Standard Deviation

Overview

Standard deviation statistically measures the difference between the closing prices and the average prices over a number of time periods. It is a good indicator of the volatility of the target exchange rate: the higher the standard deviation, the higher the volatility.

Formula

First calculate the average mid-price over the last n time periods:

MAn = (MP(t) + MP(t-1) + ... + MP(t-n+1) ) / n

where MP(t) is the mid-price of the latest period, and n is the number of periods considered.

Then, the standard deviation can be calculated as follows:

Std.Dev. = Sqrt( ( (CP(t))^2 + (CP(t-1))^2 + ... + (CP(t-n+1))^2 ) / n )

where CP(t) is the closing price of the latest period, "Sqrt" is the square root, and "^2" means "to the power of two".

Parameters

The standard deviation calculation has one parameter, namely n, specifying the number of periods to include in the calculation.

Interpretation

When the standard deviation peaks, this is often interpreted as a signal that the rates will change direction: on a high peak, the rates are expected to go down and on a low peak, the rates are expected to go up.