Considering the DAPM: Low-beta and High-beta Industries
Are low- and high-risk industries empirically consistent with the DAPM?
Abstract
This thesis researches if the Dichotomous Asset Pricing Model (DAPM) is consistent with industry portfolio’s. A distinction between low-risk and high-risk industries is made and the beta will be used to measure this riskiness. Low-risk industries are defined as industries having a beta below 0.8 and are labelled as industries where demand will by stable overtime (e.g. healthcare). High-risk industries are defined as industries having a beta above 1.2 and are labelled as pro-cyclical and sensitive to the conditions of the market (e.g. luxurious companies). Neutral industries (beta between 0.8 and 1.2) are not the subject of this thesis. Results show that low-risk industries are more or less consistent with the DAPM whereas high-risk industries show some deviations. These deviations from the DAPM can be explained by using concepts from behavioral finance and transaction cost theory.
Table of Content
1. Introduction ... 3
2. Literature Review ... 6
2.1. Low-beta and high-beta industries ... 6
2.2. Dichotomous Asset Pricing Model (DAPM) ... 10
3. Methodology ... 14
3.1. Data ... 14
3.2. Two-pass regression model ... 15
3.3. Ratio’s ... 16
4. Results ... 17
4.1. Low- and High-beta industry analysis ... 17
4.2. Lower- and upper economic environment ... 18
4.3. High-beta industries recovering from an economic downturn ... 22
5. Conclusion ... 29 Appendix I ... 31 Appendix II ... 42 Appendix III ... 54 References ... 55 University of Amsterdam Thesis July, 2014 Claire de Jager Studentnumber: 10409890 Supervisor: Dr. L. Zou 2
1. Introduction
Asset pricing theory makes an attempt to understand and determine prices or values that should be paid for an asset in theory (Cochrane, 2000). To value an asset, several models have been developed to determine the appropriate rate of return of an asset considering its risk. Using the rate of return and the level of risk (usually measured by the “beta” of the asset), the value of the asset or portfolio can be determined. To construct optimal portfolios, the investor attempts to maximize expected return and minimize risk by having various assets in a portfolio, also called Modern Portfolio Theory (Shipway, 2009). Using asset pricing models, beta is a good indicator of what will be the level of risk for investors, where a low beta indicates less risk while a high beta indicates substantial higher risk.
Several investment strategies have been outlined to create an optimized portfolio and generate returns against lowest possible risk (see for example Dybvig, 1988; Merton, Scholes and Gladstein, 1978). These strategies are used by investors to make investment decisions that will yield long-term excessive returns on their portfolio (Woolridge and Snow, 1990; Hayes and Abernathy, 1980). These strategies make use of diversification to construct an optimal portfolio for the investor; investing in different companies, different industries and different types of assets can mitigate the risk and increase return (Bloomfield, Leftwich, and Long Jr., 1997).
As mentioned above, one of the ways to diversify could be by constructing a portfolio of stocks in different industries (based on Lessard, 1976). This thesis makes a distinction between low-risk versus high-risk industries where low-risk industries are labelled as industries where demand will by stable overtime, even in a downturn economy or scarcity (e.g. health care) (Wilson, 1999). High-risk industries are labelled as pro-cyclical and sensitive to the conditions of the market (e.g. luxurious companies) (ibid). Indicating low-risk industries (i.e. industries with a low beta) and high-risk industries (i.e. industries with a high beta) is important for investors to execute their investment strategy which implies assessing
the riskiness of these industries and optimize their portfolio (based on Asness, Frazzini and Pedersen, 2013).
In the history of modern portfolio theory, several models have been developed to value assets and compose optimal portfolios. One of the latest development in the field of asset pricing is the Dichotomous Asset Pricing Model (DAPM). The DAPM makes a distinction between the value of an asset when the market is in an economic downturn or upturn (Zou, 2005). According to this model, the riskiness of the firm can be divided according to these two different growth stages (the market is in an upturn or in a downturn), therefore, the beta of the firm can be separated into a beta when the market is in an economic downturn and a beta when the market is in an economic upturn. In other words, the DAPM will value the riskiness of the asset individually, i.e. when the market is in an upper-state and when the market is in a lower-state. The DAPM predicts and confirms that the beta in the lower-state will equal the beta in the higher-state, therefore the difference in betas of the asset will equal zero.
Combining the distinction between low-beta and high-beta industries (based on Wilson, 1998) and the DAPM as an asset pricing model (Zou, 2005), the investment strategies in low- and high-risk industries should empirically be consistent with the DAPM. This means that the beta in the lower-state will equal the beta in the upper-state, and this will hold for all industries (i.e. for all low-risk and high-risk industries). The first part of this thesis will investigate whether this statement is true. The second part of this thesis will investigate why industries or a cluster of industries will deviate from this statement (i.e. low and high beta-industries are not consistent with the DAPM). Therefore, the objective of this thesis is in twofold: “are the low- and high-beta industries empirically consistent with the DAPM? If not, what can be the reasons for this inconsistency?”.
Fama and French provide several industry classifications based on SIC-codes (Standard Industrial Classification, used by the government of the United States). This system classifies firms according to their division, major group and industry group. Fama and French base their categorization on these codes and classify American firms ranging from 5 to 49 different industries. This thesis used a specification of 30 industries where daily average value weighted return in the US market and the daily risk free rate was subtracted from the data of Fama and French. The CRSP database provided average market returns. With this
information, the beta (in lower- and upper-state) according to the DAPM was calculated. For all data, a time period between 01-01-2003 and 31-12-2013 was chosen.
Results are statistically not significant, however, a closer look showed that low-beta industries are more or less consistent with the DAPM (Δβ ≈ 0 or Δβ > 0), whereas high-beta industries showed some deviations (i.e. negative Δβ for most inconsistent industries) Arguments about loss-aversion, bounded rationality and future prospects and overconfident investors explain the results from a behavioral point of view. The results also confirm a decrease in transaction costs and the presence of high frequency traders, where high frequency traders function as market-makers.
This thesis makes a contribution in two ways, first, a distinction between low-risk and high-risk industries is made. Previous research has not labelled industries as more or less high-risky, this distinction clarifies which industries could add/eliminate risk according to the investor’s portfolio and preferences. Second, this thesis shows some regularity among inconsistent industries when using the DAPM. Several explanations are provided why some high-beta industries are not consistent with the DAPM and show a negative difference between the beta in the upper-state and the beta in the lower-state. Arguments are mostly found in behavioral finance but also transaction costs theory gives reasonable explanations.
This thesis proceeds as follows, section 2 will review important literature concerning the distinction between low-risk and high-risk industries and development of the DAPM. An outline of the data and methodology will be given in section 3. Section 4 will analyze the results. Lastly, section 5 will summarize and conclude.
2. Literature Review
This chapter will outline important theory and empirical findings in the literature regarding the riskiness of an industry. This thesis will make a distinction between high-risk and low-risk industries where the beta will be the indicator to measure that risk. In that sense, low-beta and high-beta industries are considered. Furthermore, the Dichotomous Asset Pricing Model (DAPM) is explained. Combining the concepts of low- and high-beta industries and the DAPM will lead to some assumptions and hypothesis at the end of this chapter.
2.1. Low-beta and high-beta industries
As Markowitz (1952) explains, preferences of the investor shape their portfolios but the overall goal of investment portfolios is to maximize return and minimize risk. To hedge risk, the investor’s portfolio consists of several assets with different characteristics to diversify as much as possible (this way, risk is reduced). By investing in low-risk stocks yielding a lower return and investing in high-risk stocks yielding a higher return, the investor has a balanced strategy. According to his preferences and utility, the investor can take more risk by having more high-risk stocks or the investor can take less risk by having more low-risk stocks in his portfolio. In this case, the systematic risk of an individual assets contributing to the portfolio can increase or decrease the overall risk/return relationship of that portfolio (Klemkosky and Martin, 1975).
