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Volatility is the measure of the variation (or the dispersion) of the returns (profits/losses) of a Future over a certain period of time.

One could say: the riskier the asset, the higher the volatility (think of market crashes). The lower an asset's risk, the lower its volatility (think of the summer lull). So, in highly volatile markets one could expect large moves of the Future where at low volatile markets there might be days where the Future hardly moves.

THE PROBABILITY DISTRIBUTION OF THE VALUE OF A FUTURE AFTER ONE YEAR OF TRADING

In option trading volatility is expressed on an annualised basis. It is a calculation of the daily returns based on a full year's expectation of the combined returns. The annualised volatility predicts the probability of the outcome of the value of a Future after one year of trading (usually 256 trading days).

The probability is based on the Gaussian distribution. With low volatility (for example, 10 % as depicted in Chart 3.1), one could expect the Future, which initially started at 50, to settle somewhere between 40 and 60 after one year of trading. (Here a 95 % confidence level has been applied, being 95 % of all probable occurrences, and hence 2 standard deviations of 10 %.) If the volatility is twice as high (20 %), the range for the Future to settle after one year of trading would (almost) double as well, now between 30 and 70.

Chart 3.1 Probability distribution at 10 % volatility

When volatility is at 40 %, the range (almost) doubles again.

NORMAL DISTRIBUTION VERSUS LOG-NORMAL DISTRIBUTION

Charts 3.1, 3.2 and 3.3 show that the distribution range for the Future to settle after one year of trading would double with double volatility, however the word “almost” has been added between brackets. This is the result of the convention in the financial markets to apply a log-normal distribution rather than a normal distribution.

Chart 3.2 Probability distribution at 20 % volatility

Chart 3.2 Probability distribution at 40 % volatility

The application of a log-normal scale serves two purposes:

a. the Future cannot become negative;

b. the Future, not being able to go below zero, could in fact increase towards many times the initial value.

A Future, now trading at 50, can lose a maximum of $50 but could easily gain several hundreds of dollars. On a logarithmic scale the impact of an asset going up from 50 to 100 is equivalent to an asset going up from 100 to 200 – or, mathematically expressed in logarithmic returns: . This is why the downside is somewhat limited (showing a 25 to 50 move being equivalent to a 50 to 100 move). In this way a $25 range on the downside is equivalent to a $50 range on the upside. Also a 10 to 50 range will be equivalent to a move from 50 to 250, a scenario where there is $40 on the downside versus $200 on the upside. When not applying the ln sign, the relationship will be clear as well: or .