# What is the difference between volatility and dispersion in finance?

I am confuse whether the volatility and dispersion is same or not because are use to measure the risk associated with asset. Even if they are different than what is the relationship between, if exist.

Dispersion (also called variability, scatter, or spread) is the extent to which a distribution varies (to the left and right) from its central tendency. Sample variance, $$\sigma^2$$ is the most common measure of dispersion. The square root of variance, $$\sqrt{\sigma^2}$$, is standard deviation, $$\sigma$$.
In finance, risk is proxied with volatility, which is measured using the standard deviation, $$\sigma$$.
For an index $$I$$ with constituent prices $$S_1,\dots,S_n$$ and weights $$w_1,\dots,w_n$$ the volatility $$\sigma_I$$ of index returns is: \begin{align} \sigma_I =\sqrt{\sum_{i,j}w_iw_j\sigma_i\sigma_j\rho_{ij}} \end{align} where $$\sigma_i$$ are constituents' price volatilities and $$\rho_{ij}$$ their pairwise correlations. When you are long dispersion you are betting that these pairwise correlations will go down; you short index options but you hedge any change in the component vols $$\sigma_1,\dots,\sigma_n$$ by being long options on the individual components.