Important is the notion of systematic risk of the asset. Different types and categories of financial risk are researched. For example, Artzner, et al. (1999) provide two broad categories of risk: market and nonmarket, also called systematic and non-systematic risk. Dowd (2002) distinguishes also different types of financial risks: market risk, credit risk, operational risk, etc. This thesis will only consider market (systematic) risk. Broadly defined, market risk is
“the risk of loss (or gain) arising from unexpected changes in the market prices (e.g., such as security prices) or market rates (e.g., such as interest or exchange rates)” (Dowd, 2002, p.1). Throughout this thesis, risk will refer to systematic (market) risk unless stated differently.
The beta of a company (partly) reflects its sensitivity to systematic (market) risk and thus its level of return considering the riskiness of that company (Campell and Mei, 1993). The first model that demonstrated this relationship was the Capital Asset Pricing Model (CAPM), where a high beta indicates an asset with higher risk but also the likelihood of higher returns while a low beta indicates a less risky asset with more stable returns (chapter 2.2 will elaborate more on the CAPM) (Sharpe, 1964; Lintner, 1965). Risk is created through, among others, uncertainty in the general environment, industry and/or firm-specific variables (Miller, 1992). Uncertainty in the general environment is created because of political and governmental instability, and uncertainty coming from the macroeconomic environment (ibid). Uncertainty related to the industry includes input and product market, competition and technologies (ibid). Lastly, firm-specific uncertainty is related to firm-specific operations, management and employees (ibid). This thesis will only focus on industry risk, other forms of risk will be considered as constant.
Different risk levels due to the nature of the industry has received significant attention in the literature (i.e. Lessard, 1976; King, 1966). King (1966) shows that differences in risk/return levels between industries are large enough to subscribe these differences to the industry effect. He concludes that the industry structure explains the similar risk/return relations for all firms in that industry, based on this notion, it makes sense to divide industries according to their riskiness (i.e. low-beta and high-beta industries) (Wilson, 1998). Low-beta industries will be industries less sensitive to market changes and can be seen as more safely industries than the market average. Investing in these industries provides less risk but also lower returns. Conversely, high-beta industries will be industries more sensitive to market changes and can be seen as more risky industries than the market average. Investing in these industries provide more risk but also higher returns. Implicitly, there is an assumption made about the relationship between the average industry beta and the risk of that industry which is the basic idea behind the CAPM: the beta of the industry reflects the riskiness of that specific industry. However, this thesis stretches the meaning of the CAPM over industries and not specifically to firms. In other words, it is assumed that the beta does not only measure risk for firms but will also hold across industries as a good indicator to measure risk.
Assumption 1: The riskiness of the industry is measured by the average beta of all the firms in that industry, as theorized by the CAPM.
How important are these industry effects? Schmalensee (1985) researches the influence of industry effects on accounting rates of return at a business level and he finds that performance is strongly influenced by industry effects. King (1966) finds that 20% of the variance in stock prices can be explained because of differences between industries. Other studies find somewhat moderate confirmation. Hawanini and Subramanian (2001) show that for “a few dominant value creators” [firms that are frontrunners in their industry] and “destroyers” [firms that are stragglers in their industry] firm-specific factors matter more than industry factors. However, “for most of firms, i.e. for those that are not notable leaders or losers in their industry, the industry effect turns out to be an important determinant for the level of performance rather than firm-specific factors” (Hawanini and Subramanian, 2001, p. 2). Livingston (1977) empirically investigates the co-movement of stocks within industries and concludes that there are different industry patterns per industry which supports the view that efficient diversification can be achieved by having multiple stocks across different industries. Overall, previous research implies that it makes sense to divide firms in industry clusters. Therefore, it is assumed that firms can be categorized according to their industry and industries can be categorized according to their average riskiness.
What is the nature of these differences between industries? In other words, what factors contribute to the difference in risk across industries? As King (1966) points out, the stock market is exposed to information that will affect the value of an asset or firm. If there is new information, this will impact the price of stock A, however, the nature of information may not only be subjected to stock A. Rather, the information may be important for the industry (or sub-industry) in which stock A is active. In other words, information (e.g. policy changes, regulation) is most often relevant for the whole industry and not specifically affecting one firm (it will also affect stock B, stock C, etc. who are active in the same industry).
Another explanation could be the competitiveness within the industry. MacKay and Phillips (2005) explain that decisions of the firm (and thus the value of the firm) are partly determined by the position a firm occupies within the industry. In a competitive industry, the riskiness of the firm partly depends on actions of other firms in the industry and “its status as entrant,
incumbent or existing firm” (MacKay and Phillips, 2005, p. 1433). Maksimowic and Zechner (1991) represent an example concerning technology. They assume that firms can choose to adopt a safe technology at a marginal cost, implying lower returns against lower risk, or adopt a riskier technology at an uncertain cost, implying higher returns against higher risk. In a competitive environment, it will be most attractive for all firms to adopt the riskier technology financed with debt to outperform and to compete with each other, therefore, most firms will do so. In other words, strategic and financing decisions (thus the level of risk) are jointly determined within competitive industries. In a less competitive environment, there is no force to choose the risky technology because there is less pressure to outperform, therefore, each firm does not make decisions based on the industry standard. The extra risk added when adopting a “riskier” technology is not hedged in a less competitive industry because other firms within the industry are not forced to meet a specific industry standard in order to compete. Therefore, less competition within an industry will reduce risk-taking behavior while highly competitive industries will induce risk-taking behavior in order to be able to compete.
Furthermore, uncertainty may also be attributable to the industry life cycle (Klepper and Graddy, 1990; Suarez and Utterback, 1995). Three stages in the industry can be distinguished: early exploratory stage, intermediated development stage, and mature stage” (Klepper, 1997, pp. 146/147). The first stage is characterized by a few firms adopting new technologies and involves a high degree of uncertainty (and thus risk). In the next stage, intermediate development stage, technologies will be more refined and fit with the demand of the market. This stage is characterized with less uncertainty compared to the previous stage. The last stage is characterized by stable and predictable growth where there are no new innovation but just refinements and improvements. At the end of the mature stage, the industry can experience renewal (where a new technology takes over the industry) or decline (where the industry decreases in volume and eventually become extinct) which might increase the degree of uncertainty. Each stage, especially the exploratory and the possibility of renewal in the mature stage, brings uncertainty because of market approval of the majority and/or new competitors entering the industry with a more advanced technology (early adaptors).
Note that the division between industry- and firm-specific factors might have some overlap. Some firms within the industry will be early adaptors (firm-specific), while sometimes the whole industry will adopt a new technology (industry-specific). Similarly, some firms can
become extinct (firm-specific) but also the entire industry can become irrelevant because of a new invention (industry-specific).
2.2.Dichotomous Asset Pricing Model (DAPM)
As previously stated, asset pricing models are used to assess the relationship between risk and return of an asset. In history, the Capital Asset Pricing Model (CAPM) of Sharpe (1964) and Linter (1965) has been the most prominent and discussed asset pricing model. The model was widely accepted by the financial community because of its theoretical appeal, simplicity and applicability. The CAPM describes a linear relation between the asset’s expected excess return and the market expected excess return. The CAPM implies that assets with higher sensitivity to the market (i.e. these assets bear more risk) should offer higher expected return as a compensation for bearing such risk. According to the CAPM, the beta is a well-known indicator to measure the sensitivity of the company to the market (i.e. to measure systematic or market risk). The Security Market Line (SML) represents a graphical explanation of the relationship between the expected return and the risk of a company (see figure 1). The risk-free rate (rf) imposes no risk to the investor, every increase in beta (β) (thus additional risk) results in higher return (E(ri)) for the investor. Higher return compensates the investor for the additional risk he takes compared to the market. Therefore, CAPM can be expressed as 𝐸𝐸(𝑟𝑟) = 𝑟𝑟𝑓𝑓+ 𝛽𝛽𝑖𝑖(𝐸𝐸(𝑟𝑟𝑚𝑚) − 𝑟𝑟𝑓𝑓 or rewritten in expected asset’s payoff as 𝐸𝐸(𝑥𝑥) = 𝛽𝛽𝑖𝑖(𝐸𝐸(𝑥𝑥𝑚𝑚).
