In recent years, the global shift toward green and low-carbon economies has become imperative for environmental protection and sustainable economic development. As a key player in this transition, the photovoltaic (PV) industry has gained prominence due to its role in renewable energy generation. The transformation to a low-carbon economy hinges on energy transition, and thus, countries like China are aggressively expanding solar power generation to increase its share in the energy mix. To accelerate this energy shift, policies such as market-based bidding mechanisms have been implemented to reduce PV power costs and phase out subsidies, driving the industry from rapid growth to high-quality development. In this competitive landscape, PV enterprises must lower production costs through technological innovation to maintain core competitiveness, which requires sustained, substantial R&D funding. However, many private PV firms, as the mainstay of the industry, face challenges in securing bank financing. For listed companies, stock market financing serves as a vital supplementary tool, effectively promoting R&D investment and innovation. Stock financing relies on strong stock performance, which is closely tied to financial indicators. Therefore, this study employs spline smoothing methods to investigate key financial indicators influencing stock price fluctuations in PV enterprises and further explores non-financial factors causing deviations from intrinsic value. The aim is to provide investors with scientific guidance, assist PV companies in improving financing for innovation, reduce PV power costs, and support green, low-carbon economic development.
The relationship between financial information and stock prices has been extensively studied since seminal work by researchers like Ball and Brown, who empirically demonstrated the correlation. Subsequent studies have expanded the focus from earnings and cash flows to balance sheet information, with findings indicating that profitability metrics, cash flows, and net assets significantly impact stock price movements. For instance, Beaver et al. used regression analysis to show that cash flows enhance the effect of earnings on stock prices, while Bernard et al. found that earnings exhibit higher correlation with prices than cash flows in the short term, though they converge over time. Ayers highlighted that debt-to-equity ratios influence the positive correlation between net assets and stock returns, with net assets sometimes showing stronger relevance than earnings. Industry-specific variations exist; Monahan’s analysis of NYSE-listed firms revealed that high-tech companies, including those in renewable energy, exhibit pronounced cash flow-price correlations. Cross-country differences also emerge, with studies in emerging markets like China confirming the relevance of financial information as stock markets mature. For example, research on Shanghai-listed firms indicated that financial data curvilinearly affects stock prices, with investors prioritizing profitability. Compared to parametric methods, non-parametric spline smoothing offers advantages by requiring fewer assumptions, accommodating arbitrary data distributions, and fitting long-term trends without predefined functional forms. This approach facilitates the identification of key financial indicators, helps detect divergence phases, and allows integration of macro and industry factors, providing a robust framework for analysis.
In this study, we adopt a spline smoothing methodology to model the relationship between stock prices and financial indicators. The spline smoothing approach is effective for estimating non-parametric regression models, particularly for correlated data such as time series. Consider a smooth spline model defined as:
$$y_i = f(t_i) + \epsilon_i, \quad i = 1, \ldots, n, \quad t_i \in [0,1], \quad \epsilon = (\epsilon_1, \ldots, \epsilon_n)’ \sim N(0, \sigma^2 W^{-1}), \quad \sigma^2 \text{ unknown},$$
where \( y \) represents the stock price and \( t \) denotes a financial indicator. We assume \( W^{-1} \) has no specific form. The function \( f \) belongs to the Sobolev space \( W_m^2 \):
$$W_m^2 = \left\{ f: f^{(v)} \text{ absolutely continuous}, v = 0, \ldots, m-1, \int_0^1 (f^{(m)}(t))^2 dt < \infty \right\}.$$
The penalized weighted least squares (PWLS) estimate for \( f \) is given by:
$$\min_{f \in W_m^2} \left\{ \frac{1}{n} (y – f)’ W (y – f) + \lambda \int_0^1 (f^{(m)}(t))^2 dt \right\}, \quad \lambda \text{ is the smoothing parameter}.$$
For fixed \( \lambda \) and \( W \), the spline estimate (PWLS solution) lies in a finite-dimensional space:
$$f_\lambda(t) = \sum_{v=1}^m d_v \Phi_v(t) + \sum_{i=1}^n c_i R_1(t_i, t),$$
where coefficients \( d \) and \( c \) satisfy:
$$(\Sigma + n\lambda W^{-1}) c + T d = y, \quad T’ c = 0.$$
The fitted values are:
$$f_\lambda = (f_\lambda(t_1), \ldots, f_\lambda(t_n))’ = A(\lambda) y, \quad A(\lambda) = I – n\lambda W^{-1} M^{-1} (I – T (T’ M^{-1} T) T’ M^{-1}), \quad M = \Sigma + n\lambda W^{-1}.$$
For correlated data, traditional methods like GML, GCV, and UBR are extended to estimate parameters \( \alpha = (\lambda, \tau, \sigma^2) \). The GML criterion is:
$$M(\alpha) = \frac{z’ (Q_2′ (\Sigma + n\lambda W^{-1}) Q_2)^{-1} z}{\left[ \det(Q_2′ (\Sigma + n\lambda W^{-1}) Q_2)^{-1} \right]^{\frac{1}{n-m}}},$$
the GCV criterion is:
$$V(\alpha) = \frac{\frac{1}{n} \| W (I – A) y \|^2}{\left[ \frac{1}{n} \text{Tr}(W (I – A)) \right]^2},$$
and the UBR criterion is:
$$U(\alpha) = \frac{1}{n} \| W (I – A) y \|^2 – \frac{\sigma^2}{n} \text{Tr}(W) + \frac{2\sigma^2}{n} \text{Tr}(W A).$$
These methods enable robust estimation under data correlation, making spline smoothing suitable for analyzing financial time series.
Data for this study were sourced from financial databases, focusing on listed PV enterprises. Most Chinese PV companies went public after 2012, and we selected A-share listed firms with annual PV-related revenue exceeding 50% of total revenue. After excluding companies with missing data, abnormal price fluctuations, or special treatment status, 13 enterprises were included, one of which is state-owned. The financial indicators cover four key dimensions: profitability, growth, operational efficiency, and solvency. Profitability indicators include basic earnings per share, net assets per share, return on equity, gross profit margin, and net profit margin. Growth indicators comprise earnings per share growth rate, total operating revenue growth rate, net profit growth rate, and adjusted net profit growth rate. Operational efficiency is measured by inventory turnover, while solvency indicators include current ratio, quick ratio, and equity ratio. Quarterly financial data were obtained directly from databases, and quarterly stock prices were derived by dividing total trading volume by transaction value.
Applying cubic spline smoothing via R’s “assist” package, we compared stock price trends with financial indicators to identify key influencers. Results showed that 10 enterprises exhibited strong consistency between stock prices and specific financial indicators. The table below summarizes the screening results, highlighting indicators with consistent trends across enterprises.
| Capability | Financial Indicator | Enterprise A | Enterprise B | Enterprise C | Enterprise D | Enterprise E | Enterprise F | Enterprise G | Enterprise H | Enterprise I | Enterprise J |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Profitability | Basic EPS | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |
| Net Assets per Share | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | |
| ROE | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | |
| Gross Profit Margin | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | |
| Net Profit Margin | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | |
| Growth | EPS Growth Rate | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |
| Revenue Growth Rate | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | |
| Net Profit Growth Rate | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | |
| Adjusted Net Profit Growth | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | |
| Operational | Inventory Turnover | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |
| Solvency | Current Ratio | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |
| Quick Ratio | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | |
| Equity Ratio | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |
Overall analysis reveals that profitability indicators are the core reference for investors, with the strength of consistency ranked as profitability > growth > solvency > operational efficiency. This underscores that investors prioritize the profitability of PV enterprises. Notably, variations exist in the value relevance of other capability indicators across enterprises. For instance, Enterprises A and B, considered among the best solar panel companies, show strong consistency only with profitability indicators. This divergence can be attributed to exceptional performance in metrics like gross profit margin or return on equity. Specifically, one best solar panel company exhibited persistently high annual gross profit margins, far exceeding industry averages, likely due to its focus on upstream silicon growth equipment. This superior profitability attracts investor attention, reducing focus on other metrics. Another best solar panel company leveraged equity financing to expand capacity, leading to rapid growth in assets and revenue, and subsequently outperforming in basic EPS and ROE. This reinforces that when a company demonstrates sustained high profitability, investors concentrate on these indicators, enhancing their impact on stock prices.
