Classical Capital Asset Pricing Model Research Articles

A modelling framework for equity portfolio projections under different carbon price scenarios

It is recognised that climate risks (including carbon pricing policy) are a new source of risk for the financial system. We propose a modelling framework for medium-term projections of stock returns under different carbon price scenarios. First, we construct a green factor to augment the classic capital asset pricing model (CAPM) and capture a firm’s exposure to climate policy risks. Then, we project to 2040 the factors of the CAPM, conditional on different carbon price pathways, using the estimated medium-scale Bayesian vector autoregressive model (MBVAR). Finally, we project the stock returns of each firm in the portfolio. Our scenarios suggest that the impacts of a carbon price policy are not confined to the most polluting firms (mining and quarrying, transportation and storage firms) for the effect of systematic risk. Moreover, in the short term, the negative impacts of a carbon price policy are more accentuated under a disorderly than an orderly transition. In the medium term, the projections suggest that the stock market progressively adapts to new conditions and believes in the benefits of rigorous carbon policies to incentivise the transition to a low-carbon economy. The proposed toolbox may represent effective support for investors in preparing portfolios for climate transition risks in the context of uncertainty regarding the timing of the introduction of a carbon policy. For policymakers, it can help shed light on how policies to prevent or mitigate climate change effects can affect financial stability.

A capital asset pricing model based on the value at risk under asymmetric Laplace distribution

PurposeFinancial asset return series usually exhibit nonnormal characteristics such as high peaks, heavy tails and asymmetry. Traditional risk measures like standard deviation or variance are inadequate for nonnormal distributions. Value at Risk (VaR) is consistent with people's psychological perception of risk. The asymmetric Laplace distribution (ALD) captures the heavy-tailed and biased features of the distribution. VaR is therefore used as a risk measure to explore the problem of VaR-based asset pricing. Assuming returns obey ALD, the study explores the impact of high peaks, heavy tails and asymmetric features of financial asset return data on asset pricing.Design/methodology/approachA VaR-based capital asset pricing model (CAPM) was constructed under the ALD that follows the logic of the classical CAPM and derive the corresponding VaR-β coefficients under ALD.FindingsALD-based VaR exhibits a minor tail risk than VaR under normal distribution as the mean increases. The theoretical derivation yields a more complex capital asset pricing formula involving β coefficients compared to the traditional CAPM.The empirical analysis shows that the CAPM under ALD can reflect the β-return relationship, and the results are robust. Finally, comparing the two CAPMs reveals that the β coefficients derived in this paper are smaller than those in the traditional CAPM in 69–80% of cases.Originality/valueThe paper uses VaR as a risk measure for financial time series data following ALD to explore asset pricing problems. The findings complement existing literature on the effects of high peaks, heavy tails and asymmetry on asset pricing, providing valuable insights for investors, policymakers and regulators.

Estimating the cost of equity capital for small companies: an empirical analysis of the effectiveness of an alternative method in calculating economic value added

Abstract: Although initially developed for large corporations, economic value added (EVA) is a potential performance indicator to be used in small businesses (SME)s. EVA is calculated based on the cost of capital (equity and third party´s capital). Usually, the cost of equity capital is estimated using the classical Capital Asset Pricing Model (CAPM), whose parameters are estimated by market data. In general, the CAPM becomes impracticable in SMEs due to the scarcity or absence of stocks traded on the stock exchange. As literature presents some alternative methods to calculate the cost of equity for small private companies, the objective of this study is to evaluate the effectiveness of the alternative method proposed by Boudreaux et al. (2011) compared to the classical CAPM, when both methods are used to calculate the EVA indicator. From a sample composed of 34 companies listed on the Brazilian stock exchange (B3), the results show that the method is useful for estimating the cost of equity capital in the calculation of the EVA indicator. Keywords: Small businesses; SME; EVA indicator; Cost of equity capital; Cost of capital; Capital Asset Pricing Model; CAPM.

