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What is Exchange Rate Volatility?

June 7, 2024June 13th, 2024No Comments

Exchange rate volatility refers to the historic or expected movement of an exchange rate over a specified period of time. For UK businesses and individuals with significant exposure to foreign exchange, understanding and assessing volatility is crucial for effective risk management. This article explores three methods to evaluate exchange rate volatility: two backward-looking methods—Average True Range (ATR) and returns distribution—and one forward-looking method, implied volatility. By using all three of these assessments together, you will gain a highly accurate and probable understanding of exchange rate movements, providing insights into past and expected future fluctuations and helping you make informed decisions. It should also be noted that the volatility analysis covered here is a quantitative assessment and should be complemented with a qualitative assessment. While exchange rates are ultimately driven by fundamental economic factors, this volatility assessment will help us understand the possible and probable movements based on the fundamental predisposition.

Average True Range (ATR)

The Average True Range (ATR) is a technical analysis tool that measures the volatility of a currency pair by calculating the average price ranges over a specified period. Unlike a returns distributions that looks only at open to close data, ATR uses open, high, low, and close data to provide a clearer picture of the actual price movements within each trading period. The true range is the following:

  • The current high minus the current low: This measures the range of the price movements within the current trading period.
  • The absolute value of the current high minus the previous close: This accounts for any gap up that may have occurred from the previous period’s close to the current period’s high.
  • The absolute value of the current low minus the previous close: This captures any gap down from the previous period’s close to the current period’s low.

This data is then averaged over the period you want to consider, such as 1 week, 2 weeks, 1 month, etc. By incorporating these three components, ATR provides a more comprehensive view of volatility, reflecting not just the closing price changes but also the intraday highs and lows and any gaps between trading periods. This approach allows you to better understand the extent of price movements and potential volatility risks, leading to more informed decision-making and effective risk management strategies.


Calculation of ATR


ATR Calculation

Collect Historical Price Data: Gather daily high, low, and closing prices for a currency pair.

Compute True Range (TR): For each day, calculate the true range using the formula:

TRt = max{Ht - Lt, |Ht - Ct-1|, |Lt - Ct-1|}

where Ht is the high, Lt is the low, and Ct-1 is the previous day’s close.

Calculate ATR: Compute the ATR over a chosen period (e.g., 14 days) by averaging the true ranges:

ATR = (1/n) Σi=1n TRi

The formula above is provided for informational purposes, as the ATR is typically calculated for you by charting software. Additionally, you can obtain the ATR from your Rutland FX account manager upon request.

Example of using Average True Range (ATR)

Imagine you are an importer of aerospace equipment with a requirement to buy USD every month to pay your suppliers. You want to try and time your conversions as best as possible because your supplier gives you flexible 30-day payment terms. The current exchange rate for GBP/USD is 1.2700, and the most recent low is 1.2678. The current 30-day Average True Range (ATR) is 1%, which means you could potentially target an exchange rate of 1.2804 with a limit order. Of course, in this example, no consideration is made for the exchange rate markup, which you would also need to consider.

Returns Distribution

Returns distribution is the statistical analysis of the frequency of returns of a currency pair over a period. This analysis provides insights into the nature and behavior of currency returns but does not consider the price movements that occur between these returns. This is why returns distribution works well when used together with ATR, which accounts for intraday price movements.

When displayed in a chart, the returns distribution can immediately reveal whether a currency pair or another asset has a normal or abnormal distribution. This information is crucial for understanding the underlying volatility and risk associated with the asset. By analysing the returns distribution, you can determine the standard deviation of returns, which helps in identifying the likelihood of a large move becoming a sustained return or if it is likely to revert to the mean.

One key concept that returns distribution analysis highlights is tail risk. Tail risk refers to the probability of extreme events occurring at the tails of the distribution, which are much rarer but can have significant impacts. In a normal distribution, tail events are less frequent and less extreme, whereas in an abnormal distribution, such as one with fat tails, these extreme events are more frequent and more severe. Understanding tail risk is essential for risk management, as it helps businesses and individuals anticipate and prepare for unlikely but impactful market movements.

