This risk is most often considered in the context of the modern portfolio theory, and capital asset pricing model (CAPM) proposed independently by Sharpe [15], Lintner [16], and Mossin [17]. The first is the theory of risk-based decision-making based on the diversification technique. The second is a method of determining the equilibrium prices of securities depending on the risk they represent. This model identifies the sources and risk measures that are appropriate from the point of view of the portfolio theory. Empirical confirmation of the relationship between profitability and risk is important for decisions making regarding the selection of portfolios.

The CAPM stems from the equilibrium theory in which investors maximize an expected utility function that is based on the mean and variance of returns of their portfolio, and the distributions of return are normal. Despite this, variance may be considered an inappropriate measure of risk. Most of the distributions of rates of return are neither symmetrical nor normal, which is confirmed by many empirical studies. Moreover, investors, usually unevenly risk-averse, treat deviations above the threshold (e.g., expected value) as a profit and below deviation as a potential loss. Risk aversion creates a new concept called downside risk, the possibility of achieving the returns below the assumed rate of return. The main measure of the total downside risk is the semi-variance or semi-deviation of returns. For symmetric distributions, the semi-variance is at least the same appropriate measure of risk as variance, while asymmetric distributions present a much more useful measure than a variance. Semi-variance belongs to the group of asymmetric measures known as lower partial moments (LPM). Bawa (1975) [18] showed that semi-variance is a second-order LPM, and in the case of investors with decreasing risk aversion, it is an appropriate measure of total risk. In addition, downside risk measures can be viewed in the context of the joint changes of two risky assets or portfolios. These measures are asymmetric covariance. Semi-covariance is an example of such measures and was proposed by Hogan and Warren [19]. Bawa and Lindenberg [20] incorporated semi-covariance in the structure of n-degree LPM measures, often called asymmetric co-LPM. The analysis of the mean-risk relationship in the context of the semi-variance for the assumed rate of return can also be found in Fishburn [21]. The risk measures described in the above studies contributed to the development of the CAPM in downside framework theory. The first study in this area was the research by Hogan and Warren [19], who demonstrated the permanence of the downside CAPM (D-CAPM) with the conventional CAPM. Subsequently, Bawa and Lindenberg [20] showed that the conventional CAPM is a mean-lower partial moment model in which the threshold is equal to the risk-free rate. Another more general approach was taken by Harlow and Rao [22], assuming the threshold rate of return as the average rate of return.

Many empirical studies based on risk measures in conventional and downside approaches compared the results regarding the construction of optimal portfolios and capital assets pricing. The construction of a portfolio based on semi-variance was first developed by Markowitz [23]. According to Foo and Eng [24], asset returns are skewed, and then mean-variance portfolio optimization is ineffective. Moreover, when risk aversion is ignored, the (LPM) framework affords a more efficient risk measure. Further, this research shows how to include investor risk aversion into a downside risk asset optimization model. Salah et al. [25] proved that the downside risk model for portfolio optimization overcomes the weakness of the conventional mean-variance model concerning the skewness of returns and the perception of risk among investors. Research supporting the use of downside risk measures in portfolio theory can be found in other works [26,27,28,29].

Further work shows the importance of the downside approach to risk in the pricing of assets. The studies of Estrada [30,31], conducted on developed and emerging capital markets, also show the superiority of downside risk measures over conventional measures based on CAPM. Ang, Chen, and Xing [32], based on individual companies listed on the NYSE, AMEX, and NASDAQ, prove that investors are rewarded with a market premium for the downside risk, which means that securities with higher downside beta ratios achieve higher rates of return on average. Galagedera [33] reveals that the association between the two approaches to systematic risk measures is to a great extent dependent on the volatility of the market portfolio returns and the deviation of the target rate from the risk-free rate. Moreover, downside models indicate a higher level of explanation volatility of rates of return than the classic CAPM [34,35]. Ajrapetova [36] demonstrated that downside beta outperformed conventional beta and other total or systematic risk measures in the developed markets. However, the results of these studies were not confirmed in emerging markets, where total risk measures performed the best. Its results also imply that in emerging markets, the diversifiable risk should be priced. Extensive research in emerging markets, such as those of Slovenia, Croatia, and Serbia, demonstrated that the downside risk is the variable that statistically and significantly explained mean returns [37].

Another point of view is to consider the risk of the company looking at the variability (semi-variability) of profitability ratios. The whole set of measures based on accounting data can be named accounting risk measures. In the article, two kinds of accounting risk measures are used: measures of the total variability (semi-variability) of profitability ratios [9] and accounting betas proposed by Hill and Stone [38], and downside accounting beta proposed by Rutkowska-Ziarko [12].

Many different concepts for measuring a company’s risk from accounting information can be found in the literature. A broad review of the various methods is described in the works of Amorim et al. [39], Latif and Shah [40], or Huang et al. [41]. In this study, the term “accounting beta” (“downside accounting beta”) is understood as a measure of systematic risk that expresses a change in the accounting profitability of a given enterprise caused by a change in the accounting profitability of the relevant sector or market.