September 2, 2024
Author: Lewin Hafner
One of the key notions that the broad public holds is that the stock market is a representation or leading indicator of the aggregate economy. Research shows that this premise is true to some degree1,2,3 - but ask any practicioner and you will realize that it certainly falls short of the inherent complexity that characterizes markets. The main objectives of this piece of work are (i) the development of an indicator that informs investors how attractive equities are, based on the prevailing macroeconomic conditions and (ii) exploring a handful of timeless linkages between both elements. It is thus divided into two parts: In the first one, we establish a systemic-like view on the relationship between markets and economies by introducing the key causal linkages that underlie them. In the latter, we attempt to capture this relationship and develop an indicator that informs us how one side of the equation is doing relative to the other (i.e. use macroeconomic variables as risk metrics to gauge whether to be in equities or not). Note that this is not a research paper, investment advice or a thoroughly thought-out "model" that should be put into use, but rather a selection and synthetization of ideas I've accumulated over time and want to present.
In the spirit of methodological individualism, the explanation of social phenomena should be rooted in a micro-level, bottom-up approach. To adopt this framework we introduce Household A (Individual A) and Company X as our economic agents wherever it seems suitable.
Linkages between markets and economies
Linkage 1: Wealth effect. Individual spending (which together with business investment and government spending amounts to aggregate spending) is mainly financed through three sources: income (wage, dividend payments, social benefits etc.), credit (mortgage, credit cards etc.) and dissaving (savings accounts, asset sales etc.). Now let's assume Household A holds equity in Company X and the respective share price recently rose to new all-time-highs. As per the wealth-effect, this rise in Household A's net-worth should translate into higher spending for two primary reasons. First, gains in net-worth tend to make a Household more confident and optimistic about its financial situation and thus more inclined to spend. Arguably, the inclination to spend is either due to perceived (unrealized) gains in net-worth or real (realized) gains that result in dissaving (asset sales). The second reasoning behind this dynamic is that assets like stocks and real estate are a source of collateral to borrow against. Lenders typically look for a borrower with high creditworthiness (stable source of income, track record of paying debt & service payments back in time etc.). A rising stock price will thus grant Household A access to more credit to fund its spending.
Linkage 2: Equity issuance. Companies have a variety of options to finance themselves, including issuing equity shares on a stock exchange. If the share price of Company X rises, additional funding through equity issuance will be less expensive as a lesser quantity of stocks need to be emitted. This increased access to capital promotes investment and spending (e.g. in research & development).
Linkage 3: Interest Rates. A Central Bank like the Federal Reserve pursues (i) price stability and (ii) maximum employment as part of its dual mandate. The primary policy lever to do so is setting the key interest rate which acts as a monetary impulse that gets transmitted to the economy through different channels (e.g. balance sheet channel, exchange rate channel etc.). Besides those channels that directly affect the economy, the most direct channel to the markets is the asset price channel. Equity valuation methods like DCF or DDM rely on a risk-free rate (usually the yield on a 10-year bond) to account for the time value of money, i.e. the foregone opportunity of holding cash that generates interest. Thus, lower interest rates translate into higher equity prices as the time value of money decreases and (in the case of DCF) the present value of future cash flows is higher. Additionally, pricing models like CAPM usually involve a risk-free rate to compare different assets based on their risk/return profile, again reinforcing the linkage between interest rates and equities.
General linkages
Linkage 4: Spending is the source of income and income the source of spending. Most economic transactions (with exceptions like transfer payments) involve two parties that exchange goods, services or financial assets for money or credit. What academia refers to as the "circular flow of income" is a model that describes how households and businesses exchange production factors, which ultimately creates a self-reinforcing relationship between income and spending.
Relationship between UR, Inflation and Yield-Curve
Risk and return is an inherently connected pair of shoes. Government bonds of different maturities carry different risks and are thus associated with different returns. Usually, the further out you go on the curve, the higher the yield (steepening curve) - because the further you go into the future, the more uncertainty is involved in forecasting economic conditions (inflation, growth, monetary policy etc.). Note the emphasis on usually - because yield-curves can be (and are in a number of countries right now) inverted, whereby long-term rates are lower than short-term ones. What this signals is that for bond investors, a) near-term risks (usually the risk of a recession) outweight longer-term risks and b) participants expect rate cuts in response to a). In the context of our indicator we have to be careful.
We've established that an inverted yield-curve is a potential precursor to a recession - but how does it relate to other economic variables? In terms of the labour market, we'd expect a relatively low unemployment rate, akin to classic business cycle theory. High employment, on the other hand, raises aggregate income and puts upward pressure on prices as spending growth (remember income is the source of spending) outpaces output growth. Think about it - when the economy is already operating at full capacity, output growth can be achieved either through a) a larger workforce or b) an increase in labour productivity. In the short run, neither of the two are viable options.