For example, if the returns distribution shows a high frequency of large moves, it indicates high volatility, suggesting that such moves are more common. Conversely, a distribution with most returns clustered around the mean indicates lower volatility, suggesting that large moves are less likely to be sustained. Understanding these patterns helps traders and analysts make more informed decisions about potential risks and opportunities in the market. Recognising tail risks allows stakeholders to better anticipate and mitigate the potential for significant losses during extreme market conditions.

Calculation of Returns Distribution


Collect Historical Price Data: Gather daily closing prices for a currency pair.

Compute Daily Returns: For each day, calculate the daily return using the formula:

Rt = (Ct - Ct-1) / Ct-1

where Ct is the current day's closing price and Ct-1 is the previous day's closing price.

Analyse Distribution: Collect the daily returns over the desired period (e.g., 1 month, 1 year) and plot the frequency distribution of these returns. This can be done using statistical software or charting tools.

Identify Key Metrics: Determine the mean, standard deviation, and skewness of the returns distribution to assess the central tendency, volatility, and asymmetry of the currency pair's returns.


Above is an example of a “normal distribution”, In a normal distribution, approximately 68.27% of the data falls within one standard deviation of the mean. When considering two standard deviations from the mean, about 95.45% of the data is included. Extending to three standard deviations, nearly all the data, specifically 99.73%, is encompassed. These percentages illustrate the empirical rule, also known as the 68-95-99.7 rule, highlighting how data in a normal distribution clusters around the mean. As mentioned before, the calculations above are provided for informational purposes, as the returns distribution is typically calculated for you by charting software. Additionally, you can obtain an Excel returns distribution from your Rutland FX account manager upon request.

In evaluating the risk and performance of a currency pair, several statistical measures can be insightful. Average Returns indicate the overall trend of the currency pair, showing whether it is generally appreciating or depreciating over a given period. When considering the question Is the Distribution “Normal”?, if the returns distribution is normal, it suggests that extreme values (outliers) are relatively rare, indicating lower tail risk. This implies that the asset may be considered less volatile compared to distributions with heavier tails, such as those exhibiting significant skewness or kurtosis. However, it is important to note that a normal distribution does not eliminate all risk; it merely indicates that returns are symmetrically distributed around the mean, with most values clustering around the center and fewer extreme deviations.

Volatility, measured by the standard deviation, provides a quantifiable gauge of how spread out the returns are, reflecting the degree of variability or risk associated with the asset. Additionally, the Risk Profile, which includes measures of skewness and kurtosis, helps in understanding the likelihood of extreme movements. Skewness indicates the asymmetry of the distribution, while kurtosis measures the “tailedness,” or the propensity for extreme deviations from the mean. Together, these metrics offer a comprehensive view of the asset’s risk and return characteristics.


Example of using a Returns Distribution

Imagine you are a high-volume importer of vehicles from Japan and some economic data has been released, causing the GBP to JPY exchange rate to rally 1% in a day. You have a supplier to pay in JPY and you are unsure whether to take the 1% better rate now or to wait in case the rate keeps going up. If you had a returns distribution for the GBP to JPY exchange rate, you would know that a 1% move in a day would fall between a 1 and 2 standard deviation return. This means it is highly unlikely that the rate would keep increasing beyond 1%, and even more unlikely that it would close above a 1% return. Knowing this information, you can make an informed decision on whether to take the better rate now or wait longer. Conversely, if the rate had only increased by 0.3%, then based on the average positive return of GBP to JPY, which is currently 0.53%, it might be worth waiting longer to see if the rate improves further.

Implied Volatility

Implied volatility (IV) is derived from the prices of options on the currency pair. It represents the market’s expectations of future volatility over the option’s life. Unlike the Average True Range (ATR) and returns distribution, which are backward-looking measures based on historical data, implied volatility is forward-looking.

