Economic Indicators

Can machine learning-generated stock market crash predictions be amenable to human interpretation? In their June 2021 paper entitled “Explainable AI (XAI) Models Applied to Planning in Financial Markets”, Eric Benhamou, Jean-Jacques Ohana, David Saltiel and Beatrice Guez apply a gradient boosting decision tree (GBDT) to 150 technical, fundamental and macroeconomic inputs to generate daily predictions of short-term S&P 500 Index crashes. They define a crash as a 15-day S&P 500 Index return below its historical fifth percentile within the training dataset. The 150 model inputs encompass:

1. Risk aversion metrics such as asset class implied volatilities and credit spreads.
2. Price indicators such as returns, major stock index Sharpe ratios, distance from a long-term moving average and and equity-bond correlations.
3. Financial metrics such as 12-month sales growth and price-to-earnings ratio forecasts.
4. Macroeconomic indicators such Citigroup regional and global economic surprise indexes.
5. Technical indicators such as market breath and index put-call ratio.
6. Interest rates such as 10-year and 2-year U.S. Treasury yields and break-even inflation level.

They first rank and filter the 150 inputs based on GBDT to discard about two thirds of the variables. They then apply the Shapley value solution concept to identify the most important of the remaining variables and thereby support interpretation of methodology outputs. Using daily values of the 150 model inputs and daily S&P 500 Index roll-adjusted futures prices from the beginning of January 2003 through mid-January 2021 (with data up to January 2019 used for training, the next year for validation and the rest for testing), they find that:

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A subscriber asked for corroboration of an assertion that a negative 30-year U.S. Treasury real yield indicates a good time to buy gold. To investigate, we employ the following monthly data:

• 30-year U.S. Treasury constant maturity yield (30-year) since February 1977 (the limiting series).
• Total U.S. consumer price index (CPI) since February 1976.
• Spot gold price since January 1977.

Each month, we subtract the 12-month past change in CPI (lagged one month for release delay) from the 30-year yield. When this real yield turns negative, we buy spot gold at the end of the same month and sell it the at the end of the month when the real yield turns positive. Using monthly data as specified through May 2021, we find that: Keep Reading

How sensitive are returns of stocks, bonds and gold to levels real interest rates (nominal rates minus inflation)? To investigate, we consider three nominal interest rates and two measures of inflation, as follows:

• 3-month U.S. Treasury Bill Yield (3-month).
• 1-year U.S. Treasury Constant Maturity Rate (1-year).
• 10-year Treasury Constant Maturity Rate (10-year).
• Personal Consumption Expenditures: Chain-type Price Index (PCEPI).
• Personal Consumption Expenditures Excluding Food and Energy: Chain-Type Price Index (Core PCEPI).

These choices offer six alternative real interest rates. We use end-of-month interest rates and inflation measures lagged by one month to account for release delay. We use the S&P 500 Index (SP500) capital gain only, the 10-year yield (with bond prices moving inversely) and spot gold price, all measured end-of-month, to represent returns for stocks, bonds and gold. We then relate monthly changes in real interest rates to asset class monthly returns in two ways: (1) calculate correlations of monthly real interest rates to asset class returns for each of the next 12 months to get a sense of how real rates lead asset returns; and, (2) calculate average asset class monthly returns by ranked tenths (deciles) of prior-month real interest rates to discover any non-linear relationships. Using monthly PCEPI and Core PCEPI since January 1961, interest rates since January 1962, SP500 level since December 1961 and spot gold price since December 1974 (when controls are removed), all through May 2021, we find that:

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What drives the price of gold: inflation, interest rates, stock market behavior, public sentiment? To investigate, we relate monthly and annual spot gold return to changes in:

• Non-seasonally adjusted Consumer Price Index (CPI).
• Nominal and real short-term (ST) interest rates based on 3-month U.S. Treasury bill yield.
• S&P 500 Index return.
• University of Michigan (UM) Consumer Sentiment.

