Weekly S&P ProyectionSince the market did not correct as expected, this opens up the possibility for a new period of euphoria. As show in the graph this has happened before from the year 2020 to 2022. Price is typically considered to not follow a normal distribution, therefore using one to estimate if price is over extended has its flaws. This is because the true distribution of a security is a multinomial distribution, where price can either go up, down or stay equal.
The reason price behaves in such an odd manner is because price, has 2 unknown probabilities. Such probabilities can be calculated for the past, but not for the future. These are the probability of a price increase, and the probability of price staying the same, consequently the probability of price decreasing will be 1 minus the sum of the two previous probabilities. The value of such probabilities also fluctuates, and is determined by the market. When a market becomes overexcited, the probability of price increasing is closer to 1 than it's other counter probabilities. When this happens, a normal model no longer becomes suitable for estimating the limits of the distribution.
If one has a multinomial distribution, thought of as a graph with nodes in a shape of a 3D tree, where each node has a relationship with 3 subsequent nodes. Where each relationship carries one of the probabilities mentioned before (with no repetitions). Starting with 1 initial node, then 4 then 16 … previous+previous*3n. One is able to create a mental map of true, the price action distribution. From these, one could calculate new limits, by using bootstrapping.
However, since the computational power of such algorithm is complex, we can use the mean returns indicator to evaluate the trend and see that currently the trend is positive. This would mean that the probability of increasing is most likely also closer to one. If the mean returns were at 0 then the probability of price staying the same would be closer to one, and if it's below zero the same is true for a downtrend. Currently, the trend is positive, and not close to the theoretical limits of price action. This means that the probability of seeing a skewed distribution in the future are relatively high. However, if you still use a normal distribution to estimate the limits, then price is due for a correction. Only time will tell, as over excitement can move markets past their technical limits, and that is something that will always be a flaw in any technical approach to model price action.
