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The quotient of random variables with normal distributions is examined andproven to have have power law decay, with density $f\left( x\right) \simeqf_{0}x^{-2}$, with the coefficient depending on the means and variances of thenumerator and denominator and their correlation. We also obtain the conditionalprobability densities for each of the four quadrants given by the signs of thenumerator and denominator for arbitrary correlation $\rho \in\lbrack-1,1).$ For$\rho=-1$ we obtain a particularly simple closed form solution for all $x\in$$\mathbb{R}$. The results are applied to a basic issue in economics andfinance, namely the density of relative price changes. Classical financestipulates a normal distribution of relative price changes, though empiricalstudies suggest a power law at the tail end. By considering the supply anddemand in a basic price change model, we prove that the relative price changehas density that decays with an $x^{-2}$ power law. Various parameter limitsare established.

The Quotient of Normal Random Variables And Application to Asset Price Fat Tails