Nuclear Hazard and Asset Prices: Implications of Nuclear Disasters in the Cross-Sectional Behavior of Stock Returns

Using stock return data for the Japanese equity market, for the period from July 1983 to June 2018, we analyze the effect of major nuclear disasters worldwide on Japanese discount rates. For that purpose, we compare the performance of the capital asset pricing model (CAPM) conditional on the event of nuclear disasters with that of the classic CAPM and the Fama–French three- and five-factor models. In order to control for nuclear disasters, we use an instrument that allows us to parameterize the linear stochastic discount factor of the conditional CAPM and transform the classic CAPM into a three-factor model. In this regard, the use of nuclear disasters as an explanatory variable for the cross-sectional behavior of stock returns is a novel contribution of this research. Our results suggest that nuclear disasters account for a large fraction of the variation of stock returns, allowing the CAPM to perform similarly to the Fama–French three- and five-factor models. Furthermore, our results show that, in general, nuclear disasters are positively related to the expected returns of a large number of assets under study. Our results have important implications for the task of estimating the cost of equity and constitute a step forward in understanding the relationship between equity risk premiums and nuclear disasters.

Comparative analyses of mean-variance and mean-semivariance approaches on global and local single factor market model for developed and emerging markets

PurposeThe beta coefficient used for the cost of equity calculation is at the heart of the valuation process. This study conducts comparative analyses of the classical capital asset pricing model (CAPM) and downside CAPM risk parameters to gain further insight into which risk parameter leads to better performing risk measures at explaining stock returns.Design/methodology/approachThe study conducts a comparative analysis of 16 risk measures at explaining the stock returns of 4531 companies of 20 developed and 25 emerging market index for 2000–2018. The analyses are conducted using both the global and local indices and both USD and local currency returns. Calculated risk measures are analyzed in a panel data setup using a univariate model. Results are investigated in country-specific and model-specific subsets.FindingsThe results show that (1) downside betas are better than CAPM betas at explaining the stock returns, (2) both risk measure groups perform better for emerging markets, (3) global downside beta model performs better than global beta model, implying the existence of the contagion effect, (4) high significance levels of total risk and unsystematic risk measures further support the shortfall of CAPM betas and (5) higher correlation of markets after negative shocks such as pandemics puts global CAPM based downside beta to a more reliable position.Research limitations/implicationsThe data are limited to the index securities as beta could be time varying.Practical implicationsResults overall provide insight into the cost of equity calculation and emerging market assets valuation.Originality/valueThe framework and methodology enable us to compare and contrast CAPM and downside-CAPM risk measures at the firm level, at the global/local level and in terms of the level of market development.

Capital Asset Pricing Model (CAPM) Study in Mean-Gini Model

The valuation of financial assets is taking on an important dimension today. It is at the heart of turbulent financial actuality as it helps in understanding and quantifying the relationship between the risk and the return on financial assets. Traditionally, the Capital Asset Pricing Model (CAPM), developed by Sharpe (1964); Lintner (1965) and Mossin (1966) has been essential for understanding this relationship. This model is unquestionably the most well-known valuation model used since its empirical validation by several studies (Black, Jensen, and Scholes (1972); Fama and James (1973)). Unfortunately, several empirical studies have weakened this model by showing the existence of various anomalies (Bantz (1981); Chan and Chen (1991); Basu (1977); Fama and French (1992); Fama and French (1993)). Later, Shalit and Yitzhaki (1984) developed an alternative based on the Mean-Gini model while retaining the main assumptions of the classic CAPM. However, instead of holding efficient medium-variance portfolios, investors build market portfolios that are effective Mean-Gini subsets. This article presents and compares the financial asset valuation models: CAPM derived from Mean-Variance and CAPM derived from Mean-Gini. The results show that the two models are very close in terms of valuation of asset returns.

