Asset Pricing Models to Predict Returns: A Comparative Study

In this study, the applicability of the Capital Asset Pricing Model (CAPM) and the Fama and French Three-Factor Model (FFTFM) is examined and compared in the Indian context. The study is undertaken on the companies in the Nifty-100 index covering a period of twelve years (March 2011 to March 2023). The portfolios for explanatory variables are formed considering market capitalization and value. The findings adequately evidence to draw the conclusion that the FFTFM is more effective. The results of the GRS (Gibbons, Ross, and Shanken) test also supported the use of the FFTFM in explaining stock return variations.

Introduction

Asset pricing models specify how return and risk relate to one another. The first model to elucidate the risk-return association in the financial market was Modern Portfolio Theory (MPT). In 1952, Harry Markowitz proposed MPT in his seminal paper “Portfolio Selection”. According to MPT, investors who wish to minimize their risk create diversified portfolios to optimize their rewards.

In the 1960s, a new model dubbed the Capital Asset Pricing Model (CAPM) was developed based on Markowitz’s MPT by William Sharpe (1964), John Lintner, and Jan Mossin autonomously. Although the CAPM is frequently used and well-known, it has received unsatisfactory results in earlier empirical studies like Basu (1977), Banz (1981), Rosenberg, Reid and Lanstein (1984), Bhandari (1988), and Fama and French (1993). This has driven many researchers to attempt and identify other factors ignored by the single-beta CAPM.

Fama and French collaborated in 1992 and 1993 to test the single-factor model by adding market capitalization (size) and book-to-market equity (value) factors. Their findings led to the development of the Fama-French Three-Factor Model (FFTFM), a well-known alternative model to CAPM. Additionally, they argued that their three-factor model outperformed CAPM in accurately predicting stock and portfolio returns.

Subsequent literature in India and globally has validated this multi-factor paradigm:

• Naughton and Veeraraghavan (2005) proved that the CAPM alone is inadequate to explain portfolio returns and concluded that the FFTFM is an appropriate model.
• Yash Pal Taneja (2010) found that the FFTFM is an effective predictor in the elucidation of asset returns in India.
• Sanjay Sehgal and A. Balakrishnan (2013) re-examined the efficacy of CAPM and FFTFM and found that FFTFM outperforms CAPM in explaining returns on most portfolios.
• Veysel Eraslan (2013) concluded that the FFTFM has limited ability on the Istanbul Stock Exchange.
• Nenavath Sreenu (2018) showed that FFTFM offers clearer elucidation for return disparities across NSE and BSE.
• Mobin Anwar and Sanjay Kumar (2018) revealed that while FFTFM did not adequately capture individual asset returns, it robustly explained portfolio returns sorted by size and value.
• Zankhana Atodaria (2020) and Debaditya Mohanti & Ravi Kumar Jain (2020) confirmed that market capitalization and value factors significantly influence returns, capturing systematic risk better than CAPM in the Indian market.

Research Methodology

The study relies on secondary data covering a period of twelve years, ranging from March 2011 to March 2023. Eighty-two companies listed in the S&P CNX Nifty-100 Index were selected. Required financial data was retrieved from annual reports, Yahoo Finance, Moneycontrol, and the Reserve Bank of India (RBI) Bulletin.

• Market Return ($R_m$): S&P CNX Nifty-100 Index returns are used as the proxy for market return.
• Risk-Free Rate ($R_f$): Return on 365-day Government of India Treasury Bills (from the RBI Bulletin) serves as the risk-free benchmark.
• Portfolio Formation: At the end of March each year ($t$), firms are univariate-sorted into five size-sorted portfolios ($P_1$ to $P_5$) and five book-to-market equity sorted portfolios ($P_1$ to $P_5$). For each portfolio, monthly average equally-weighted returns are computed.
• Joint Test of Intercepts: The GRS.test package in R is used to determine whether the models completely explain portfolio returns (testing the joint null hypothesis $H_0: \alpha_1 = \dots = \alpha_{10} = 0$).

Data Analysis: Descriptive Statistics

Table 2 presents descriptive statistics and correlations for the independent variables. The mean value is positive for the market premium at 0.587% per month, while the size ($SMB$) and value ($HML$) factors are negative (consistent with Taneja, 2010).

• A negative size premium ($-0.129\%$) indicates that large-cap stocks outperformed small-cap stocks within the Nifty-100 over this period.
• A negative value premium ($-1.184\%$) indicates that growth stocks yielded higher average returns than value stocks.
• The value factor ($HML$) exhibited the highest volatility with a standard deviation of 5.526%.
• The market factor ($EMR$) displays a leptokurtic distribution with kurtosis of 6.313 (> 3) and negative skewness ($-1.132$).
• Correlations between explanatory factors are low to moderate, ruling out multi-collinearity concerns.

OLS Regression Estimates for CAPM

Table 3 details the empirical estimation of the single-factor CAPM across size-sorted and book-to-market-sorted portfolios.

OLS Regression Estimates for Fama-French Three-Factor Model

Table 4 summarizes the multi-factor regression estimates incorporating the $SMB$ and $HML$ factors.

Comparative Performance: Predicted Returns & Goodness of Fit

From the single-factor model to the three-factor model, the explanatory power ($R^2$) increased across all ten portfolios:

• In the size-sorted portfolios, $R^2$ rose to a peak of 94.2% for large-caps ($P_5$).
• In the value-sorted portfolios, growth portfolio ($P_1$) fit jumped dramatically from 59.3% under CAPM to 83.1% under FFTFM.
• The GRS test statistic decreased from 7.917 for CAPM to 6.025 for FFTFM, confirming that the three-factor model captures return variations with lower pricing errors.

Conclusion

This study examined and compared the applicability of the CAPM and FFTFM in the Indian stock market using 82 companies from the S&P CNX Nifty-100 index between March 2011 and March 2023. The estimated empirical results demonstrate that the Fama and French Three-Factor Model is superior in explaining variations in portfolio returns. FFTFM outperforms CAPM in terms of positivity and statistical significance of intercepts, reduction in pricing errors (lower GRS statistic), and overall goodness of fit ($R^2$).

These findings match the empirical conclusions of Fama & French (1993), Naughton & Veeraraghavan (2005), Taneja (2010), Sehgal & Balakrishnan (2013), and Mohanti & Jain (2020), underscoring that institutional investors and Chartered Accountants must incorporate multi-factor modeling for portfolio management, hurdle rate estimation, and cost of capital determination.