relative volatility is time-varying.
Even without forecasting, these numbers can help you describe behavior such as “periods when one pair became more variable than the other.”
Limitations and risks
At least one material limitation is that volatility is not a stable property; it changes with market conditions, liquidity, and event timing.
Other important failure modes:
- Sampling frequency and window length: A metric computed from hourly returns can differ from a metric computed from daily returns. Longer windows smooth more variation.
- Data and construction differences: Different feeds can provide slightly different high/low values, or different definitions of the “same” timestamp. That changes range-based volatility.
- Currency conversion consistency: If you compare volatility across pairs derived from different underlying sources or conversions, you must ensure both are expressed in the same quote format and built consistently.
- Market microstructure and costs: If you later use volatility for any execution-related purpose, spreads, slippage, and commission structure can dominate realized movement versus what price-based volatility suggests.
- Historical relationships don’t ensure future results: Past volatility levels or past relative rankings between AUD USD and NZD USD do not guarantee future behavior.
Verification or next question
To independently verify the measurement, reproduce the calculations on the same historical dataset you plan to use. Confirm that:
- You can recompute returns from the published price series. - Your windowing logic (how many observations, and which days) matches your definition.