# Average Return

The Average Return is the expected two year return of the stock market given the current interest rate environment. Using historical stock market prices that are grouped by their respective Yield Curves, we have found a negative correlation that suggests the Yield Curve has predictive stock market return power. Alas, the higher the Yield Curve value, the lower the stock market two year average return. Let's explore further on how this value is determined.

## The Data

We start with monthly stock market and interest rate data from as far back as 1959. The stock market data is represented by S&P 500 prices from which returns are calculated by taking the logarithm of observed prices divided by their two year future prices. The interest rate data is represented by historical monthly Federal Funds Rates and 10 Year Interest Rates that are used to calculate a value we call the Yield Curve. This measure is a simple ratio of the Federal Funds Rate and the 10 Year Treasury Rates for each of the historical monthly observations.

## Mapping the Data

Each stock market return is placed in a matrix called the Data Map which rows are represented by 0.01 point increments of returns and columns are represented by 0.05 point increments of Yield Curve groups. The result is a table of frequencies, or series of histograms, that can be used for further statistical analysis including the weighting of observations by Yield Curve group.

## Weighted Average Returns Table

Each point in the Data Map represents a frequency of observations for a given return and Yield Curve value. Each frequency is divided by its Yield Curve group's total frequency (column total) to determine its weight in the histogram. The weight is then multiplied by the value that categorizes that frequency's return. This calculation is repeated for each row and then summed to provide the weighted average return for that Yield Curve. This method is repeated for each Yield Curve group resulting in a series of Average Returns per Yield Curve group. Plotting the averages with a 2nd order polynomial regression trend line illustrates a downward sloping line that suggests the higher the Yield Curve value, the lower the historical average return of the stock market.