THE WALL STREET EQUATION: POLYNOMIAL MODELING AND POWER CYCLES IN THE S&P 500

 

This explains precisely how politics and macroeconomics define the behavior of the S&P 500, structured as follows:

1. The political factor: The presidential election cycle sets the pace, government decisions, and priorities according to the stage of the term, and the pursuit of reelection generates the pattern of rises, falls, and volatility that repeats historically

2. The macroeconomic factor: The Federal Reserve's monetary policy (interest rates, liquidity), inflation, and general economic conditions can reinforce, modify, or even cancel out the political pattern.

3. Interaction: It is shown that the market does not move solely based on figures or corporate profits; it responds very sensitively to political decisions and the macroeconomic scenario, although unexpected external events can also disrupt this dynamic. The entire analysis demonstrates that the S&P 500 is profoundly influenced by the combination of political cycles and macroeconomic conditions.

The polynomial-fit analysis of the S&P 500's performance over the past five years allows us to clearly identify the structure of its cycles, the duration of its upward and downward phases, and where we stand today.

Duration of the phases: Upward phases extend on average between 32 and 36 days, with moderate variation in their trajectory to reach the peak. Downward phases have a similar or slightly shorter duration, between 28 and 32 days, showing that declines tend to occur more rapidly than recoveries during this period.

If the complete cycle is analyzed, from a trough to the next decline, the entire cycle takes approximately 96 to 98 days, a pattern that has been consistently repeated over the five-year period analyzed.

Current Index Position

At this time, the S&P 500 is clearly at the top of its cycle, very close to the all-time highs identified in the analysis.

 This position, combined with patterns from previous cycles, suggests that a correction is very likely in the short to medium term—an adjustment phase that would lead the index to seek support levels before beginning a new recovery phase. It is important to remember that this analysis is based on historical patterns and does not constitute investment advice, as economic, financial, or geopolitical events can alter the duration and magnitude of these phases.

The mathematical, polynomial, and derivative analysis presented in this study, which models peaks, troughs, concavities, and inflection points using sixth-degree functions, is an excellent tool for understanding theoretical oscillation cycles.

If we apply this analytical and quantitative approach to the actual cyclical behavior of the S&P 500 over a 5-year horizon, we find a pattern strongly influenced by macroeconomics and politics: the 4- to 5-year presidential cycle (Yale Hirsch Presidential Cycle Theory).

The historical behavior of the US market is sharply divided according to the year of the political-economic cycle.

 Year 1 is defined as the "Honeymoon" period (post-election). Its performance is typically characterized by a year of moderate to strong growth.

The new (or re-elected) president takes office with political capital. The first reforms are implemented, and there is an atmosphere of certainty now that the elections are over. The market tends to react positively to the new fiscal policies.

Year 2 represents the "Trough" of the cycle (midterm election year). Historically, its performance in this year is the weakest and most volatile of the entire 5-year cycle. The dynamic or critical low point, where investors and voters grow impatient with the lack of quick results. It is the year in which decisions are made More difficult, painful, or unpopular political decisions (fiscal adjustments, interest rate hikes) are made so that the political cost is diluted before the next election.

The S&P 500 typically experiences significant corrections (with average declines of between 10% and 15%), reaching a "trough" (cyclical low) between the second and third quarters of the year.

In year 3, it shows a strong "rise" due to being a pre-election year.

This performance is notable for being the strongest year of the cycle; it demonstrates a change in concavity—an upward inflection point. Once the midterm elections are over, political uncertainty drops dramatically.

The government begins paving the way for reelection, which usually translates into more accommodative policies, economic stimulus, or liquidity injections.

Historically, the S&P 500 rises strongly during this period, registering average double-digit returns. Year 4 is distinguished as the "peak" or election year. Its performance shows solid returns but is accompanied by high volatility in the second half of the year.

In market dynamics, the first half typically continues the momentum of year 3. As the general elections approach in November, the market experiences fluctuations due to opinion polls. However, once the election results are in, a "year-end rally" typically occurs, consolidating a "peak" or cyclical high.

In year 5, characterized by the transition and restart of the cycle, a return to the market's historical average is observed.

The cycle overlaps with year 1 of the next administration. The S&P 500 consolidates previous gains and begins to readjust its valuations based on the new realities of interest rates and corporate earnings per share (EPS).

The key factors that alter this behavior, as well as the variables in the polynomial equation, can vary, altering the shape of the curve. The S&P 500 cycle is distorted by external factors such as liquidity cycles (Federal Reserve policies). If year 3 coincides with a period of high or restrictive interest rates by the Fed to combat inflation, the natural expansionary return may be mitigated.

Historically, if an incumbent president seeks reelection, the incentives to stimulate the economy in years 3 and 4 are much greater, making these years exceptionally bullish.

"Black swan" events or unforeseen crises (such as pandemics, geopolitical conflicts, or systemic bankruptcies) act as an exogenous force that temporarily disrupts the mathematical seasonality of the cycle.