Ditch the Beta: Why AI is the New Cost of Capital King (And Why Your CFO Should Care)
Corporate financial strategy hinges on the ability of management to make optimal investment decisions, typically defined by two primary rationales: maximizing profit and/or maximizing market value. An asset should only be acquired if the expected rate of return surpasses the interest rate (profit maximization) or if the cost of acquisition is less than the value it adds to the corporation’s market value (market value maximization). Central to these critical determinations is the calculation of the cost of capital, which is essential for guiding investment strategies. The cost of capital represents the minimum return expected from any investment made by a firm and is derived from the sum of the debt and equity components that form the firm’s capital structure. For managers to maximize corporate value, maintaining an optimum rate for the cost of capital is essential, balancing benefits and costs to maximize profits. However, recent market volatilities, exemplified by financial crises, have made the accurate estimation of the cost of equity capital increasingly difficult, consequently influencing the overall cost of capital determination.
The Enduring Challenge of Traditional Cost of Capital Calculation
The necessity of accurately estimating the cost of capital is historical; for instance, in the early 1980s, U.S. companies were found to have a much higher cost of capital than Japanese firms, a factor that influenced long-term managerial decisions and allowed Japanese companies to gain competitiveness, mainly due to a low cost of debt combined with high debt-equity ratios. Today, however, the cost of equity is the most critical factor influencing the overall cost of capital.
The estimation of the cost of equity traditionally relies heavily on the Capital Asset Pricing Model (CAPM). CAPM relies on several key parameters, each introducing potential inaccuracies. One such parameter is the risk-free rate of return, often benchmarked using the average yield to maturity on default-free government securities over an extended period (10 to 30 years in the U.S.). Using this long-term average helps eliminate the sensitivity to sudden drops and rises in security values, especially critical during periods like the 2008 financial crisis, but it remains a simplification.
Another critical volatile parameter is the equity risk premium, which is the excess return over the risk-free rate obtained from the stock market. The volatility associated with investments in securities necessitated the development of beta ($\beta$), a parameter designed to show a company’s stock volatility relative to the market for a defined duration. Beta is an essential requirement for CAPM calculation. However, analysts must make simplifications to estimate beta for use in asset pricing models, introducing further errors into the cost of capital calculations. Since CAPM relies on the linear prediction of asset returns compared to the market, and beta is calculated through linear regression analysis over a long period of historical data, it is argued that this linear estimation of risk is inaccurate because the market does not behave linearly. These simplifications, particularly those associated with time and risk in calculating the cost of equity, form the main problem that innovative techniques, like Artificial Intelligence (AI), seek to address to enable more accurate estimation of expected returns.
Introducing Artificial Intelligence to Finance
Artificial intelligence (AI) is generally defined as an algorithm capable of learning and thinking. Learning involves updating coefficients and parameters of an algorithm to recognize patterns between input and output data. AI, in the form of mathematical models such as deep learning and neural networks, has gained tremendous momentum due to its ability to find intricate patterns and forecast future events more accurately. In finance, AI is extensively used for pattern recognition and prediction of future events. For example, AI algorithms have been proposed to calculate financial distress more accurately than traditional simplified equations that are prone to high degrees of error. Similarly, due to the nonlinearity and complexity of financial information, AI has been successfully applied to predict stock values, offering valuable information that can benefit corporate governance and decision-making.
The study described in the source utilizes AI to tackle the accuracy challenges in CAPM estimation. The research focused on 10 high-tech US-based public companies listed in the S&P 500, selected for their high volatility and reliance on debt. The methodology aimed to compare traditional CAPM calculations with two new approaches leveraging AI predictions.
The specific AI algorithm chosen for predicting future stock performance was the Recurrent Neural Network (RNN). RNNs are the most advanced and powerful AI capable of processing sequential data, such as stock prices, where each new data point arrives at a specific stage and is time-dependent. Unlike standard feedforward neural networks (FFNN) where data moves in one direction and past data is lost, RNN employs a loop structure, enabling it to remember the past alongside new data—a crucial feature for predicting sequential financial data like stock prices.
To overcome a major flaw in RNNs known as the Vanishing Gradient problem (where partial derivatives become too small, preventing weights from having an effect), the study implemented Long Short Term Memory (LSTM), a new method that is optimally suited for time series sequential data. The LSTM architecture, which includes input, output, and forget gates, acts as a regulator of information, allowing the cell to remember data for extended periods and preventing the vanishing problem. The deep learning architecture developed utilized multiple LSTM layers combined with dropout layers, followed by a final dense layer to reduce the output to a single predicted value.
The AI Advantage: New Methods for Calculating Returns
The research proposed two novel methods for incorporating AI into expected return calculations, utilizing stock prices predicted by the trained neural network (LSTM):
AI Predicted Return: Calculating the annual return on the security directly from the predicted AI stock prices using the logarithmic method.
