- Neural Nets
_aioseop_keywords: Market crash, Nasdaq, Monte Carlo, Simulation, Guassian, bell
curve, histogram, neural nets
The markets have been very volatile lately, can you guess why? It starts with the letter "s" and ends with "prime." In the midst of this selloff and rumors of a market crash, I decided to see just how volatile the Nasdaq has been over the past 10 trading years (255 trading days per year) and compared the actual results with a Monte Carlo simulation using a standard Gaussian distribution.
I came up with 2513 observations over a 10 year period of the Nasdaq (figuring in holidays and subtracting one observation to calculate a daily Rate of Change (ROC)) and surprisingly enough the "Black Swans" of the Nasdaq weren't captured effectively by the Monte Carlo simulation.
The first bar chart to the left is the actual observations of the ROC for the Nasdaq over the past 10 years. The value on the Y-axis is the number of observations per the X-axis interval. A value of -0.01 on the X-axis indicates a -1% or greater move in the Nasdaq (by greater I mean closer to zero). The observations for -0.02 indicates the total number of observations between -0.01 and -0.02, and so forth.
If you look closely at the actual results, you'll see the Nasdaq experienced 44 observations less than -0.04 (by less than I mean the observations between -0.04 to -0.09). By contrast, the Monte Carlo simulation chart to the left (using a Gaussian distribution) estimated 34 observations. Its close but off by 10 observations. Those 10 "out of left field" observations must've made some money manager cry that day. :)