## Overview

As of August 31, 2023, the S&P500 is currently trading 46% above its modern-era historical trend value, (about 1.3 standard deviations), indicating that the market is Overvalued.

#### Why it Matters

This is a basic model based on a fitted exponential growth rate for the S&P500. To continuously stay above the trend line suggests that the stock market must continue to grow at a continuously higher growth rate. Such explosive growth is not sustainable over long periods.

## Theory & Data

##### Mean Reversion

Mean reversion, the basic principal that what goes up must come down, is a commonly held belief among market participants. While the daily movements of the stock market may be chaotic and unpredictable, long-term stock market returns tend to follow a somewhat predictable upward trend. Deviations from this trend can last for extended periods, even decades. As such, mean reversion is not an effective strategy for short-term trading but rather a useful indicator of overall market valuation relative to historical trends.

##### S&P500

We use S&P500 daily close data, available from Yahoo Finance back to 1950. This data is not inflation adjusted, so we index it to current dollars using CPI data from the US Bureau of Labor Statistics. One could just as easily use other broad market indices (Russell 2000, Wilshire 5000) and get very similar results, though the S&P500 data is the most easily available and likly to be familiar to most investors. The data is shown below, along with an exponential regression line showing the trend over time.

## Current Values & Analysis

##### Exponential Growth

The above S&P chart clearly shows the last ~70 years of upward economic progress. The exponential regression shows the approximate 10% annual returns that investors have become accustomed to receiving in the modern era. Clear outliers on the chart are the bear market all through the 1970's and early '80's, the internet bubble of the late 90's (and subsequent collapse), as well as the great recession of 2008. From the beginning of recovery in 2009 we've enjoyed a bull market in length and scale greater than any other in modern times. Despite the recent market corrections in 2022, we remain well above the historical trend line.

It is critical to use an exponential growth trend line here, rather than a traditional mean, to capture the dramatic productivity gains in the market over the timeframe. The composition of the stock market has changed considerably since 1950, with high-tech firms driving incredible innovation and productivity. Using an exponential regression captures that parabolic growth, and prices it into our future expectations.

##### De-trending the Data

We can see that the S&P500 is currently priced above the trend line, but it isn't intuitive or obvious how far away we are from the trend relative to prior peaks.

Instead, we'll chart the data again, this time showing the historical trend line as a straight line (the x-axis), and the S&P500 on the y-axis as a percentage over/under the trend value. Note that the trend line here is the exact same exponential line from the chart above, we are just showing it as a straight line to make the comparison against the actual S&P500 easier. Instead of showing the S&P by its actual dollar values, we instead chart it as a % above/below the trend line:

##### Standard Deviations

Lastly, we can show the exact same chart, but instead switch the y-axis to show the number of standard deviations the S&P500 is from the trend line. This is consistent with our ratings and other models, and is a more intuitive way to view how extreme the peaks and valleys are in terms of valuation.

##### Results

The de-trended data shows that the S&P500 is currently 1.3 standard deviations above its historical trend line, suggesting the market is currently Overvalued.

## Data Sources

Data sources used to create the models: