Unexpectedly Intriguing!
09 April 2020

What is the value of m?

Before we answer that question, we should probably take a moment to explain what m is:

The basic relationship we've observed that exists between changes in the rate of growth of stock prices and changes in the rate of growth of their dividends per share, or in our terminology, their accelerations, is given by the equation:


Where Ap is the change in the rate of growth of stock prices and Ad is the change in the rate of growth of dividends per share. m is an amplification factor that varies over long periods of time but can be nearly constant for short-to-intermediate periods of time, which we'll focus more upon in future posts.

That explanation of what m is has been there from the very beginning of when we first formulated the dividend futures-based model we use to forecast stock prices from the observations that preceded it just over 11 years ago, during the stock market crash of 2008-2009.

Finding the value of m is something that can only be done by empirical observation, where we can use historic stock price and dividend futures data to solve that simple relationship for m. Doing that was especially challenging 11 years ago, because quarterly dividend futures as we know them today didn't exist at the time. It wasn't until the Chicago Board of Exchange first introduced them in March 2010, which were subsequently discontinued and replaced by the CME Group's quarterly dividend futures in 2015 that we could fully flesh out the potential of the dividend futures-based model we had defined.

What we found when the quarterly dividend futures data came into existence is that the value of m was 5. And that value held constant through Friday, 20 March 2020.

That's when things really started to go haywire for the dividend futures-based model's forecasts of the alternative trajectories the S&P 500 would be most likely to take based on how far forward in time investors were looking as they made their current day investment decisions, with the actual value of the S&P 500 moving outside the levels the model indicated it would most likely go with the amplification factor set to 5, the first time that has happened in the model's history.

Going back to our week-by-week news archive of market-moving events, we think the trigger that effectively reset the value of the amplification factor m was the Fed's over-the-weekend firing of its 'bazooka' to backstop the commercial paper market, which companies typically use to borrow money, but which had nearly completely broken down as part of the economic impact of the coronavirus pandemic.

After trading resumed on Monday, 23 March 2020, investors appear to be using a different amplification factor. The question is what is the new value for m?

As best as we can tell, the new value of m since 20 March 2020 is somewhere between 1 and 2. In the following animated chart, we're showing what the dividend futures-based model would forecast for the period from 23 March 2020 onward looks like when m = 5, when m = 2, and when m = 1, with all other values based on data available through the close of trading on 8 April 2020.

Animation: Alternative Futures - SP 500 - 2020Q1 and 2020Q2 - Standard Model with m = 5, m = 2, and m = 1 - Snapshot on 8 April 2020

Given the ongoing elevated level of volatility in stock prices, it may be a while before we can get to a relatively quiet point where we can properly calibrate the model and determine what the value of m has become. We can however answer a question we've had since 23 April 2009: A "short-to-intermediate period of time" in the U.S. stock market may last for a decade!

Whether that's "up to a decade", "at least a decade", or "a decade on average", will take a lot longer to discover.

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