THE DONALD, THE MOOCH, AND THE STOCK MARKET
Federal Funds Interest Rate
I mentioned in a previous article – Trump Sophomore Year Economic Report Card – that President Trump tried to attribute the poor, negative stock market return of 2018 to the increases in the federal funds interest rate that occurred during the year. That is wrong because if annual figures are used, there is no significant correlation between the annual stock market return and the effective[1] annual interest rate over the 64 year period 1955[2] to 2018. For the price return the correlation is only -8.7% and the scatterplot is shown in Figure 1.
FIGURE 1
Although the slope of the regression line and the correlation coefficient are negative, less than 0.8% of the variation in market return could possibly be due to the federal funds interest rate.
The results are not much different for total return (including dividends). Correlation is only -3.8% and less than 0.2% of the variation could be due to the interest rate. Figure 2 illustrates.
FIGURE 2
Because both quantities can change multiple times over one year, I also looked at quarterly data, and there found a small negative correlation, statistically significant at the 0.05 level. Significant at the 0.05 level means that the probability that the correlation is really zero is less than 5%. The correlation coefficient is -15.7% and the scatterplot is shown in Figure 3. You can see that the slope of the regression line is negative: generally lower stock market return with higher interest rates. However, the slope is quite small and the only reason this result reaches the level of statistical significance at the 0.05 level is because it is calculated over so many (256) points. You can also see that the scatter is quite large, so that the coefficient of determination is only 0.025. That means that only 2.5% of the variation in market return could possibly be due to higher federal funds interest rate. So the interest rate hikes by the Federal Reserve make a very poor scapegoat for the market collapse of 2018; Trump is not totally wrong, just 97.5% wrong.
FIGURE 3
Tax Cut
The stock market return for 2018 was very poor, but the market has soared so far in 2019, reaching new record highs. On the MSNBC show Saturday Night Politics, which aired on 20 July 2019, Anthony Scaramucci, White House Communications Director for 10 days in 2017, expressed absolute certitude that the Trump tax cut was responsible for the bull market. None of the other panelists that night took exception, even though the tax cut was in effect for all of 2018 and the market took its huge plunge in December of that year.
His absolute certainty is a perfect example of confirmation bias. Having come from the financial sector, he obviously believes that lower taxes are always better, a cure for any economic problem. He sees a tax cut and he sees a bull market so he confirms his natural bias by attributing the latter to the former, without considering any more data.
I decided to actually investigate the data, of which there is an abundance. At www.macrotrends.net/2526/sp-500-historical-annual-market-returns you can find the annual market price returns from the present all the way back to 1928. Total returns are available at www.slickcharts.com/sp500/returns. Similarly you can find all federal income tax rates from the beginning (1913) up to the present at the IRS website or The Tax Foundation website. I usually start my analyses at 1950 to avoid the economic distortions of World War II and The Great Depression. First looking at price return I found a correlation of only 2% and a regression line slope very close to zero, both certainly far below any statistical significance. Figure 4 shows the scatterplot and regression line.
FIGURE 4
Even the very small correlation that exists is positive, not negative as “The Mooch” apparently believes.
Next I looked at total return, which includes not just the stock prices but also the dividends paid during the year; it is always larger than price return. Here the correlation is even more positive (8%), but still not statistically significant. The scatterplot is shown in Figure 5.
FIGURE 5
These positive correlations and regression line slopes mean that it is essentially impossible that higher tax rates hurt the stock market, and the lack of statistical significance indicates that tax rates probably don’t affect the market at all.
Worried that I might myself be practicing confirmation bias, and since the data was available, I pushed the analyses back to 1930, a total of 89 years – 20 more than the above calculations. With these 89 years of data the correlation values become still more positive: 7% for price return and 12% for total return, with neither reaching the level of statistical significance. These results just reinforce the conclusions of the previous paragraph.
The top marginal, long-term, capital gains tax rate also went down (from 25% to 20%). Therefore I also looked at the relation between that tax rate and stock market return. The correlations between the capital gains tax rate and either the price return or the total return are not statistically significant (-3% and 0.12%). The long-term, capital gains tax rate changes over the 69 year period can account for less than 1% of either stock market return. Another possible interpretation of Scaramucci’s opinion is ruled out by these numbers. I have not included the scatterplots, but they are available upon request.
What Drives the Stock Market?
Actually many things drive the stock market, including the quirks of individual investors, the bets by big players, automated trading programs, and even rumors and mass hysteria sometimes. There are so many factors affecting the stock market that a version of the central limit theorem must apply. The central limit theorem is a mathematical theorem that says if a variable (like stock market return) is a sum of many independent, random variables, then no matter how the independent variables that go into the sum are distributed in probability, the sum (or average) of all of them will approach a normally distributed random variable. A normal probability distribution is the famous “bell curve”.
There are six tests[3] for “normality” in the statistics software (Origin 2015) that I use. These tests look at the set of sample values and decide if they are likely drawn from a normal distribution. The total returns from 1930 to 2018, the total returns from 1950 to 2018, the price returns from 1930 to 2018, and the price returns from 1950 to 2018 all pass all six tests: they are all likely (95% probability) random variables described by normal distributions. Every normal distribution is characterized by a mean value (the center of the bell curve) and a standard deviation (how much the bell curve flares to the sides). The table below gives the means and standard deviations for each.
MEANS AND STANDARD DEVIATIONS FOR MARKET RETURNS
Note that the returns from 1930 to 2018 are less than those from 1950 to 2018. That result, I think, stems from the fact that the former period encompasses The Great Depression while the latter excludes it. From here forward I will concentrate on returns from 1950-2018 for the sake of brevity, and because I believe the last 69 years, rather than the last 89, is more pertinent to today’s economy.
Further evidence that this quantity is really a normally distributed random variable is provided by histograms of the 69 sample values. A histogram simply shows the number of values that fall into small contiguous ranges, known as bins (see Figures 6 & 7). Also shown are the bell curves with the means and standard deviations of the set of values.
FIGURE 6
FIGURE 7
The histograms approximate the bell curves. The random nature of annual stock market return means that no one can predict what the return for 2020, or even 2019, will be. All one can do is give probabilities. It is worth noting, however, that the mean is positive. If you invest in a Standard and Poor’s 500 Index fund, you can expect 12.52% return, or at least 8.85% on price alone, over the long run. Nevertheless, in any given year you might have a net loss: the histograms show a number of years with negative returns.
There is a method for calculating the probability that a normally distributed random variable falls below (or above) any particular value. I won’t bore the reader with the details, but rather just give the results for total annual stock market return being negative (<0): P = 0.233 or approximately once every four years. Over 69 years there should have been about 0.233X69 ≈ 16 years with losses in total return. When I look at the raw data I find exactly 15 years since 1950 with negative total stock market return as measured by the S&P 500 index. On the other hand, for price return P = 0.295. The number of annual losses for price return is calculated to be about 20; there are 18 by actual count.
Conclusions
“The Donald” is wrong; interest rate hikes by the Federal Reserve did not cause the negative market return in 2018. “The Mooch“ is wrong: tax cuts did not cause the bull market of the first half of 2019. Market return is a normally distributed random variable, little affected by either interest rates or tax rates. Or at least that is what the last 69 years of real world data say.
Gary Waldman
August 2019
[1] Annual federal funds interest rate is calculated as the average of the 12 monthly rates.
[2] Federal funds interest rates from the Federal Reserve are available only back to 1955.
[3] The test names are Shapiro-Wilk, Lilliefors, Kolmogorov-Smirnov, Anderson-Darling, D’Agostino-K squared, and Chen-Shapiro
Comments