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Index of dispersion - Variance-to-Mean Ratio - VMR
As with the coefficient of variation, the index of dispersion is a ratio that is used to measure the dispersion of a probability distribution. It tells us whether prices or technical indicator values are dispersed or clustered compared to a standard statistical model.
Index of dispersion, also called dispersion index or variance to mean ratio, is a normalized measure unlike the standard deviation. It can be used, for example, to compare the volatility of different assets.
VMR (variance-to-mean ratio = index of dispersion) is equal to zero in the case of a constant random variable (not dispersed). It is equal to one in a Poisson distribution, higher than one in a negative binomial distribution (over dispersed) and between zero and one in a binomial distribution (under dispersed).
The function or trading indicator gets a time-series and a lookback period. Its formula consists of dividing the variance (Square of the standard deviation) by the mean. It is valid only when the mean is different from zero.
Example of its use:
a = close - sma(close, 30);
a = CoefficientDispersion(a, 30);
Plot(a, "");
The above formula displays on a chart the index of dispersion of the difference between the close price and the 30-Bar simple moving average.
Trading financial instruments, including foreign exchange on margin, carries a high level of risk and is not suitable for all investors. The high degree of leverage can work against you as well as for you. Before deciding to invest in financial instruments or foreign exchange you should carefully consider your investment objectives, level of experience, and risk appetite. The possibility exists that you could sustain a loss of some or all of your initial investment and therefore you should not invest money that you cannot afford to lose. You should be aware of all the risks associated with trading and seek advice from an independent financial advisor if you have any doubts.
