The Stock Market is Highly Overvalued

The use of a trend-line reversion model to evaluate the gap between current stock prices and sane stock prices

Abstract: This analysis develops an empirical estimation of the gap between current stock market pricing and its long-term structural equilibrium. The estimation process isolates a sane historical base year and projects the future baseline fair value from historic stock averages. The model identifies the 2012–2013 window as the sane anchor for the S&P 500. The final valuation gap is sensitive to stock price growth rate assumptions. The procedure is also used to find the valuation gap for large-cap growth and large-cap value portfolios.

Every investor knows the stock market feels expensive today. But how expensive? 30%? 50%? Is a correction imminent, or are we simply operating in a new structural regime of higher permanent growth?

If you turn to Wall Street for answers, you usually get trapped in a circular argument. Analysts will tell you the S&P 500 is valued fairly compared to next year’s forward earnings estimates. But those earnings estimates are based on corporate revenue projections, which are heavily influenced by current market sentiment. It’s a self-referencing echo chamber.

To find a true, uncorrupted fundamental anchor, my son and I recently sat down to solve this quantitative puzzle. We developed an independent Trend-Line Reversion Model designed to answer two precise questions:

1. When was the last time the stock market cleared at a reasonable price reflecting long-term structural equilibrium?

2. Based on that anchor, what is the gap between the current and estimate realistic stock price?

This paper uses a trend-line reversion model to obtain valuation gap estimates for the S&P 500 under different assumptions and valuation gap estimates for portfolios of large-cap value and growth stocks.

The Trend-Line Reversion Methodology:

We assume that over long horizons, the stock market compounds at a reasonable rate, perhaps 7 percent per year. If we knew the year the stock market was a sane or reasonable estimate, we could estimate over or under valuation as the difference between the actual price and a projected reasonable price equal to S(1.07)^t where S is the value in the sane year.

A random choice of a sane year could warp the analysis. An analysis anchored to the top of the Dot-Com expansion would make subsequent decades look cheap while an analysis anchored to the absolute depth of the financial crisis would exaggerate the size of the bubble.

To eliminate cognitive bias and guesswork, we designed a Scoreboard Optimization Loop using a point-by-point least-squares percentage comparison.

We isolated a 20-year historical window (2005 through 2025) and tested every single year as a candidate baseline anchor. For each candidate year, the model projects a 7% compounding trend line forward and backward through the calibration timeline. It then compiles the Sum of Squared Percentage Errors (SSPE) between that specific trend line and actual historical data:

By squaring the percentage errors, we ensure two things: overvaluations and under valuations are penalized equally, and the math strips away raw dollar scale (so a deviation in 2005 carries the same analytical weight as a deviation in 2025).

The candidate year that finishes with the lowest total error score represents the true geometric center of gravity for the modern market—the historical point where market prices sat perfectly on the sustainable long-term trend.

Scenario 1: The S&P 500 at a 7% Normal Growth Rate

When we ran the broad S&P 500 data through the optimization loop assuming a standard historical price growth rate of 7%, the scoreboard lit up with a definitive best anchor year: 2012.

· 2005 — Total Error Score (SSPE): 1.84 | Highly Distorted (Pre-Crisis Bubble Baseline)

· 2008 — Total Error Score (SSPE): 1.12 | Displaced (Market Crisis / Undervalued Baseline)

· 2011 — Total Error Score (SSPE): 0.38 | Near Structural Fair Value

· 2012 — Total Error Score (SSPE): 0.31 (GLOBAL MINIMUM) | Optimized Structural Fair Value Equilibrium

· 2013 — Total Error Score (SSPE): 0.44 | Near Structural Fair Value

· 2016 — Total Error Score (SSPE): 0.89 | Moderate Structural Premium

· 2020 — Total Error Score (SSPE): 2.45 | Exceptionally Distorted (Emergency Stimulus Baseline)

Anchoring the model to the high-stimulus valuation of 2020 creates an enormous error score (2.45) because it forces the historical trend line way below where the market actually cleared in the mid-2000s.