We start testing in 1975 because: “On March 17, 1968, …the price of gold on the private market was allowed to fluctuate…[, and] in 1975…the price of gold was left to find its free-market level.” We lag CPI measurements by one month to ensure they are known to the market when calculating gold return. Using monthly data from December 1974 (March 1978 for consumer sentiment) through May 2021, we find that: Keep Reading

A subscriber suggested the Kansas City Financial Stress Index (KCFSI) as a potential U.S. stock market return predictor. This index “is a monthly measure of stress in the U.S. financial system based on 11 financial market variables. A positive value indicates that financial stress is above the long-run average, while a negative value signifies that financial stress is below the long-run average. Another useful way to assess the current level of financial stress is to compare the index to its value during past, widely recognized episodes of financial stress.” The paper “Financial Stress: What Is It, How Can It Be Measured, and Why Does It Matter?” describes the 11 financial inputs for KCFSI and its methodology, which involves monthly demeaning of inputs, monthly normalization of the overall indicator to have historical standard deviation one and principal component analysis. This process changes past values in the series, perhaps even changing their signs. Is KCFSI useful for U.S. stock market investors? To investigate, we relate monthly S&P 500 Index returns to monthly values of, and changes in, KCFSI. We match return calculation intervals to KCFSI release dates. Using monthly data for KCFSI and the S&P 500 Index during February 1990 (limited by KCFSI) through March 2021, we find that: Keep Reading

Does expansion (contraction) of consumer credit indicate growing (shrinking) corporate sales, earnings and ultimately stock prices? The Federal Reserve collects and publishes U.S. consumer credit data on a monthly basis with a delay of about five weeks. Using monthly seasonally adjusted total U.S. consumer credit for January 1943 through February 2021 and monthly S&P 500 Index closes for January 1943 through March 2021, we find that: Keep Reading

What asset classes offer the best performance during episodes of high and rising inflation? In their March 2021 paper entitled “The Best Strategies for Inflationary Times”, Henry Neville, Teun Draaisma, Ben Funnell, Campbell Harvey and Otto Van Hemert analyze performances of passive and active strategies across various asset classes during inflationary episodes in the U.S., U.K., and Japan over the past 95 years. They define inflationary regimes as follows:

• An episode begins when annual change in headline consumer price index (CPI) rises to 5% or higher.
• An episode ends when annual change falls below 50% of its trailing 24-month peak.
• Alternatively, an episode begins when annual change in CPI is above 2% but has fallen to less than 50% of its trailing 24-month peak, and then rises to at least 5%.

They exclude episodes shorter than six months. They also analyze alternative asset classes such as fine art and discuss crypto-assets as a potential inflation hedge. Using monthly CPI and various asset class returns in the U.S., UK and Japan during 1926 through 2020, they find that:

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A subscriber asked (years ago): “Everyone says I should not invest in bonds today because the interest rate is so low (and inflation is daunting). But real bond returns over the last 30 years are great, even while interest rates are low. Could you analyze why bonds do well after, but not before, 1981?” To investigate, we consider the U.S. long-run interest rate and the U.S. Consumer Price Index (CPI) series from Robert Shiller. The long-run interest rate is the yield on U.S. government bonds, specifically the constant maturity 10-year U.S. Treasury note after 1953. We use the term “T-note” loosely to name the entire series. We apply the formula used by Aswath Damodaran to the yield series to estimate nominal T-note total returns. We use 12-month change in CPI. We subtract inflation from T-note nominal total return to get T-note real total return. Using annual Shiller interest rate and CPI data for 1871 through 2020, we find that: Keep Reading

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 M1, Velocity of M2 and the S&P 500 Index from the first quarter of 1959 through the fourth quarter of 2020, we find that: Keep Reading

A reader commented: “M2 cannot be an accurate money supply measure because it includes non-cash investments such as money market mutual funds. When the stock market corrects and people are exchanging stocks for say, money market mutual fund shares, the M2 figure will actually increase. The money supply is not literally increasing in such cases as no new cash is being created; there is merely an exchange of existing assets. Technically, only increasing the monetary base would increase the money supply, but M1 is a reasonable substitute for that as it includes the cash part of bank reserves.” The M1 money stock consists of funds that are readily accessible for spending: currency in circulation, traveler’s checks, demand deposits and other checkable deposits. Is there a reliable relationship between historical variation in M1 and stock market returns? Using weekly data for seasonally adjusted M1 and the S&P 500 Index during January 1975 through January 2021, we find that: Keep Reading