Besides the great insides of the CAPM, numerous empirical studies have shown that the CAPM has some failures, e.g. the CAPM fails to explain the cross-section of average stock returns (Campbell and Voulteenaho, 2003).
Figure 1. Security Market Line
Source: e.g. Sharpe (1964) and Linter (1965)
Since the CAPM, multiple variations of asset pricing models have come across. One of the variations is the Dichotomous Asset Pricing Model (DAPM). The DAPM is one of the newest asset pricing models by Zou (2005) allowing investors to make rational decisions about their investments. The basic rationale behind asset pricing models, as described above, will hold because the DAPM is an extension of the CAPM. The DAPM model considers a two-state model where the market can be in an upper-state or lower-state. If it is more profitable to invest in the market than in a risk-free asset, the market is in an upper-state (i.e. 𝑟𝑟𝑚𝑚 > 𝑟𝑟0). If it is more profitable to invest in a risk-free asset than in the market, the market is in a lower-state (i.e. 𝑟𝑟𝑚𝑚 ≤ 𝑟𝑟0). Therefore, the return of asset i (ri) depends whether the market is in an upturn or downturn. It follows for all assets i, their upper-market expected gain equals x�i = ri− r0, 𝑖𝑖𝑖𝑖 rm > r0 𝑎𝑎𝑎𝑎𝑎𝑎 x�i = 0 otherwise. Similarly, for all assets i, their
lower-market expected loss equals 𝑥𝑥i = r0− ri, 𝑖𝑖𝑖𝑖 rm≤ r0 𝑎𝑎𝑎𝑎𝑎𝑎 𝑥𝑥i = 0 otherwise. Following the logic of the CAPM (written in asset’s expected payoff),
𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑟𝑟 𝑚𝑚𝑎𝑎𝑟𝑟𝑚𝑚𝑈𝑈𝑚𝑚 𝑠𝑠𝑚𝑚𝑎𝑎𝑚𝑚𝑈𝑈: 𝐸𝐸(𝑥𝑥𝑖𝑖) = 𝛽𝛽𝑖𝑖+𝐸𝐸(𝑥𝑥𝑚𝑚), 𝛽𝛽𝑖𝑖+ = 𝐸𝐸(𝑥𝑥𝑚𝑚𝑥𝑥𝑖𝑖)
𝐸𝐸�𝑥𝑥𝑚𝑚2�
𝐿𝐿𝐿𝐿𝐿𝐿𝑈𝑈𝑟𝑟 𝑚𝑚𝑎𝑎𝑟𝑟𝑚𝑚𝑈𝑈𝑚𝑚 𝑠𝑠𝑚𝑚𝑎𝑎𝑚𝑚𝑈𝑈: 𝐸𝐸�𝑥𝑥𝑖𝑖� = 𝛽𝛽𝑖𝑖−𝐸𝐸�𝑥𝑥𝑚𝑚�, 𝛽𝛽𝑖𝑖− = 𝐸𝐸(𝑥𝑥𝐸𝐸�𝑥𝑥𝑚𝑚𝑥𝑥𝑖𝑖) 𝑚𝑚2�
In theory, the DAPM will hold if the market portfolio meets two conditions. First, the market portfolio should be mean-variance (MV) efficient (see condition 1). This implies that that the portfolio should minimize the variance for any given value of the mean. In other words, there is no other portfolio that has a higher return (E(rm)) against lower risk (r𝑚𝑚) than the market portfolio. This condition is met when the market portfolio has the highest Sharpe ratio (𝜂𝜂2) compared to all other portfolios. Second, the portfolio should be gain-loss (GL) efficient (see condition 2). This implies that the market portfolio has the highest gain-loss ratio, i.e. portfolio has the highest gains (𝐸𝐸𝑥𝑥̅) against the lowest possible losses (𝐸𝐸𝑥𝑥). In this case, there is no investment strategy that will generate higher returns against possible losses than the market portfolio (Zou, 2005). It is assumed that the market MV and GL efficient when using the DAPM, i.e. the following conditions hold:
Condition 1: 𝜂𝜂2(𝑥𝑥𝑖𝑖) ≤ 𝜂𝜂2(𝑥𝑥𝑚𝑚) < 1, 𝐿𝐿ℎ𝑈𝑈𝑟𝑟𝑈𝑈 𝜂𝜂(𝑥𝑥) = 𝐸𝐸(𝑥𝑥)
�𝐸𝐸(𝑥𝑥2)
Condition 2: 𝑍𝑍(𝑥𝑥𝑖𝑖) ≤ 𝑍𝑍(𝑥𝑥𝑚𝑚) < ∞, 𝐿𝐿ℎ𝑈𝑈𝑟𝑟𝑈𝑈 𝑍𝑍(𝑥𝑥) = 𝐸𝐸(𝑥𝑥+)
𝐸𝐸(−𝑥𝑥−)
When the market is MV and GL efficient, i.e. condition 1 and 2 are met, the beta in the upper market state will be equal to the beta in the lower market state. Intuitively explained; when the market is MV and GL efficient, the expected return of the investor’s portfolio cannot be higher than the return of the market because the market portfolio will generate the highest expected return, holding risk constant (i.e. no arbitrage). This also holds for the level of risk: the level of risk the investor’s portfolio bears cannot be lower than the risk of the market because the market portfolio will provide the lowest possible level of risk, holding return constant (i.e. no risk arbitrage). This implies that an investor cannot profit from opportunities where an asset will have different risk/return levels, i.e. 𝛽𝛽𝑖𝑖+ = 𝛽𝛽𝑖𝑖−. For a mathematical proof, see Zou (2005).
Difference between the DAPM and CAPM is the extension of a two-state model where the beta of an asset is expressed in different states of the economy (i.e. lower-state or higher-state). Where the CAPM assumes one beta, regardless the state of the market, the DAPM takes the external economic conditions into account. Furthermore, the DAPM implies the CAPM but not the other way around. Because of MV efficiency, the CAPM should hold but the DAPM will only hold if there is also GL efficiency. As pointed out before, similarities exist because of the same rationale (i.e. the DAPM is based on the CAPM with some additional insights).
As stated before, this thesis will consider the rationale behind asset pricing models not solely for individual assets or firms but across industries (assumption 1). Therefore, combining the DAPM and the distinction between low- and high-beta industries, the DAPM in this thesis can be written as,
Expressed in asset return:
High-beta industry Low-beta industry
Upper market state 𝐸𝐸(𝑟𝑟𝑖𝑖) − 𝑟𝑟𝑓𝑓 = 𝛽𝛽ℎ𝑖𝑖𝑖𝑖ℎ+ (𝐸𝐸(𝑟𝑟𝑚𝑚) − 𝑟𝑟𝑓𝑓) 𝐸𝐸(𝑟𝑟𝑖𝑖) − 𝑟𝑟𝑓𝑓= 𝛽𝛽𝑙𝑙𝑙𝑙𝑙𝑙+ (𝐸𝐸(𝑟𝑟𝑚𝑚) − 𝑟𝑟𝑓𝑓) Lower market state 𝐸𝐸�𝑟𝑟𝑖𝑖� − 𝑟𝑟𝑓𝑓= 𝛽𝛽ℎ𝑖𝑖𝑖𝑖ℎ− (𝐸𝐸�𝑟𝑟𝑚𝑚� − 𝑟𝑟𝑓𝑓) 𝐸𝐸�𝑟𝑟𝑖𝑖� − 𝑟𝑟𝑓𝑓 = 𝛽𝛽𝑙𝑙𝑙𝑙𝑙𝑙− (𝐸𝐸�𝑟𝑟𝑚𝑚� − 𝑟𝑟𝑓𝑓)
Expressed in asset payoff:
High-beta industry Low-beta industry
Upper market state 𝐸𝐸(𝑥𝑥𝑖𝑖) = 𝛽𝛽ℎ𝑖𝑖𝑖𝑖ℎ+ 𝐸𝐸(𝑥𝑥𝑚𝑚) 𝐸𝐸(𝑥𝑥𝑖𝑖) = 𝛽𝛽𝑙𝑙𝑙𝑙𝑙𝑙+ 𝐸𝐸(𝑥𝑥𝑚𝑚) Lower market state 𝐸𝐸�𝑥𝑥𝑖𝑖� = 𝛽𝛽ℎ𝑖𝑖𝑖𝑖ℎ− 𝐸𝐸�𝑥𝑥𝑚𝑚� 𝐸𝐸�𝑥𝑥𝑖𝑖� = 𝛽𝛽𝑙𝑙𝑙𝑙𝑙𝑙− 𝐸𝐸�𝑥𝑥𝑚𝑚�
Where 𝛽𝛽𝑙𝑙𝑙𝑙𝑙𝑙 represents the beta of the industries that are less sensitive to market changes, i.e. these industries provides less risk but also lower returns for investors and 𝛽𝛽ℎ𝑖𝑖𝑖𝑖ℎ represents the beta of the industries that are more sensitive to market changes, i.e. these industries provide more risk but also higher returns for investors. Since a high beta indicates higher risk but also the likelihood of higher returns, this is characterizing for high-beta industries. Conversely, a low beta indicates a less risky assets with more stable returns, characterizing low-beta industries. The plus (𝛽𝛽ℎ𝑖𝑖𝑖𝑖ℎ/𝑙𝑙𝑙𝑙𝑙𝑙+ ) and minus (𝛽𝛽ℎ𝑖𝑖𝑖𝑖ℎ/𝑙𝑙𝑙𝑙𝑙𝑙− ) signs indicate respectively if the market is in an upturn or downturn.