AI Predicted CAPM: Repeating the CAPM calculation, but instead of using historical data to derive risk metrics (like Beta), using the AI-predicted data to estimate risk and market returns.
For the purpose of analysis, adjusted closing stock prices of the 10 high-tech companies and the S&P 500 index were studied from January 2013 to January 2019. The network was trained using one year of historical data to predict the returns for the upcoming year. After training and testing the network, it was found to accurately predict stock prices, demonstrating its suitability for the rest of the study.
Empirical Results: Quantifying AI’s Superiority
The findings strongly supported the hypotheses that AI could be used in cost of capital calculation to improve predictability and provide a more accurate estimation of returns than traditional methods.
A comparison of the three calculated return values (Traditional CAPM, AI Predicted CAPM, and AI Predicted Return) against the actual returns revealed significant differences. The study found that the use of AI improved the accuracy of cost of equity estimations by over 60%.
Specifically:
Traditional CAPM consistently underestimated returns in all ten companies across five years, resulting in a substantial average absolute error of 102% for all companies.
AI Predicted CAPM performed better than the traditional method, reducing the average error by 18%.
AI Predicted Return was consistently closer to the actual returns. Quantitatively, this method was found to be 60% more accurate than traditional CAPM. Furthermore, the AI Predicted Return had the smallest standard deviation, indicating a reasonable consistency in the prediction of future returns and proving more reliable and accurate overall.
The robust ability of the deep learning neural network chosen to predict stock prices resulted in an increase in the accuracy of estimating returns by at least 18%.
Disrupting Capital Structure Theory and Practice
These empirical findings carry profound implications for corporate finance and investment strategy. The fact that stock prices could be predicted accurately for up to one year, compatible with the findings of other studies that criticized the Efficient Market Hypothesis (EMH), contradicts the Random Walk Theory which claims prediction is impossible.
First, the research suggests that current asset pricing models like CAPM, which rely on historical data and linear methods, may become obsolete. The cost of equity should not be estimated using asset pricing models such as CAPM anymore, as the future can be predicted with reasonable accuracy using AI. This goes beyond the existing debate in literature claiming that "beta is dead".
Consequently, the traditional definition of risk (beta) may no longer be necessary. Risk should instead be redefined in a manner related to the uncertainty associated with AI stock price predictions. Two methods are suggested: incorporating a new algorithm that uses uncertainty (probability of occurrence) as a multiplier to predicted returns, or evaluating the reliability of historical predictions and incorporating the standard deviation as the associated uncertainty. Ultimately, as the community trusts AI predictions, a new parameter is needed to replace beta.
Second, the consistent finding that traditional CAPM significantly underestimates the cost of equity suggests that its application leads to a lower calculated Weighted Average Cost of Capital (WACC) than is accurate. If firms adopt the new, more accurate AI-driven method, the calculated cost of equity capital will likely increase, disturbing the balance for the optimum capital structure. To maintain the same overall cost of capital and maximize firm value, corporations might need to increase the debt portion of their capital structure.
Despite the potential complexity arising from the need for programming, mathematical, and financial knowledge to develop AI software, the advantages are clear. A significantly positive advantage of using AI in cost of capital calculations is the ability to estimate this value accurately and instantaneously. This enables firms to plan more precisely to optimize their capital structure, providing an essential asset for financial decision-making by Chief Financial Officers (CFOs). This pioneering study, applying AI to the estimation of the cost of equity for the first time, sets the stage for a new era in financial research where linear or simplistic approaches are no longer considered adequate solutions.
CAPM Researchers:
William F. Sharpe
Contribution: Sharpe developed the CAPM in a 1964 paper, building on the portfolio theory of Harry Markowitz. His model established a formal relationship between an asset's risk (as measured by beta) and its expected return.
Key Concept: The model suggests that the expected return of an asset is the risk-free rate plus a risk premium that is proportional to the asset's systematic risk (beta).
Nobel Prize: For his work on CAPM, Sharpe was a joint recipient of the 1990 Nobel Memorial Prize in Economic Sciences.
John Lintner
Contribution: Working independently of Sharpe, Lintner published his own version of the CAPM in 1965. His work reinforced and formalized the theoretical underpinnings of the model.
Key Concept: His research also focused on the valuation of risky assets and how investors select risky investments for their portfolios.
Fischer Black
Contribution: Fischer Black is known for developing the "zero-beta" version of the CAPM in 1972, which does not rely on the assumption of a risk-free asset.
Key Concept: This version of the model addressed the critique that a true risk-free asset does not exist in reality, making the CAPM more robust to empirical testing. Black's work was foundational to later research that challenged and refined the CAPM, including studies that explored its limitations.
