Using calculus to understand the financial markets – Expert Investment Views: Invesco Blog

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.

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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.