Assuming categorization of industries according to their beta, one could distinguish low-, neutral- and high-risk industries (as explained above, this thesis will focus on the difference between low- and high-beta industries). According to the CAPM (and DAPM), a risk-free asset has a beta of 0 and the market has an average beta of 1 (Sharpe, 1964; Lintner, 1965). Therefore, low-risk industries should have a beta between 0 and >1, neutral-risk industries have a beta around 1, and high-risk industries should have a beta higher than 1. For simplicity, it is assumed that an industry with a beta below 0.8 is indicated as a low-risk industry and an industry with a beta above 1.2 will be labelled as a high-risk industry. Everything in between will be considered as a neutral-“risk” industry and not be relevant for this thesis. Note that the term neutral-risk does not mean risk-free, it means that the differences with the risk/return of the market portfolio are not substantial enough to classify themselves as low- or high-risk industries. In that sense, neutral-risk industries have more or less the same characteristics as the market portfolio and were therefore not mentioned before.
Assumption 2: Industries can be categorized according to their riskiness of the average firm within that industry measured by calculating the beta. A distinction between low-, neutral- and risky industries can be made where;
Beta < 0.8 is categorized as low-beta industry (βlow)
0.8 ≤ Beta ≤ 1 is categorized as neutral-beta industry (βneutral)
Beta > 1 is categorized as high-beta industry (βhigh)
Logically, βlow < βhigh. Besides the separation between low- and high-beta industries, the DAPM includes the dynamics of the overall economic environment. Because the beta in an upturn equals the beta in a downturn, assumption 2 implicitly validates 𝛽𝛽𝑙𝑙𝑙𝑙𝑙𝑙+ = 𝛽𝛽𝑙𝑙𝑙𝑙𝑙𝑙− < 𝛽𝛽ℎ𝑖𝑖𝑖𝑖ℎ+ = 𝛽𝛽ℎ𝑖𝑖𝑖𝑖ℎ− . Next, the DAPM will be consistent with low- and high-risk industries if the following
hypothesis holds:
Hypothesis: Because the market is MV and GL efficient, the beta in an upturn and the beta in a downturn will be equal across industries, therefore,
∆𝛽𝛽𝑙𝑙𝑙𝑙𝑙𝑙 = 𝛽𝛽𝑙𝑙𝑙𝑙𝑙𝑙+ − 𝛽𝛽𝑙𝑙𝑙𝑙𝑙𝑙− = 0
∆𝛽𝛽ℎ𝑖𝑖𝑖𝑖ℎ = 𝛽𝛽ℎ𝑖𝑖𝑖𝑖ℎ+ − 𝛽𝛽ℎ𝑖𝑖𝑖𝑖ℎ− = 0
3. Methodology
Testing the assumptions and hypothesis, two different analyses should be done. First, an industry analysis should indicate which industries can be labelled as low- or high-beta industries. Second, the upper- or lower-state of the economic environment and the beta in each state should be examined per industry in order to test the hypothesis.
3.1. Data
To test the hypothesis, a distinction in industries should be made to indicate which industries bear more (high-beta industry) or less risk (low-beta industry) compared to the market. According to the U.S. Security and Exchange Commission (SEC) there are 12 industries (labelled as A/D) and several sub-industries (labelled as SIC). Appendix I gives an overview of all the industries and sub-industries according to the SEC. Within an industry, there exist differences in risk per company due to company-specific characteristics. However, following Fama and French it is assumed that the industry average will display an even picture despite some outliers, therefore, the average beta industry will give a clear indication about the overall riskiness of the industry. Fama and French provide several industry portfolios based on the SEC and data according to these industry portfolios, therefore, their research data will be used. The range of these portfolios differs; e.g. Fama and French provide several definitions of industries and their sub-industries where they divide U.S. firms in 5, 10, 12, 17, 14
30, 38, 48 or 49 different industry portfolios. Using a narrow definition of industry groups (e.g. separating all companies in 5 different industries) might cause extreme outliers but still have an average beta because of the large differences within the industry. However, a wide definition of industry groups (e.g. separating all companies in 49 different industries) might lead to fragmentation and will make it more difficult to analyze. Therefore, a specification of 30 industries is used. A definition of the industries according to the SIC-codes can be found in appendix II. For each industry, the daily average value weighted return (𝑟𝑟𝑖𝑖) in the period 01-01-2003 until 31-12-2013 in the US market will be used. Also the daily risk-free rate (𝑟𝑟𝑓𝑓) is available in this database for the same time-period (risk-free rate is based on the T-bill rate). In order to calculate the beta of the industry, market return should be used. The CRSP database provides returns on the market (𝑟𝑟𝑚𝑚) and therefore, the market premium (𝑟𝑟𝑚𝑚 - 𝑟𝑟𝑓𝑓) can be calculated.
3.2. Two-pass regression model
The DAPM consists of a two-pass regression model. In order to obtain the beta of the industry, only the first pass of the model is needed. In the first pass, the return of each industry is regressed on the market return to obtain the beta of the industry. It is expected that the lower-market and upper-market return of any industry is proportional to its beta in the lower-state (𝛽𝛽𝑖𝑖−) or its beta in the upper-state (𝛽𝛽𝑖𝑖+). If the DAPM holds, the intercept of the security market line (SML) will be zero. In other words, the SML+ and SML- will pass through the origin. Figure 2 gives a graphical explanation.
Figure 2. Graphical explanation DAPM Source: Zou (2005)
The SML is important to determine which industries can be classified as low- or high-beta industries. Theory assumes that the SML represents the relationship between the expected return and risk of an asset (in this case, an industry). Consider a positive market (i.e. upturn) where the industry is plotted above the SML+, this means that the industry is undervalued because the investor will expect a greater return given the risk he/she is taking. Conversely, if the industry is below the SML+, the industry will be overvalued because the investor accepts less return given the risk of that particular industry. The same holds when the market is in a negative spiral: industries above the SML- provide the same risk but against a lower return and therefore, are overvalued. Conversely, if the industry is below the SML- the industry is undervalued. Empirical studies show that the real SML (the real relationship between risk and return) is less steep than the hypothesized SML (displayed in figure 2) due to the market premium (in reality there is no riskless asset). The area between the real and hypothesized SML is the “abnormal extra return [or loss] over the market”, denoted as alpha (Jensen, 1969). Therefore, the alpha represents the average return above the expected return predicted by the hypothesized SML, ceteris paribus the portfolio’s beta and market return. In other words, the alpha can be seen as residuals of all means excess return, which is also calculated in the first pass. The second pass will see if condition 1 (MV-efficient) and condition 2 (GL-efficient) are satisfied. However, as explained before, these conditions are assumed to be met and therefore the second pass will not be used.