Limitations & Bottom-Line
In reality the relationship is way more complex, so it's worth touching upon a few key points. First, there are numerous linkages that we didn't address here - e.g. how changes in the key interest rate drive interest rate differentials, which drive FX, which in turn affect the earnings of export-sensitive companies and thus their share price. Second, these linkages do not exist in isolation but rather in interaction - e.g. the effect of a change in the key target rate is not limited to earnings and the respective stock price, as changes in the stock price will again in turn affect the cost associated with equity issuances, which in turn will modulate business investment on a micro-level and thus GDP growth on the macro-level. This is why financial markets and economies are best thought of as complex systems with non-linear, potentially self-reinforcing relationships. Here, we intentionally focused on key causal chains that a) highlight a more or less straight relationship between equities and economies and b) are necessary to move from the micro to the macro level.
The bottom line of Part I is that the relationship between markets and economies is bidirectional and not unidirectional (with each element influencing one another) and thus non-linear in nature. On aggregate we can expect that low (high) unemployment, high (low) inflation and a steepening (inverted) yield-curve should be associated with toppish (decreasing) stock prices.
In Part I we highlighted a handful of causal relationships between equities and their respective economies. We identified the unemployment and inflation rate as well as the yield-curve as potential informants of how well equities could be doing based on macroeconomic conditions. In Part II we dive into the methodology and implementation of our indicator.
Data and Methodology
Data for the unemployment rate (UR), inflation rate (IR) and yield-curve (YC) has been gathered from Fred.org. Price data for the SP500 was fetched from TradingView.com. All time-series refer to the US economy, beginning in January 1977 and ending in August 2024. Our main objective is to build an indicator that informs us how "risky" it is to be in stocks based on the aforementioned economic variables. Given our derivation of how these might be related to the market, there's a high chance that some peaks and throughs in them will relate to those in equity prices - but we face two major challenges here:
The proposed solution here is to calculate percentiles that relate a certain value to its historical distribution and range from 0-1. Percentiles essentially tell us how high (low) any given value in a dataset is compared to all other values. As an example, a percentile of 0.8 indicates that a certain value is higher than 80% and lower than 20% of the data points (relatively high). Each time-series is standardized and expressed in terms of percentiles.
Implementation
We could, of course, take the path of least resistance and simply use the built-in functions in Excel to arrive at our percentiles - but we miss out on understanding what's really going on under the hood, which is why I will apply (at least some) formulas manually.
We begin by calculating both the arithmetic mean and the standard deviation for all our variables. Next, we normalize our data so each value is expressed in terms of standard deviations from the mean (so called Z-Score). We apply the following formula:
Z-Score: Z = ((x - mean)/stdev)
To go from Z-Scores to Percentiles manually is actually no big of a deal - but a process prone to errors. We therefore use a built-in function that comes with Excel. The logic here is that a CDF (cumulative distribution function) measures the area under a PDF (probability density function) curve up until a certain value, which in other words basically means that a all probabilities equal to or below that certain value are added together (which essentially represents our definition of percentiles above).
We call the "Norm.S.Dist(Z-Score; TRUE)" function and feed it with our Z-Scores.
As outlined above, our method of aggregation is simply averaging these percentiles out. We arrive at something like this:
Results & Validation
There exists a wide range of possibilities to validate how well our macro indicator relates to the SP500. We keep it simple and use a combination of visual inspection and statistics.
Here's a log-chart of the SP500, colorcoded by our indicator that ranges from 0 (blue) to 1 (red). To me, it doesn't look too promising.
Validating how well the SP500 and our indicator relate to each other is ultimately a question of how changes are related. Below is a chart plotting 24-month returns & our indicator. Visually, it seems like there is a relationship between the two that appears to be stronger in times of distress (2000; 2008).
The caveat here is that rising correlations tend to be a feature of market distress in general4. Rolling 3-Year correlations confirm this to some degree: peaks usually occur when both stocks and the economy have been hit already (e.g. 2001 Dot-com, 2009 GFC).
Another way to analyze the two is through the use of a scatter plot. If low (high) values in one variable would correspond to low (high) values in the other, we would expect a straight (positively sloped) regression line. The chart below essentially rules out any significant relationship, confirmed by a relatively low R2.
In conclusion, our indicator should not be used to gauge whether to buy equities or not. There is, however, room for improvement.
References & Related Literature
1 Stock Market Wealth and the Real Economy: A Local Labor Market Approach
2 Stock prices and economic growth