Using calculus to understand the financial markets

What matters most to markets isn’t simply change, but the rate of change

All I really need to know I learned in calculus class. I say that with apologies to author Robert Fulghum and his theory that we receive all of life’s pertinent information in kindergarten. Those lessons all still apply, particularly now the point about washing our hands before we eat. More specifically, all I really need to know right now to answer investors’ most recurrent question, I learned in calculus class. “How is it that the economy is cratering, but equity markets are rallying?

In calculus class, you spend an inordinate amount of time learning about the first derivative, or the rate of change of the slope of a given function. In simple terms, the first derivative primarily tells us about the direction the function is going (i.e., increasing or decreasing). For example, consider a car going 55 miles per hour. The miles driven are increasing at a consistent rate of change with respect to time. The second derivative would determine the change in that rate of change. In the car example, the second derivative determines whether the driver’s speed is accelerating or decelerating from that 55 miles per hour.

Why does this matter? It’s because equity markets generally don’t trade on whether the economic data are increasing or decreasing, but rather on whether the rate of change is accelerating or decelerating. It’s not about whether things are good or bad, but rather whether they are getting better or worse, or, in this instance, worse more slowly. It’s the second derivative that matters.

Consider US initial jobless claims, which track the number of people who have filed jobless claims for the first time during a specified period with the appropriate government labor office. Here’s the chart. It’s disastrous. The recent rise in the number of people filing jobless claims is so historically bad that it renders the jobless claims during the 2008 financial crisis as barely a blip on the chart!1

We all know that the direction is bad. It’s still increasing. Last week alone, 3.2 million of our friends and loved ones filed for unemployment.2 While that creates considerable hardship for those affected, there was one positive indicator for the broad economy. The change in that rate of change is slowing: from early April, when 6.6 million new claims were filed in the week, to mid-April, when 4.4 million new claims were filed in the week, to Thursday, May 7, when it was reported that 3.2 million new claims were filed in the week.3 The numbers are alarming but are deteriorating at a less alarming rate. It’s the second derivative.

Historically, following a recession, the weekly jobless claims numbers tend to not get back to the long-term average until years after the market has troughed.4 During the global financial crisis, for example, jobless claims peaked in March 2009, the same month the market troughed, and didn’t fall below the long-term average until June 2013.5 In none of those in-between months was the direction good (still increasing per week above the average), but the change in that rate of change was improving. In that time, the equity market, as represented by the S&P 500 Index, climbed 120%.6

A similar story could be told for the number of COVID-19 cases in the hardest hit parts of the country and the world. The number of new cases is increasing but, like the jobless claims data, is getting worse more slowly.7 As the rate of change has slowed in places such as China, Korea, Italy, and the US (largely driven by New York), markets have responded.8

Could things get worse again? Of course. There is still a lot we don’t know about this virus. But that is not the point of this writing. Rather it is to answer the most consistent question I am receiving from investors and to remind them that the market may ultimately not wait for them to believe that things are finally “good.” Again, it’s about better or worse, or worse more slowly.

Perhaps, as investors, instead of us binge-watching the news and lamenting the lack of “good” in our situation, we should look for signs of improvement. It is certainly true that things are very difficult now, and we commiserate with everyone who has been adversely affected. Still, there is at least one indicator that, for the economy and financial markets, things may be getting less worse.

  1. Source: US Department of Labor, Bloomberg L.P. As of 5/1/2020
  2. Source: US Department of Labor, Bloomberg L.P. As of 5/1/2020
  3. Source: US Department of Labor, Bloomberg L.P. As of 5/1/2020
  4. Source: US Department of Labor, Bloomberg L.P. As of 5/1/2020. The stock market is represented by the S&P 500 Index. Indexes are unmanaged and cannot be purchased directly by investors. Past performance does not guarantee future results.
  5. Source: US Department of Labor, Bloomberg L.P. As of 5/1/2020
  6. Source: Standard & Poor’s, Bloomberg L.P. As of 5/1/2020
  7. Source: Bloomberg News and Johns Hopkins. As of 5/7/2020
  8. Source: Source: MSCI and Bloomberg L.P., as of 5/7/2020. Markets are represented by the MSCI China Index, MSCI Korea Index, MSCI Italy Index, and the S&P 500 Index. The MSCI China Index captures large and mid-cap representation across China A shares, H shares, B shares, Red chips, P chips and foreign listings (e.g. ADRs). With 704 constituents, the index covers about 85% of this China equity universe. Currently, the index includes Large Cap A and Mid Cap A shares represented at 20% of their free float adjusted market capitalization. The MSCI Korea Index is designed to measure the performance of the large- and mid-cap segments of the South Korean market. With 110 constituents, the index covers about 85% of the Korean equity universe. The MSCI Italy Index is designed to measure the performance of the large- and mid-cap segments of the Italian market. With 24 constituents, the index covers about 85% of the equity universe in Italy. The Standard & Poor’s 500 Index is a market-capitalization-weighted index of the 500 largest U.S. publicly traded companies. Indexes are unmanaged and cannot be purchased directly by investors. Past performance does not guarantee future results.

Blog Header Image: PeopleImages / iStock

Important Information

The opinions referenced above are those of the authors as of May 11, 2020. These comments should not be construed as recommendations, but as an illustration of broader themes. Forward-looking statements are not guarantees of future results. They involve risks, uncertainties and assumptions; there can be no assurance that actual results will not differ materially from expectations.

Brian Levitt is the Global Market Strategist, focusing on North America, for Invesco. He is responsible for the development and communication of the firm’s investment outlooks and insights.

Mr. Levitt has two decades of investment experience in the asset management industry. In April 2000, he joined OppenheimerFunds, starting in fixed income product management and then transitioning into the macro and investment strategy group in 2005. Mr. Levitt co-hosted the OppenheimerFunds World Financial Podcast, which explored global long-term investing trends. He joined Invesco when the firm combined with Oppenheimer Funds in 2019.

Mr. Levitt earned a BA degree in economics from the University of Michigan and an MBA with honors in finance and international business from Fordham University. He is frequently quoted in the press, including Barron’s, Financial Times and The Wall Street Journal. He appears regularly on CNBC, Bloomberg and PBS’s Nightly Business Report.

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