3.3. Ratio’s
To assess the link between the industries and their risk, several variables can be used. In order to identify the riskiness of the industry, the beta and alpha will be used. The beta is defined according to the best-beta (measures the beta for all states, no distinction between lower- and upper-state), 𝛽𝛽 =𝐸𝐸(𝑥𝑥𝑚𝑚𝑥𝑥)
𝐸𝐸(𝑥𝑥𝑚𝑚2), where a beta > 1.2 indicates a more risky investment compared to the market average and a beta < 0.8 indicates a less risky investment compared to the market average (see assumption 2). The alpha will be defined as 𝛼𝛼 = 𝐸𝐸(𝑥𝑥𝑖𝑖) − 𝛽𝛽𝐸𝐸(𝑥𝑥𝑚𝑚), where alpha < 0 implies that the asset earned too little given its risk and alpha > 0 implies excess return for the assumed risk for the investor. The beta will be used to divide industries in low-beta or high-beta industries, the alpha will be an additional indicator and give information about the correctness of the division.
This thesis focusses specifically on the difference between low-beta and high-beta industries because of the more extreme difference in their risk/return relationship. As explained before, neutral-risk industries will have similar results since their risk/return relation is less extreme and results will be less obvious. Therefore, the beta in the upper state and lower state will be computed for the low-beta and high-beta industry following the DAPM;
𝛽𝛽𝑖𝑖− = 𝐸𝐸(𝑥𝑥𝑚𝑚𝑥𝑥𝑖𝑖)
𝐸𝐸�𝑥𝑥𝑚𝑚2� , 𝛽𝛽𝑖𝑖
+ = 𝐸𝐸(𝑥𝑥𝑚𝑚𝑥𝑥𝑖𝑖)
𝐸𝐸�𝑥𝑥𝑚𝑚2�
Thereafter, ∆𝛽𝛽𝑙𝑙𝑙𝑙𝑙𝑙 and ∆𝛽𝛽ℎ𝑖𝑖𝑖𝑖ℎ are computed and its t-statistic which is defined as 𝑚𝑚 − 𝑠𝑠𝑚𝑚𝑎𝑎𝑚𝑚𝑖𝑖𝑠𝑠𝑚𝑚𝑖𝑖𝑠𝑠 = 𝑆𝑆𝑆𝑆(∆𝛽𝛽∆𝛽𝛽𝑖𝑖 − 0 𝑖𝑖) = 𝛽𝛽𝑖𝑖+− 𝛽𝛽𝑖𝑖− �𝑉𝑉𝑉𝑉𝑉𝑉(𝛽𝛽𝑖𝑖+− 𝛽𝛽 𝑖𝑖−) = 𝛽𝛽𝑖𝑖+− 𝛽𝛽𝑖𝑖− �𝑉𝑉𝑉𝑉𝑉𝑉(𝛽𝛽𝑖𝑖+|𝐺𝐺) + 𝑉𝑉𝑉𝑉𝑉𝑉(𝛽𝛽 𝑖𝑖−|𝐿𝐿) = 𝛽𝛽𝑖𝑖+− 𝛽𝛽𝑖𝑖− �𝑇𝑇 𝜎𝜎𝑖𝑖 1𝐸𝐸(𝑥𝑥𝑚𝑚2 |𝐺𝐺)+ 𝜎𝜎𝑖𝑖 𝑇𝑇2𝐸𝐸(𝑥𝑥𝑚𝑚2|𝐿𝐿)
4. Results
This section will analyze the division of industries and analyze results across low- and high-risk industries. First, the industry analysis will outline the high-riskiness of each industry (30 industries in total). In other words, a distinction between low-, neutral- and high-risk industries is made. Next, the hypothesis across low- and high-risk industries is tested.
4.1. Low- and High-beta industry analysis
This subsection will divide 30 industries (see Appendix II) according to their riskiness. As mentioned before, a risky industry will have an estimated beta higher than 1.2. Conversely, a low-risk industry will have a beta lower than 0.8. “Neutral” industries are not the topic of this research but are given for completeness. Also the alpha is calculated to give a more complete overview of the different industries and their dynamics. Using the DAPM, the following results are found;
Low-risk Neutral High-risk
Industry Beta Alpha Industry Beta Alpha Industry Beta Alpha
Food 0,677 0,020 Games 1,187 0,013 Textiles 1,206 0,013
Beer 0,539 0,017 Books 1,105 -0,028 Construction 1,343 0,001
Smoke 0,585 0,055 Clothes 1,070 0,026 Steel 1,609 -0,001
The categorization of the industries is not surprising according to the literature (e.g. Wilson, 1998). Basic needs (“Households”, “Utilities”, “Health”, “Food”) are classified as low-risk because they will always be important even if the economy experiences a slowdown. Secondary industries, like “Beer” and “Smoke”, might be unexpected since these products will be far from essential for humans. An additional explanation might be the addictive nature of these products (people “have to” smoke and people “have to” drink), however, further research should explore these industries more in depth. Also the classification of high-risk industries are logical and predictable. Especially industries related to engineering/industrial (e.g. steel, coals, mines, construction and fabricated products) and luxury expenditures (e.g. cars) experience significant declines when the economy is in a recession. The classification of these industries will be valid across several time periods and will remain valid in the future because the nature of an industry “cannot easily, if at all, change” (Bettis and Mahajan, 1985, p. 786).
4.2. Lower- and upper economic environment
Table 2 gives an overview of the beta when the market is in an upper- or lower-state for all low-risk and high-risk industries. As explained before, the beta of low-risk and high-risk industries in an upper-state (β+) should equal the beta in a lower-state (β-) (and equal the best-beta (β)). Industries showing strong differences between the upper- and lower-beta are marked
Households 0,656 0,012 Chemicals 1,170 0,018 Fabricated Products 1,292 0,016 Health 0,710 0,014 Carry 1,012 0,029 Electrical Equipment 1,208 0,012
Utilities 0,748 0,021 Oil 1,115 0,025 Autos 1,337 -0,008
Telecom 0,960 0,009 Mines 1,286 0,014 Services 0,965 0,011 Coals 1,726 0,017 Business Equipment 1,072 0,009 Finance 1,364 -0,018 Paper 0,951 0,009 Transport 1,040 0,016 Wholesale 0,914 0,018 Retail 0,855 0,016 Meals 0,832 0,036 Other 0,916 0,000 Table 1. Low-, Neutral and High-risk industries
with red (βi+− βi− ≥ |0.03|), these industries are expected to be inconsistent with the hypothesis (i.e. Δβ ≉ 0) (table 3, next page). To see if these industries will be inconsistent with the DAPM, a t-test is used (Appendix III gives a complete overview of low-, neutral and high-risk industries).