Capital asset pricing model in Portugal: Evidence from fractal regressions

We examine risk profiles of the Portuguese stock market index component stocks using a novel approach to the classical capital asset pricing model (CAPM). Specifically, we estimate the CAPM via fractal regressions that allow studying the marginal effects at selected scales. In this way, we can reveal whether the risk is perceived differently by market participants with different investment horizons. Apart from the analysis itself, we provide new statistical insights into the issue of separating and comparing the scale-specific effects with statistical validity. We find several stocks deviating from an expected risk perception homogeneity across investment horizons. This is true for both analysed periods, i.e. before and after the global financial crisis. There are also several stocks that changed their relationship to the market portfolio in between, which has strong implications for possible portfolio construction. The proposed methodology is not limited to financial topics but can be used in any discipline where the scale-specific marginal effects might be of interest.

Comparing Entropy and Beta as Measures of Risk in Asset Pricing

The paper establishes entropy as a measure of risk in asset pricing models by comparing its explanatory power with that of classic capital asset pricing model’s beta to describe the diversity in expected risk premiums. Three different non‑parametric estimation procedures are considered to evaluate financial entropy, namely kernel density estimated Shannon entropy, kernel density estimated Rényi entropy and maximum likelihood Miller‑Madow estimated Shannon entropy. The comparison is provided based on the European stock market data, for which the basic risk‑return trade‑off is generally negative. Kernel density estimated Shannon entropy provides the most efficient results not dependent on the choice of the market benchmark and without imposing any prior model restrictions.

BEYOND THE PEARSON CORRELATION: HEAVY-TAILED RISKS, WEIGHTED GINI CORRELATIONS, AND A GINI-TYPE WEIGHTED INSURANCE PRICING MODEL

AbstractGini-type correlation coefficients have become increasingly important in a variety of research areas, including economics, insurance and finance, where modelling with heavy-tailed distributions is of pivotal importance. In such situations, naturally, the classical Pearson correlation coefficient is of little use. On the other hand, it has been observed that when light-tailed situations are of interest, and hence when both the Gini-type and Pearson correlation coefficients are well defined and finite, these coefficients are related and sometimes even coincide. In general, understanding how these correlation coefficients are related has been an illusive task. In this paper, we put forward arguments that establish such a connection via certain regression-type equations. This, in turn, allows us to introduce a Gini-type weighted insurance pricing model that works in heavy-tailed situations and thus provides a natural alternative to the classical capital asset pricing model. We illustrate our theoretical considerations using several bivariate distributions, such as elliptical and those with heavy-tailed Pareto margins.

Beyond the Pearson Correlation: Heavy-Tailed Risks, Weighted Gini Correlations, and a Gini-Type Weighted Insurance Pricing Model

Gini-type correlation coefficients have become increasingly important in a variety of research areas, including economics, insurance and finance, where modelling with heavy-tailed distributions is of pivotal importance. In such situations, naturally, the classical Pearson correlation coefficient is of little use. On the other hand, it has been observed that when light-tailed situations are of interest, and hence when both the Gini-type and Pearson correlation coefficients are well-defined and finite, then these coefficients are related and sometimes even coincide. In general, understanding how the correlation coefficients above are related has been an illusive task. In this paper we put forward arguments that establish such a connection via certain regression-type equations. This, in turn, allows us to introduce a Gini-type Weighted Insurance Pricing Model that works in heavy-tailed situation and thus provides a natural alternative to the classical Capital Asset Pricing Model. We illustrate our theoretical considerations using several bivariate distributions, such as elliptical and those with heavy-tailed Pareto margins.