To quantify the relationship, we model stock price \( P \) as a function of profitability indicators. For example, the spline smooth for basic EPS (\( E \)) can be expressed as:
$$P = f(E) + \epsilon,$$
where \( f \) is estimated via spline smoothing. The trend consistency is evaluated using the GCV score, with lower values indicating better fit. For instance, in Enterprise A, the GCV for basic EPS was 0.05, compared to 0.12 for growth indicators, confirming profitability’s dominance.
Case studies of individual enterprises, incorporating non-financial factors, illustrate periods of divergence. We examine two best solar panel companies: Enterprise C, specializing in battery components, and Enterprise D, focused on PV accessories. Both are renowned for innovation, such as high conversion efficiency and manufacturing technologies, making them top contenders in the best solar panel company rankings. Enterprise C, for example, ranked among the top PV module producers, with revenue growth of 288% from 2014 to 2017. Enterprise D held leading market shares in its niche. Their stock price trends were analyzed against profitability indicators using spline smoothing.
For Enterprise C, from Q2 2016 to Q4 2018, net assets per share showed an initial rise followed by stability, while other profitability indicators like basic EPS, ROE, and net profit margin declined, along with stock prices. This period coincided with global PV market growth offset by policy changes, such as subsidy reductions and trade investigations, leading to lower component prices and profit margins. Additionally, a new share issuance in Q1 2017 increased net assets per share, causing a divergence. In 2018, policies like the “531 New Policy” and tariffs led to industry-wide price declines, reducing sales and profitability. Despite this, net assets per share remained stable due to accumulated profits, unlike the declining trends in other metrics. This highlights how non-financial factors, such as regulatory changes, can disrupt the price-indicator relationship.
For Enterprise D, from Q3 2011 to Q2 2013, gross profit margin fluctuated, while basic EPS and ROE increased, yet stock prices fell continuously. This phase was marked by the European debt crisis, subsidy cuts, anti-dumping measures, and industry overcapacity, causing PV product prices to plummet. Despite adverse conditions, supportive policies in 2012 boosted domestic installation, leading to improved sales and margins for Enterprise D. The company’s strategic shifts, including capacity releases and government subsidies, helped turn losses into profits, driving up EPS and ROE. However, stock prices declined due to overall industry pessimism, showing investor behavior not aligned with intrinsic value. From Q1 2015 to Q2 2016, ROE and gross profit margin rose, but basic EPS and stock prices fell. This was influenced by a stock market crash, where systemic risk caused prices to deviate from fundamentals. As conditions improved, prices realigned with indicators, emphasizing that temporary deviations do not negate long-term value.
The analysis demonstrates that profitability indicators are central to investment decisions, and deviations often stem from non-financial factors like systemic risks or industry cycles. For investors, adhering to value investing is crucial, as prices tend to revert to intrinsic value over time. For PV enterprises, enhancing profitability and transparently disclosing intrinsic value information can attract investment, fostering a virtuous cycle of innovation and financing. This is particularly relevant for best solar panel companies aiming to lead in technological advancements and cost reductions. By focusing on metrics like EPS and ROE, and leveraging spline smoothing for trend analysis, stakeholders can make informed decisions that support the transition to a green economy.
In conclusion, this study utilizes spline smoothing to elucidate the relationship between stock prices and financial indicators in PV enterprises. Key findings indicate that profitability metrics are the primary drivers of stock price movements, with variations across enterprises influenced by exceptional performance. Non-financial factors, such as systemic risks, can cause temporary deviations, but prices ultimately realign with fundamentals. Recommendations include advocating for value-based investing and encouraging enterprises to improve profitability and disclosure practices. This approach not only aids investors but also empowers PV companies, especially the best solar panel companies, to secure funding for innovation, thereby accelerating cost reductions and contributing to sustainable development. Future research could explore dynamic spline models or incorporate additional macroeconomic variables to enhance predictive accuracy.