Low-risk industries High-risk industries
Industry β β+ β- Industry β β+ β
-Food 0,68 0,67 0,68 Textiles 1,21 1,21 1,20
Beer 0,54 0,56 0,52 Construction 1,34 1,34 1,35
Smoke 0,59 0,58 0,59 Steel 1,61 1,57 1,65
Household 0,66 0,67 0,64 Fabricated Products 1,29 1,30 1,29 Health 0,71 0,71 0,71 Electronic Equipment 1,21 1,22 1,19
Utilities 0,75 0,75 0,75 Autos 1,34 1,33 1,34
Mines 1,29 1,26 1,31
Coal 1,73 1,68 1,77
Finance 1,36 1,37 1,36 Table 2. Industry-betas according to the DAPM
Low-beta industries High-beta industries
Industry β+ β- β+ - β- t-stat Industry β+ β- β+ - β- t-stat
Food 0,67 0,68 0,00 -0,15 Textiles 1,21 1,20 0,00 0,07
Beer 0,56 0,52 0,05 1,56 Construction 1,34 1,35 -0,01 -0,12
Smoke 0,58 0,59 -0,01 -0,29 Steel 1,57 1,65 -0,07 -1,03
Household 0,67 0,64 0,03 0,81 Fabricated Products 1,30 1,29 0,01 0,14 Health 0,71 0,71 0,00 0,13 Electronic Equipment 1,22 1,19 0,03 0,54 Utilities 0,75 0,75 0,00 0,15 Autos 1,33 1,34 -0,02 -0,26
Mines 1,26 1,31 -0,05 -0,79 Coal 1,68 1,77 -0,10 -1,00 Finance 1,37 1,36 0,00 0,08 Table 3. Results according to the DAPM
As expected, industries where ∆β deviates significantly from zero also have higher t-statistics than industries who are more or less consistent with the DAPM. None of the t-statistics are significant at a 5% significance level (t-stat = 1.96) and therefore cannot be rejected, however, 19
one sees a clear movement of higher t-statistics when the industry differs significantly from the DAPM. Therefore, t-statistic should not be interpreted too strictly since the estimator does not give a complete overview of the correctness of the model. It can be concluded that the industries marked with green are more or less consistent with the DAPM. In other words, ∆𝛽𝛽𝑙𝑙𝑙𝑙𝑙𝑙 = 𝛽𝛽𝑙𝑙𝑙𝑙𝑙𝑙+ − 𝛽𝛽𝑙𝑙𝑙𝑙𝑙𝑙− ≈ 0 or ∆𝛽𝛽ℎ𝑖𝑖𝑖𝑖ℎ = 𝛽𝛽ℎ𝑖𝑖𝑖𝑖ℎ+ − 𝛽𝛽ℎ𝑖𝑖𝑖𝑖ℎ− ≈ 0 for these industries. The
industries marked with red are inconsistent with the DAPM. In other words, ∆𝛽𝛽𝑙𝑙𝑙𝑙𝑙𝑙 = 𝛽𝛽𝑙𝑙𝑙𝑙𝑙𝑙+ − 𝛽𝛽𝑙𝑙𝑙𝑙𝑙𝑙− ≉ 0 or ∆𝛽𝛽ℎ𝑖𝑖𝑖𝑖ℎ = 𝛽𝛽ℎ𝑖𝑖𝑖𝑖ℎ+ − 𝛽𝛽ℎ𝑖𝑖𝑖𝑖ℎ− ≉ 0 for these industries.
Industries consistent with the DAPM imply that the “net riskiness” of a low-risk industry compared to a high-risk industry should be equal and not be an issue for the investor when shaping his portfolio. In other words, low-beta industries (like “Food”, “Smoke”, “Health” and “Utilities”) should have equal risk/return levels as high-beta industries (like “Textiles”, “Construction”, “Fabricated Products”, “Auto’s” and “Finance”). Therefore, the investor could construct portfolios of solely low-beta industries or solely high-beta industries with the same amount of risk. This implies that diversification and combinations of industries in the investors’ portfolio (involving any risky industry or a combination of less risky industries) represent the preferences and utility of the investor (based on Sharpe, 1964).
When the investor is indifferent between low- and high-beta stocks, one could make a portfolio of solely low-beta industries that will outperform a portfolio of solely high-beta stocks. To construct such a portfolio (solely low-beta industries with lower risk and higher returns), investors should borrow money and invest in low-beta stocks to shift to a position with similar risk but higher returns (Black, 1972). The beta indicates how exposed the industry is to the economic environment where a higher beta will increase the average price of the stocks in that industry because of an increase in willingness to bear risk (based on Miller, 1977). As a result, the payoff on assets in a high-risk industry will be lowered because of this higher price. Assuming interest rates on equal terms for each investor, the payoff on high-beta industry will be less compared to constructing a portfolio when money is borrowed in order to invest in low-beta industries (Miller, 1977). However, the reason why investor will not invest in low-beta industries is because you need to borrow money which in itself brings additional risk. Yet, results show that completely rational investors will be indifferent between the two options (holding interest rates constant).
Overall, the DAPM model is a consistent model for investors to asses different industries and their riskiness in most cases. However, is there an explanation why the DAPM does not hold for all industries? Are there some similarities across inconsistent industries that can explain these deviations? Taking a closer look at the deviations, results show that the inconsistent low-beta industries (“Beer” and “Household”) have higher betas when the market is in an upturn and lower betas when the market is in a downturn (i.e. positive Δβ). This implies that the average risk of the industry will be higher when the economy is doing well and lower when the economy is performing badly. One could argue that industries with a positive Δβ, are the industries that experience a slow down when there is a recession but will experience superior growth as soon as the market will move towards the upper-state because of the “neediness” of that particular industry. In other words, “Households” and “Beer” are the first industries that become significant to consumers when the economy is recovering from a slowdown and therefore, profitable for investors. This means that investing in “Beer” or “Households” is a profitable opportunity because the risk (and thus return) will recover from economic downturns. This thesis will not argue why this is the case but only explain the behavior of industries with a positive Δβ.
Inconsistent high-beta industries have higher betas when the market is in a downturn and lower betas when the market is in an upturn (i.e. negative Δβ). This implies that the investor overvalues these industries, where the only exception is “Electrical Equipment” which is classified as a high-beta industry but behaves like a low-beta industry. For these high-beta industries (“Steel”, “Mines” and “Coal”), it means that the industry recovers less fast from an economic downturn (e.g. the market is moving towards the upper-state) and it will be confronted as first when there is an economic downturn. In other words, the industry will experience less growth in economic ups compared to the decline in an economic downturn because investors are hesitant to invest in these industries (i.e. leads to a negative Δβ). Why are investors cautious when investing in these industries? Is there a logical explanation that could explain the hesitance of investors to invest less in these industries when the economy is recovering from a downturn (i.e. the economy is moving towards an upper-state)? This interesting notion might be explained by using concepts from behavioral economics and the transaction cost theory. The next paragraph will explain these arguments more in depth (“Electrical Equipment” will not be explained since this industry behaves like a low-risk industry).
4.3. High-beta industries recovering from an economic downturn
As shown in table 2 and 3, high-beta industries who are inconsistent with the DAPM show some similarities with respect to the differences in their riskiness when the market is in an upturn or downturn. All inconsistent high-risk industries (except “Electrical Equipment”) have a negative Δβ. Is this coincidence? Or is there a theoretical explanation that could explain this regularity? Theories and concepts from behavioral finance and transaction cost theory might give an explanation for this effect.
Behavioral finance focusses on the psychological and social dimension of finance (Shiller, 2003). One of the new insights gathered by behavioral finance is the notion of bounded rationality. Asset pricing models assume rational investors, i.e. the investor makes optimal choices that benefit the utility of the investor (Simon, 1997). However, in the real world investors’ rational is limited, also called bounded rationality; decision-making has “systematic biases that separate the beliefs that people have and the choices they make from the optimal beliefs and choices that rational investors would make” (Kahneman, 2003, p. 1449). This means that investors will not make optimal choices because their psyche limits them to do so.
An example of bounded rationality is loss-aversion. Loss-aversion means that investors are more sensitive to losses than to gains (Benartzi, and Thailer, 1995) and could explain a negative Δβ for inconsistent high-beta industries. This concept is used in the prospect theory of Kahneman and Tversky (1979), where it is argued that the utility function of investors comes from gains and losses in pay-off. In this case, the investor will not make optimal choices because its utility depends on relative returns and the (investment) decision is not evaluated on an absolute level, i.e. the final outcome is less relevant to the investor than the value of gains and losses. Figure 3a and 3b illustrate the prospect theory where the value displays the reference point between what is experienced as a loss or gain by the investor. Note: investors can be more/less loss averse, therefore, the value function might differ between investors; figure 3a displays an investor who is very loss-averse while the investor displayed in figure 3b values his losses to a lesser extent.