Re-exploring the CCAPM: The Case of US Industry Returns with Different Price Deflators

<p>Extending US samples, this paper re-examines the classic consumption-based capital asset pricing model (CCAPM) by the generalized method of moments (GMM). Our re-exploration using US three industry returns and different price deflators supplies the following evidence. First, 1) regarding the CCAPM using the US consumption for nondurable goods and the deflator of total personal consumption expenditures (PCEs), the discount rate and risk aversion parameters show plausible values; and according to the <em>J</em>-tests, our above first CCAPM is generally supported. Second, 2) as for the CCAPM with the US consumption for nondurable goods and services and the deflator of total PCEs, both discount rate and risk aversion parameters generally exhibit plausible values and our <em>J</em>-tests show that our above second CCAPM is highly supported. Third, 3) as for the CCAPM using the US consumption for nondurable goods and the deflator of the PCEs for nondurable goods, both parameters of the discount rate and risk aversion are highly stable and our <em>J</em>-tests indicate that our above third CCAPM is highly supported. Finally, 4) as regards the CCAPM using the US consumption for nondurable goods and services and the calculated implicit deflator of the PCEs for nondurable goods and services, the parameters of the discount rate generally exhibit plausible values, while the risk aversion parameters are not so stable. However, according to the <em>J</em>-tests, our above fourth CCAPM is also highly supported.</p>

W-MPS risk aversion and the shadow CAPM: theory and empirical evidence

This paper presents the shadow capital asset pricing model (CAPM) of Ma [2011a. Advanced Asset Pricing Theory. London: Imperial College Press] as an intertemporal equilibrium asset pricing model, and tests it empirically. In contrast to the classical CAPM – a single-factor model based on a strong behavioral or distributional assumption – the shadow CAPM can be represented as a two-factor model, and only requires a modest behavioral assumption of weak form mean-preserving spread risk aversion. The empirical tests provide support in favor of the shadow CAPM over the classical CAPM, the consumption CAPM, or the Epstein and Zin [1991. “Substitution, Risk Aversion and the Temporal Behavior of Consumption and Asset Returns: An Empirical Analysis”. Journal of Political Economy 99, 263–286] model. Moreover, the shadow CAPM provides a consistent explanation for the cross-sectional variations of expected returns on the stocks and for the time-varying equity premium.

Testing the capital asset pricing model in the Italian market

In this paper we provide an empirical investigation of the classic Capital Asset Pricing Model (CAPM) on all firms listed in the Italian stock exchange at the monthly frequency. We intend to show that the CAPM, despite the heavy critical comments, still holds in the Italian market when returns are measured at the monthly frequency. Most importantly, our evidence indicates that the market portfolio fully explains the cross section of stock returns and there is no need to appeal for additional determinants. Our results have very important implications for long term investors who can forecast the expected excess stock returns by simply determining the B of the stock and the expected excess market return

W-MPS Risk Aversion and the Shadow CAPM: Theory and Empirical Evidence

This paper presents the shadow Capital Asset Pricing Model (CAPM) of Ma (2011a) as an intertemporal equilibrium asset pricing model, and tests it empirically. In contrast to the classical CAPM - a single factor model based on a strong behavioral or distributional assumption, the shadow CAPM can be represented as a two factor model, and only requires a modest behavioral assumption of weak form mean-preserving spread (w-MPS) risk aversion. The empirical tests provide support in favor of the shadow CAPM over the classical CAPM, the Consumption CAPM, or the Epstein and Zin (1991) model. Moreover, the shadow CAPM provides a consistent explanation for the cross-sectional variations of expected returns on the stocks and for the time-varying equity premium.

A THRESHOLD MODEL APPROACH TO ESTIMATING THE ABNORMAL STOCK RETURNS

The classical capital asset pricing model postulates a linear relationship between stock returns and stock risks. However, a number of subsequent empirical studies have revealed some anomalies in this relationship, especially for firms with small size and high book-to-market values. A possible explanation for the anomalies is the existence of threshold effects in the proxies of stock risks. However, conventional threshold models only allow for one threshold variable, which limits their applicability in this context. In this paper, we address this issue by applying the econometric technique developed by Bai et al. (2012). We estimate the joint threshold effects of firm size and book-to-market equity ratio on the stock returns using a sample of 5,271 US firms. The test results yield clear evidence for the existence of threshold effects in both firm features. We find that abnormal returns exist when the firm size falls below 52.04 million USD and the book-to-market ratio exceeds 0.4085.