Implied volatility is calculated by options market makers who consider the historical volatility assessments, such as ATR and returns distribution, as well as any upcoming known catalysts in the markets. These catalysts include significant events such as interest rate decisions, major economic data releases, political events, and other factors that could impact the currency markets. By incorporating these elements, market makers gauge the expected future volatility of an asset.

For instance, if there is an anticipated central bank meeting where an interest rate change is expected, the implied volatility for the currency pair might increase as the market prepares for potential price swings. Similarly, significant economic events or geopolitical developments can lead to higher implied volatility as traders expect larger movements in the exchange rate.

Implied volatility is crucial for businesses and individuals with exposure to currency markets because it provides insight into the market’s future expectations. This can help in making more informed decisions regarding hedging strategies and risk management. Since IV reflects what traders collectively think will happen, it is a valuable tool for anticipating future market conditions and preparing accordingly.

  • Collect Options Prices: Obtain the prices of options for GBP/USD with various strike prices and maturities.
  • Use an Options Pricing Model: Apply models like Black-Scholes to solve for implied volatility, which equates the theoretical option price with the market price.
  • Analyse Implied Volatility: IV can be extracted from market data provided by financial platforms and brokerage services.

If you want to know the implied volatility for a currency pair Rutland FX can provide you with this data upon request.

Example of Using Implied Volatility

Imagine a UK business that imports electronic goods from China, requiring regular payments in USD. The business monitors the GBP/USD exchange rate and notices that the implied volatility for the currency pair is currently at 6% annualised. This means the market expects the exchange rate to experience annual volatility of 6%.

To convert this annualised volatility to a monthly figure, you divide by the square root of 12 (3.4641) (since there are 12 months in a year) in this example the market expects the GBP/USD exchange rate to fluctuate by approximately 1.73% per month.

Given this information, the UK business can decide whether to hedge its currency exposure based on its risk tolerance and market outlook. Here are two possible scenarios:

High-Risk Tolerance:

If the business believes that the implied volatility of 1.73% per month is manageable and expects the GBP to strengthen against the USD, it might choose to take on the currency risk. The business might opt not to hedge, hoping to benefit from favorable exchange rate movements.

Low-Risk Tolerance:

If the business is risk-averse and prefers to have predictable costs, it might decide to hedge its currency exposure. By locking in the current exchange rate through forward contracts or options, the business can protect itself from adverse movements beyond the expected 1.73% monthly volatility.

For example, if the business has significant payments due in USD and cannot afford potential adverse movements in the exchange rate, it might enter into a forward contract to lock in the current rate. This way, even if the exchange rate moves unfavorably, the business’s costs remain predictable.

By using implied volatility, the business can better gauge the potential risk and decide whether to accept that risk or mitigate it through hedging strategies. This approach allows the business to make more informed and strategic decisions based on market expectations.


Assessing exchange rate volatility through Average True Range (ATR), returns distribution, and implied volatility offers a comprehensive approach to understanding both historical and expected future fluctuations. Each method provides unique insights into the currency’s behavior:

  • Average True Range (ATR): This backward-looking measure considers intraday price movements, offering a detailed view of volatility based on high, low, and close prices over a specified period.
  • Returns Distribution: Also a backward-looking method, it analyses the frequency of returns to identify patterns and assess the likelihood of extreme movements, highlighting tail risk.
  • Implied Volatility: A forward-looking measure derived from options prices, it reflects market expectations of future volatility, incorporating upcoming economic events and market catalysts.

UK businesses and individuals can leverage these methods to manage currency risk more effectively, optimising their exposure and making informed financial decisions. By combining backward-looking and forward-looking approaches, you can take the guesswork out of currency decisions and gain a well-rounded view of currency volatility, enhancing your strategic planning and risk management efforts. This integrated approach helps anticipate potential risks and opportunities, ensuring more robust financial strategies in a dynamic market environment.

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