Figure 3a and 3b. Examples of value functions from investors Source: Kahneman and Tversky (1979)
Because loss-averse investors will value losses more intensive than gains, even when the loss- or gain-differential is equal, investors will try to avoid losses as much as possible even if the compensation to avoid losses is imbalanced with the actual loss. In other words, where rational investors would take the loss to avoid additional risk, a loss-averse investor would avoid the loss even if the additional risk involved is not rational. Taking a look at the results of inconsistent high-beta industries, one sees that in the lower state the investor is willing to take more risk (i.e. 𝛽𝛽ℎ𝑖𝑖𝑖𝑖ℎ+ < 𝛽𝛽ℎ𝑖𝑖𝑖𝑖ℎ− ) even if the additional loss in return is not proportional to the additional risk. Because investors put greater weight on the losses, they “demand additional compensation” for these industries when the economy is in a downturn (based on Ang, Chen, and Xing, 2006, pp. 1191). In other words, they will value these industries as more risky and therefore the beta will increase during a downturn of the economy because the downturn will cause additional loss for the industry and thus for the investor. Compared to low-beta industries, investors will take their loss in an early stage because the deviations are less and thus the impact on the value function is limited. Concluding, when the market is going down, investors demand higher returns than the difference in return when the market is going up because they put more weight to their losses than to equal gains. In other words, the investor will demand a higher return in a downturn compared the return asked by the investors when the market is in an upturn than rational investors, holding the additional increase/decrease in risk equal.
Second, forecasting errors might be a reason for a negative Δβ. As Chandler (1990) describes, there are some industries that have continously new innovations that require firms in that
industry to adapt and develop new resources/capabilities. A good example are energy companies who need to compete and innovate for their share of “clean energy” (this includes the “Coal” and “Mine” industry). This brings additional risk for investors because a bounded rational investor cannot forcast the future and the precise pattern of the industry (or firm). A frequent used indicator for innovation is the number of patents (Lanjouw and Schankerman, 2004). For industries where there is a high number of patents, it is assumed that these industries will be most competitive on innovation and have increased uncertainty (ibid). In other words, figure 4 (next page) shows how innovative the industries in the U.S are and indeed it can be concluded that coal and mining will be industries where innovation is important and the competition is severe. This means that the forecast of these industries tend to be more difficult (Will your company still be profitable after the completion of the innovation? Will your company also beat the competition when there is a new innovation wave?), therefore, uncertainty is increased and investors will demand a higher compensation which marks a higher average beta.
In general, high-innovative industries have an uncertain future because of their systematic innovations. Because it is impossible for the investor to be completely rational, his respond to this increased uncertainty will be based on heuristics and affect. Indeed, because of this uncertainty, investors have to rely on their instincts and will tend to be more loss-averse, as explained before, loss-averse investors will hold on to their losses even if the additional risk is not proportional. This might be an explanation why industries with a highly innovative character and uncertainty have higher betas in the lower state and lower betas in the upper state.
Figure 4. Number of patents per industry in the U.S. Source: OECD statistics, number of patents per industry
Concluding, whether the market will experience an upturn or downturn, the uncertainty about the competitive industries will remain the same. However, the investor will experience the lower-state of the economy as more uncertain and they become more attached to their losses and therefore ask a higher return to compensate. Furthermore, in the lower-state of the economy the pressure to innovate in highly competitive industries might truly increase because of the limited performance and declining results (Roberts, 2003). This will increase uncertainty in the lower-state, leading to a higher beta. The exact mechanism of the two scenarios should be researched in the future. Note that human necessities (see figure 4) also have an innovative character, however, because they are considered as a basic need for human presence, innovation will not create uncertainty but rather create efficiency.
Another example of bounded rationality is an overconfident investor, defined as an investor “who overestimates the precision of his private information and underestimates the value of public information” (Daniel, Hirshleifer, and Subrahmanyam, 1998, p. 1841). Evidence supports overreaction of investors that lead to a negative correlation between stock returns and volatility (Daniel, et. al, 1998). In other words, the investor bears more risk (excess volatility) given the return than a rational investors would do. In case of the high-beta industries, investors overreact on their private information in the lower-state of the economy, probably because they want to avoid their loss (loss-averse). This implies that investor is taking excess risks in the lower state, at least in excess of what a rational investor would obtain. In the upper state, investors underreact to public information (i.e. macro-economic signals) about the industry (Daniel, et. al, 1998). This means that the investor does not adjust their risk level according to the change in return on the industry compared to rational investors (risk-averse) given the public information about the industry.
More specific, investors will be overconfident in the lower-state since they think they have more credible signals because of private information and thus overreact their accuracy of the prediction of the market based on this information (Daniel, et. al, 1998). This means that the investors will take excess risk but do not experience this additional risk as imbalanced compared to the change in return (as rational investors would do). In case of the upper state, the macro-economic signals (i.e. public information) is undervalued and investors will underreact since they do not take these signals as credible enough (Daniel, et. al, 1998). They will see the industry as “safe” while a rational investor would give more credibility to publicly available information which changes the risk level. This implies that investors will overvalue
private information in the lower-state to justify their loss-averse behavior and undervalue public information in the upper-state in order to avoid additional risk (risk-averse behavior). This leads to a lower beta in the upper-state and a higher beta in the lower-state, i.e. a negative Δβ. This might be specifically the case for high-beta industries since the investor has more to lose and more to gain. Because the deviation between “winning” and “losing” is increased, the relation to over-/under-reaction of private/public information tends to be stronger. Especially for the “Steel” and “Coal” industry, the average gain and loss will be higher since the overall beta is higher compared to the average of the high-beta industries.
Besides behavioral aspects, transaction costs and frequency traders also confirm the results. The lower- and higher-state betas of high-risk industries are consistent with the idea that high frequency traders indeed have impact on the market since they can trade repeated times a day at very low costs. Classical theory reviews the bid-ask spread as a compensation for the market maker (Madhaven, 2000). This compensation is needed because the market maker has order-handling costs, the cost of adverse selection and price risk (ibid). Logically, a market maker would prefer to have markets where these costs are as low as possible. Research shows that high frequency trades are likely to change the average transaction cost (Kirilenkoz and Cvitanik, 2010). Several costs decrease, e.g. search costs, order-processing costs and fees, because of these high frequency traders. This implies that the bid-ask spread will decrease and therefore, transaction costs improve and trades can be continuously and instantly done (Menkveld, 2011). In other words, high frequency traders will instantly sell stocks in industries that underperform because they are not stopped because of high transaction costs (i.e. transactions are insignificant to the loss that is made by the stock).
This means that a high frequency trader “enables a market-making strategy to quickly update quotes on the arrival of public information and thus reduce the risk of being adversely selected” (Menkveld, 2011, p. 5). Furthermore, the response time will decrease (i.e. low latency) which enables the high frequency trader to have a market-making role for investors (ibid). Therefore, high frequency traders will be the new market-maker who instantly can sell and buy stocks as a rational investor would do in offset of the transaction costs. Previously research shows that systematic risk (β) in an increasing function of the expected return of an stock where return is an increasing function of the bid-ask spread (i.e. asset illiquidity) (Amihud and Mendelson, 1986). If high frequency traders value in industry as more risky, they will not invest in these industries or sell the stock in these industries which will decrease
the liquidity of that industry which will increase the risk of that industry. Logically, in the lower-state of the economy, high frequency-traders will sell or not invest, and the industry will experience more risk and will demand additional return because of decreased liquidity. This particular industry will become even more illiquid and thus risk is even more increased (i.e. the loss-spiral). Indeed, the beta in the lower state will increase significantly compared to the beta in the upper state for industries that are sensitive to the economic environment because of instant trades done by the higher frequency trader.
This thesis tried to gather first insights in possible explanations for the behavior of investors when considering patterns of risk and return. The focus is on irregular high-risk industries and further research should clarify the exact mechanism behind this notion.
5. Conclusion
The central question in this thesis explores if low- and high-risk industries are empirically consistent with the DAPM. An important distinction is the division between low- and high-risk industries where low-high-risk industries are labelled as industries where demand will by stable overtime, even in a downturn economy or scarcity (e.g. health care) (Wilson, 1999). High-risk industries are labelled as pro-cyclical and sensitive to the conditions of the market (e.g. luxurious companies) (ibid). The beta is used as an indicator of the industry’s riskiness and is derived by using the DAPM. This DAPM (Zou, 2005) advances the CAPM because it makes a distinction between the upper- and lower-state of the market. Therefore, the beta of the firm (industry) can be divided into a beta when the market is in an economic downturn and a beta when the market is in an economic upturn. Overall, the thesis uses the DAPM to derive the upper-beta and lower-beta for low-risk and high-risk industries.
