# Average Risk

The Average Risk is a forward looking standard deviation relative to the interest rate environment. Measured differences between the Federal Funds Rate and the 10 Year Treasury Rate - the Yield Curve - has been found to have a positive correlation with the stock market's standard deviation. As the Yield Curve measurement rises, risk in the stock market increases. Let's review how we come to this determination.

## The Data

We begin by capturing S&P 500 prices, Federal Funds Rates, and 10 Year Treasury Rates monthly observations since 1959. The S&P 500 data is used as the index for the overall stock market. A simple ratio of the observed Federal Funds Rate and the 10 Year Treasury Rate produces a measure we call the Yield Curve which is applied to all the interest rate observations.

## Risk Measurement

Standard deviation is used to measure risk because the more returns vary from the average, the more volatile the market . To calculate standard deviation, we first take the logarithm of a stock market price divided by the previous stock market price. We do this for each observation in the data set to yield a list of monthly stock market returns. With these returns, the standard deviation is calculated using the next 24 months of observations. This forward looking approach enables us to later compare the Yield Curve with future outcomes of volatility.

## The Data Map

The monthly time series is organized into a matrix with standard deviations as rows and Yield Curves as columns. We group, or round, standard deviations at a precision level of 0.01 and Yield Curves at a precision level of 0.05. Each observation is placed within the matrix, or Data Map, to produce a series of histograms relative to Yield Curves.

## Weighted Average Risk

Each histogram's weighted average standard deviation is calculated by taking the frequency of standard deviation observations divided by that Yield Curve group's total number of observations to produce a weight. Next, we multiply the weight by the corresponding standard deviation for that row. This method is extended to each row (standard deviation) in the series and then to each histogram series resulting in a final set of Average Risk per Yield Curve grouping. A second order polynomial regression - or trend line - is derived and used as the estimate of expected two year forward risk. This upward sloping trend line illustrates the positive correlation with the interest rate environment and stock market risk.