Capital Asset Pricing Model (CAPM) with drawdown measure

The notion of drawdown is central to active portfolio management. Conditional Drawdown-at-Risk (CDaR) is defined as the average of a specified percentage of the largest drawdowns over an investment horizon and includes maximum and average drawdowns as particular cases. The necessary optimality conditions for a portfolio optimization problem with CDaR yield the capital asset pricing model (CAPM) stated in both single and multiple sample-path settings. The drawdown beta in the CAPM has a simple interpretation and is evaluated for hedge fund indices from the HFRX database in the single sample-path setting. Drawdown alpha is introduced similarly to the alpha in the classical CAPM and is evaluated for the same hedge fund indices. Both drawdown beta and drawdown alpha are used to prioritize hedge fund strategies and to identify instruments for hedging against market drawdowns.

An Asymmetric Approach to the Cost of Equity Estimation: Empirical Evidence from Russia

The choice of an appropriate model for the estimation of the cost of equity in emerging markets is still a very challenging problem. Market inefficiency, limited opportunities for diversification, as well as liquidity issues inspire researches to look for risk characteristics beyond the traditional framework of the classical capital asset pricing model. Various models have been developed over the past several decades proposing new ways of risk assessment. However, the empirical evidence of these models requires careful consideration.Most asset pricing models were developed in terms of either a symmetric mean-variance or a folded mean-semivariance framework. These models have several drawbacks in capturing investors’ attitudes to stock price movements. We provide a brief description of the recently proposed entropic risk characteristics which assign greater weight to the downside movements of asset prices and smaller weight to the upside movements.The goal of this study is to determine which model has better explanatory power for returns in the Russian capital market. We compare the performance of risk measures in the Russian stock market on a dataset of 63 stocks for the period from 2003 to 2012. Empirical results show certain advantages of entropic risk characteristics over other risk measures in explaining returns on Russian equities.

An empirical study of liquidity risk premium in Chinese stock markets

Based on a simple liquidity risk-adjusted asset pricing model, this paper empirically studied the liquidity risk premium and illiquidity compensation in Chinese stock markets. The evidence shows that there are significant illiquidity compensation and liquidity risk premiums in the stocks expected returns; the more illiquid or price impact elastic the stock is, the more significant the tests on its illiquidity compensation and liquidity risk premiums are.; a new illiquidity proxy variable can grasp liquidity risk premium in stock returns because of high cross-sectional correlations between the level of liquidity and liquidity risk. In addition, the market β of classical capital asset pricing model (CAPM) shows less power in interpreting stock return data. So the required risk premium in Chinese stock returns mainly compensates for systematical liquidity risks, not for pure price risk. Key words: Liquidity risk, stock pricing, illiquidity proxy.

Information and capital asset pricing

Investors in a market frequently update their diverse perceptions of the values of risky assets, thus invalidating the classic capital asset pricing model's (CAPM) assumption of complete agreement among investors. To accommodate information asymmetry and belief updating, we have developed an empirically testable information-adjusted CAPM, which states that the expected excess return of a risky asset/portfolio is solely determined by the information-adjusted beta rather than the market beta. The model is then used to analyze empirical anomalies of the classic CAPM, including a flatter relation between average return and the market beta than the CAPM predicts, a non-zero Jensen's alpha, insignificant explanatory power of the market beta, and size effect.

The 'Out-of-Sample' Performance of Long-Run Risk Models

This paper studies the ability of stationary and cointegrated versions of long-run risk models to explain out-of-sample asset returns during 1931-2009. The models perform similarly overall to the classical Capital Asset Pricing Model in a mean squared error sense, but have smaller average pricing errors. The long-run risk models perform relatively well on the momentum effect. A cointegrated version of the model outperforms a stationary version. A cointegrated model restricting the risk premiums to identify structural parameters has larger average pricing errors and smaller error variances than a reduced-form version of the model.