From this thesis we learn that rational investors should be indifferent between investing in low-beta or high-beta industries. Investors could achieve the same returns from a portfolio of solely low-beta stocks as they expect to generate when investing in high-beta industries, this is achieved by borrowing money. However, because investors are not rational and the borrowing rate is not constant overtime, they do not like to invest in low-beta industries because borrowing money in itself adds additional risk. Results also show that low-beta industries are more or less consistent with the DAPM (Δβ ≈ 0 or Δβ > 0). High-beta industries show some deviations (i.e. negative Δβ for most inconsistent industries) but the results are not statistically significant to reject.
The second part of this thesis tries to explain why inconsistent high-beta industries have higher betas in the lower-state and lower betas in the upper-state (i.e. negative Δβ). Reasons for a negative Δβ across high-beta industries can be found in behavioral finance and the transaction cost theory. Arguments from concepts like loss-aversion, bounded rationality, future prospects, and overconfident investors are explaining the results from a behavioral point of view. The results also confirm a decrease in transaction costs and the presence of high frequency traders, where high frequency traders function as market-makers. This thesis is just a start to explain this irregularity, further research should explore these arguments more in depth.
These findings have some important implications; first, it shows that the DAPM (as also holds for the CAPM) does not incorporate irrational behavior of investors and therefore, does not fully predict the movements of the market. However, the DAPM is a consistent model which is a useful tool for investors to get some sense of investment decisions and portfolios. Furthermore, this research highlights the importance of diversification. Holding several stocks across industries reduces market risk for investors, this way, investors can reduce risk by adding more stocks from low-beta industries but can increase risk (and thus expected return) by adding stocks from high-beta industries. This thesis gives a clear indication about creating diversified investment by investing in different industries according to the preference of the investor.
Overall, the DAPM is useful for investor when assessing their portfolio and changing the risk/return relationship of that portfolio. Assuming that investors are rational, the model can give a clear prediction of the market. However, results confirm that the assumption about full rational behavior is not representing reality. Behavioral finance gives some clear arguments why the prediction according to the DAPM does not corresponds with the actual risk/return relationship. Lastly, further development of the DAPM should incorporate transaction costs to give a more accurate and rational picture of the market.
Appendix I
Industry Sub Name
1 2833 MEDICINAL CHEMICALS & BOTANICAL PRODUCTS
1 2834 PHARMACEUTICAL PREPARATIONS
1 2835 IN VITRO & IN VIVO DIAGNOSTIC SUBSTANCES
1 2836 BIOLOGICAL PRODUCTS, (NO DISGNOSTIC SUBSTANCES)
1 5912 RETAIL-DRUG STORES AND PROPRIETARY STORES
1 6311 LIFE INSURANCE
1 6321 ACCIDENT & HEALTH INSURANCE
1 6324 HOSPITAL & MEDICAL SERVICE PLANS
1 6331 FIRE, MARINE & CASUALTY INSURANCE
1 6351 SURETY INSURANCE
1 6361 TITLE INSURANCE
1 6399 INSURANCE CARRIERS, NEC
1 6411 INSURANCE AGENTS, BROKERS & SERVICE
1 8011 SERVICES-OFFICES & CLINICS OF DOCTORS OF MEDICINE
1 8060 SERVICES-HOSPITALS
1 8062 SERVICES-GENERAL MEDICAL & SURGICAL HOSPITALS, NEC
1 8093 SERVICES-SPECIALTY OUTPATIENT FACILITIES, NEC
1 8731 SERVICES-COMMERCIAL PHYSICAL & BIOLOGICAL RESEARCH
2 2200 TEXTILE MILL PRODUCTS
2 2211 BROADWOVEN FABRIC MILLS, COTTON
2 2221 BROADWOVEN FABRIC MILLS, MAN MADE FIBER & SILK
2 2250 KNITTING MILLS
2 2273 CARPETS & RUGS
2 3873 WATCHES, CLOCKS, CLOCKWORK OPERATED DEVICES/PARTS
2 3910 JEWELRY, SILVERWARE & PLATED WARE
2 3911 JEWELRY, PRECIOUS METAL
2 4900 ELECTRIC, GAS & SANITARY SERVICES
2 4911 ELECTRIC SERVICES
2 4922 NATURAL GAS TRANSMISSION
2 4923 NATURAL GAS TRANSMISISON & DISTRIBUTION
2 4924 NATURAL GAS DISTRIBUTION
2 4931 ELECTRIC & OTHER SERVICES COMBINED
2 4932 GAS & OTHER SERVICES COMBINED
2 4941 WATER SUPPLY
2 4961 STEAM & AIR-CONDITIONING SUPPLY
2 4991 COGENERATION SERVICES & SMALL POWER PRODUCERS
2 5000 WHOLESALE-DURABLE GOODS
2 5020 WHOLESALE-FURNITURE & HOME FURNISHINGS
2 5040 WHOLESALE-PROFESSIONAL & COMMERCIAL EQUIPMENT & SUPPLIES
2 5090 WHOLESALE-MISC DURABLE GOODS
2 5094 WHOLESALE-JEWELRY, WATCHES, PRECIOUS STONES & METALS
2 5099 WHOLESALE-DURABLE GOODS, NEC
2 5140 WHOLESALE-GROCERIES & RELATED PRODUCTS
2 5141 WHOLESALE-GROCERIES, GENERAL LINE
2 5190 WHOLESALE-MISCELLANEOUS NONDURABLE GOODS
2 5271 RETAIL-MOBILE HOME DEALERS
2 5311 RETAIL-DEPARTMENT STORES
2 5331 RETAIL-VARIETY STORES
2 5399 RETAIL-MISC GENERAL MERCHANDISE STORES
2 5400 RETAIL-FOOD STORES
2 5411 RETAIL-GROCERY STORES
2 5412 RETAIL-CONVENIENCE STORES
2 5500 RETAIL-AUTO DEALERS & GASOLINE STATIONS
2 5531 RETAIL-AUTO & HOME SUPPLY STORES
2 5700 RETAIL-HOME FURNITURE, FURNISHINGS & EQUIPMENT STORES
2 5712 RETAIL-FURNITURE STORES
2 5731 RETAIL-RADIO, TV & CONSUMER ELECTRONICS STORES
2 5734 RETAIL-COMPUTER & COMPUTER SOFTWARE STORES
2 5735 RETAIL-RECORD & PRERECORDED TAPE STORES
2 5900 RETAIL-MISCELLANEOUS RETAIL
2 5940 RETAIL-MISCELLANEOUS SHOPPING GOODS STORES
2 5944 RETAIL-JEWELRY STORES
2 5945 RETAIL-HOBBY, TOY & GAME SHOPS
2 5960 RETAIL-NONSTORE RETAILERS
2 5961 RETAIL-CATALOG & MAIL-ORDER HOUSES
2 5990 RETAIL-RETAIL STORES, NEC
2 & 3 7389 SERVICES-BUSINESS SERVICES, NEC
3 3570 COMPUTER & OFFICE EQUIPMENT
3 3571 ELECTRONIC COMPUTERS
3 3572 COMPUTER STORAGE DEVICES
3 3575 COMPUTER TERMINALS
3 3576 COMPUTER COMMUNICATIONS EQUIPMENT
3 3577 COMPUTER PERIPHERAL EQUIPMENT, NEC
3 3578 CALCULATING & ACCOUNTING MACHINES (NO ELECTRONIC COMPUTERS)
3 3579 OFFICE MACHINES, NEC
3 3672 PRINTED CIRCUIT BOARDS
3 5045 WHOLESALE-COMPUTERS & PERIPHERAL EQUIPMENT & SOFTWARE
3 6794 PATENT OWNERS & LESSORS
3 7370 SERVICES-COMPUTER PROGRAMMING, DATA PROCESSING, ETC.
3 7371 SERVICES-COMPUTER PROGRAMMING SERVICES
3 7372 SERVICES-PREPACKAGED SOFTWARE
3 7373 SERVICES-COMPUTER INTEGRATED SYSTEMS DESIGN
