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Money Velocity and the Stock Market

Posted in Economic Indicators

Regarding “Money Supply (M2) and the Stock Market”, a subscriber responded: “I’ve always thought…that both M2 and velocity were needed. If there’s more money, but it is not circulating, then it doesn’t have a chance to have much impact. That’s the situation we have right now for the most part.” The Federal Reserve Bank of St. Louis tracks money velocity based either M1 or M2 money supplies at a quarterly frequency, stating that: “Velocity is a ratio of nominal GDP to a measure of the money supply. It can be thought of as the rate of turnover in the money supply–that is, the number of times one dollar is used to purchase final goods and services included in GDP.” Specifically, the bank calculates money velocity as quarterly nominal GDP divided by average money supply during the quarter. Using quarterly values for seasonally adjusted Velocity of M1Velocity of M2 and the S&P 500 Index as available from the last quarter of 1958 through the second quarter of 2016 (232 quarters), we find that:

The following chart depicts velocities of M1 and M2 (left axis) and the S&P 500 Index (right axis) on logarithmic scales over the available sample period. Visual inspection does not reveal relationships between series. It appears that the money velocity series (especially M1) are not stationary (do not revert to a specific mean), perhaps because of evolving economic structural change. Alternatively, the series may revert very slowly, perhaps based on demographics, and the sample period is not long enough to exhibit mean reversion.

To dig deeper, we try lead-lag correlations to relate stock market returns to changes in money velocity.

M1-M2-velocity-SP500

The next chart relates quarterly change in money velocity (M1 or M2) to quarterly S&P 500 Index return for offsets ranging from stock market return leads percentage changes in money velocity by four quarters (-4) to changes in money velocity leads stock market return by four quarters (4).

Results suggest that:

  • Interactions between M1 and M2 velocities with stock market returns are practically the same.
  • Stock market return has some power to predict changes in money velocity one or two quarters hence (readings for -2 and -1) with positive correlation. In other words, relatively strong (weak) stock market return predicts relatively strong (weak) changes in money velocity one and two quarters later.
  • Changes in money velocity say little about future stock market return. If anything, there are weak indications of a negative relationship at horizons of two to four quarters. In other words, relatively strong (weak) changes in money velocity predict relatively weak (strong) stock market return several quarters later. This finding may derive more from mean reversion of stock market returns than any interaction between money velocity and the stock market.

Given the approximate one-quarter delay in availability of money velocity data, only readings for relationships 2, 3 and 4 could inform stock market timing. 

Might there be an exploitable non-linear effect of money velocity on stock market returns?

SP500-return-change-in-money-velocity-quarterly-leadlag

The next chart summarizes average quarterly S&P 500 Index return two quarters hence (to ensure availability of money velocity data) by ranked fifth (quintile) of quarterly percentage changes in M1 and M2 velocities over the available sample period. There are 45-46 observations per quintile. Results do not vary systematically across quintiles. There is some indication that large drops in money velocities two quarters ago are better for the stock market than large jumps.

average-SP500-return-by-quintile-of-change-in-M1-M2-velocity

An issue with series that involve GDP is extensive backward revision. The final two charts depict percentage differences between M1 and M2 velocities (upper chart) and differences in quarterly percentage changes in M1 and M2 velocities between 11/23/11 and 5/27/16 series vintages. Results indicate that:

  • The more recent vintage increases M1 and M2 velocities by 2.5% to 4.5% compared to the older vintage. The differences are least stable in the most recent data available in both vintages.
  • The differences in quarterly percentage changes in M1 and M2 velocities vary over time and are particularly large for the most recent data available in both vintages. 

In other words, as-revised data differ substantially from data experienced in real time, confounding the use of the as-revised data for both backtesting (no such series was experienced) and forecasting (most recent values are unstable).

differences-between-M1-M2-vintages

differences-between-change-in-M1-M2-velocity-vintages

In summary, evidence from several simple tests provides perhaps very weak support for belief that quarterly changes in money velocity relate negatively to stock market behavior two to four quarters hence.

Cautions regarding findings include:

  • As noted, final GDP for a quarter is known only with a delay of about three months, so an investor using these series for money velocity experiences a significant data lag.
  • As illustrated, like the input GDP series, as-revised money velocity series are unstable across vintages, undermining their use for both backtesting and forecasting.
  • Analyses are in-sample. An investor operating in real time may draw conclusions different from those above based on inception-to-date data.
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