The 2012 base anchor cuts through the cyclical noise flawlessly. It represents the quiet post-crisis stabilization period immediately before emergency monetary interventions completely altered equity multiples.

The 7% Valuation Gap Result

When we take that optimized 2012 trend line and project its trajectory out to the beginning of 2026, it indicates that the structural fair value of the S&P 500 should be $3,552.

The actual average price of the S&P 500 at the target checkpoint was $5,000.

Under these standard baseline assumptions, the broad market entered the year trading 40.76% above its long-term fundamental compounding curve.

The Robustness Check: What if Normal Growth is 8%?

A rigorous quantitative model must be stress-tested. What if a 7% growth assumption is too conservative for a modern economy? What if structural technology gains mean that 8% is the new baseline normal?

When we adjusted the core parameter to an 8% compounding rate and re-ran the entire optimization loop, the model shifted across two separate dimensions:

1. The Anchor Year Shifts to 2013: Because an 8% compounding line climbs at a steeper angle, the optimization loop mechanically pushed the winning anchor year forward to 2013 (SSPE: 0.38). The math needed a slightly higher historical starting price to prevent the steeper line from dropping entirely below the actual market data of the mid-2000s.

2. The Valuation Gap Compresses: Because an 8% trend line accumulates baseline value much faster, it catches up to current prices aggressively. Under the 8% model, the projected fair value for 2026 rises to $4,171.

This robustness check reveals the valuation gap is highly sensitive to the normal stock price growth assumption. A 100-basis point increase in return assumptions reduces the overvaluation gap from around 41 percent to around 20 percent.

However, the model is highly robust regarding the location of fair value. Whether you assume a 7% or 8% growth engine, the algorithm persistently locks onto the 2012–2013 window as the only structurally sound, uncorrupted baseline era of the last twenty years.

Valuation gaps for large-cap growth and large-cap value Portfolios

Looking at the S&P 500 as one massive, monolithic index can mask deeper structural imbalances. To discover where the overvaluation risk is truly concentrated, we split the index into its two primary sub-components: S&P 500 Growth and S&P 500 Value.

We cannot use a uniform, index-wide “average” growth rate for both. Because of annual index rebalancing, value indices regularly prune their top overperforming companies, while growth indices hoard multiple expansions. Furthermore, Value returns rely heavily on cash dividends (which mechanically drop out of the raw stock price), while Growth relies almost entirely on capital appreciation.

To adjust for this “style drift,” we applied distinct, historically accurate price growth parameters: 9.5% for Growth and 5.0% for Value.

When we ran these independent optimization loops, a stark divergence emerged:

1. S&P 500 Value (5.0% Baseline Anchors to 2012)

The Value index aligns perfectly with our broad market model, choosing 2012 as its optimal baseline (SSPE: 0.26).

• Actual Price (Jan 2026): $1,720

• Model-Derived Fair Value: $1,351

• Value Sector Overvaluation: 27.31%

2. S&P 500 Growth (9.5% Baseline Anchors to 2016)

The Growth index experienced a profound structural forward break, shifting its optimal anchor year to 2016 (SSPE: 0.42). This marks the exact dawn of the modern, ultra-large-cap technology dominance regime.

• Actual Price (Jan 2026): $3,650

• Model-Derived Fair Value: $2,411

• Growth Sector Overvaluation: 51.39%

The Substack Bottom Line

Perhaps the most startling result of this estimation process is that even the traditionally defensive Value sector is fundamentally overvalued. Market risk is deeply asymmetrical: the Growth sector sits in an acute overvaluation regime at 51.39% above trend, while the Value sector trades at a more moderate but still significant 27.31% above trend. If historical gravity is any indicator, a macro-reversion to the mean implies that both sectors can absolutely fall from current levels, though the drawdown will hit the heavily overextended growth curve far harder than the value baseline.

Disclaimer: This analysis represents a structural trend-line model executed for quantitative research purposes and does not constitute formal investment advice. All chart metrics correspond to annual averages up to January 2026.