Industry volatility risk and expected returns

U

NIVERSITY OF

A

MSTERDAM

Faculty of Economics and Business

Master of Science in Business economics: Finance

I

NDUSTRY

V

OLATILITY

R

ISK AND

E

XPECTED

R

ETURNS

Supervisor: Liang ZOU

Author

Niccolò CAUCCI

Stud. Nr. 10602968

ABSTRACT

The well-celebrated CAPM predicts that only market risk plays a role in asset pricing in the sense that it affects a financial security's expected return. Investors should not expect a compensation for bearing risks that have little or no correlation to the volatility of the market portfolio. Many empirical studies, however, provide weak or no evidence to support this view, suggesting indeed that idiosyncratic risk could be also priced. Using aggregate industry-level idiosyncratic statistics constructed from the Zou (2005)'s dichotomous asset pricing model, this paper documents that idiosyncratic risk matters and it is positively related to expected returns. Under the Fama and MacBeth (1973) testing framework, a statistically and economically significant industry risk premium of above 12% per month surfaces in all model specifications during the period 01/1983-12/2013. Mean-variance beta, size, book-to-market, momentum or short-term reversal cannot explain this finding.

ABSTRACT 3

LIST OF FIGURES AND TABLES 5

CHAPTER I: THORETHICAL FRAMEWORK 6

1.1 INTRODUCTION 6

1.2 IDIOSYNCRATIC VOLATILITY RISK: RELATED LITERATURE 10

1.3 INDUSTRY VOLATILITY RISK: RELATED LITERATURE 12

1.4 THEORETICAL FRAMEWORK 13

1.4.1 HYPOTHESISDEVELOPMENT 14

1.4.2 CONTRIBUTION 16

CHAPTER II: ANALYTICAL FRAMEWORK 18

2.1 DATA DESCRIPTION 18

2.2 ESTIMATION OF INDUSTRY-LEVEL VOLATILITY 18

2.2.1 ECONOMETRICSINSIGHTS 20

2.3 ESTIMATION OF THE BETA 21

2.3.1 ENDOGENEITYOFMARKETRETURN 21

2.3.2 BETAANDITSINSTABILITY 23

2.4 PROPERTIES OF INDUSTRIAL VOLATILITIES 27

CHAPTER III: IS INDUSTRY RISK PRICED? 31

3.1 PORTFOLIO ANALYSIS 31

3.1.1 PORTFOLIORETURNS 31

3.2 INDUSTRY RISK FACTOR PORTFOLIO 34

3.2.1 INDUSTRY"MIGRATIONS" 36 3.2.2 PORTFOLIOCHARACTERISTICS 37 3.3 REGRESSION ANALYSIS 38 3.3.1 FAMA-MACBETH 39 3.3.2 EMPIRICALRESULTS 39 CONCLUSION 43 APPENDIX 45 REFERENCES 57

TABLE OF CONTENTS

LIST OF FIGURES AND TABLES

FIGURE 1: MISPRICING PROCESS IN THE PRESENCE OF HOLDING COSTS ...9

FIGURE 2: COMPARISON OF RAW AND CONSTRUCTED INDEX RETURNS... 23

FIGURE 3: DAPM'S EMPIRICAL SECURITIES MARKET LINES ... 25

FIGURE 4: EVOLUTION OF INDUSTRY BETAS ... 26

FIGURE 5: EVOLUTION OF INDUSTRY VOLATILITY ... 28

FIGURE 6: NUMBER OF FIRMS ... 31

FIGURE 7: COMPOUNDED RETURN OF INDUSTRY RISK SORTED PORTFOLIOS ... 36

TABLE A1: INDUSTRY DEFINITIONS ... 45

TABLE 2: DESCRIPTIVE STATISTICS OF INDUSTRY VOLATILITIES... 47

TABLE 3: INDUSTRY VOLATILITY IN SUB-SAMPLES ... 48

TABLE 4: DESCRIPTIVE STATISTICS OF 48 INDUSTRY PORTFOLIOS ... 49

TABLE 5: PORTFOLIO SORTED BY INDUSTRY-LEVEL VOLATILITY... 50

TABLE 6: INDUSTRY “MIGRATIONS” ... 51

TABLE 7: INDUSTRY RISK FACTOR PORTFOLIO’S CHARACTERISTICS ... 54

TABLE 8: FAMA-MACBETH REGRESSIONS ... 55

CHAPTER I: THORETHICAL FRAMEWORK

1.1

I

Discerning the determinants of the risk-return trade-off has been the core concern of asset pricing research ever since. According to theoretical models, in equilibrium expected returns should be related to the risk inherent in the financial security and to the compensation that investors require for bearing these risks. In studying this topic, academics and practitioners historically focused and widely accepted measures of statistical dispersion, such as the standard deviation1 of returns, as a proxy for risk. Nevertheless, no clear consensus has emerged regarding its pricing relevance. That is, whether or not investors demand a larger risk premium for holding highly volatile securities it is still an open question.

To disentangle this issue, a common asset pricing approach consists of decomposing asset returns into two components and to study volatility risk at disaggregated level. The first component of volatility usually refers to systematic or market risk and is influenced by risk factors that are both unpredictable and impossible to completely avoid such as policy changes, shift in economic forces, global security threats, and so on. The second component of volatility is called idiosyncratic since it is related to risk factors that are specific of an industry or a company. Typically, this component constitutes the largest share of a financial security's return standard deviation.

Modern portfolio theory (MPT) predicts that the impact of idiosyncratic shocks on a portfolio is inversely related to number of securities held. In other words, having disposal of an adequate number of stocks reduces the risk of investing to systematic levels. A conventional rule of thumb suggests that an equally weighted portfolio of around 20 securities can achieve this result. Interestingly, this number has recently increased up to 50 (Campbell et al., 2001, CLMX (2001) hereafter) because of the rise in idiosyncratic volatility observed in the early 2000s. All in all, a broad insight from MPT is broadly accepted: there are certain risks, mainly systematic, that require a risk premium since they can be mitigated only by costly hedging strategies. On the other hand, there are

1

other risks, largely idiosyncratic, which do not command a risk premium because they can be eliminated rather easily and inexpensively via diversification, for instance by holding a well-diversified portfolio of all available investments (the market portfolio hereafter). To this extent, investors should not expect to earn additional returns for bearing these types of risks, explicitly risks that have little or no correlation with the volatility risk of the market portfolio.

But how security’s exposure to systematic risk should be measured? The seminal publication of Markowitz (1952) "Portfolio Selection" on the Journal of Finance provided a first scientific answer to this question. The fundamental concept expressed in this article is the ability to measure the riskiness of a financial security based on the comovement of its return with other securities'. In practice, whether volatility and expected return of traded security, as well as the correlation among them are promptly available, rational investors have a rather simple rule when it comes to investing. They should allocate their financial resources among a subset of stocks, the mean-variance efficient portfolios, which provide the highest ex-ante expected return per level of risk. It is claimed that while reading Markowitz's research, Sharpe noticed a footnote in which Markowitz wondered about the implication of his prescriptions for investors. In other words, how would one measure the riskiness of individual securities if all investors are mean-variance optimizers? The well-celebrated capital asset pricing model (CAPM) of Sharpe (1964) and Lintner (1965) offers a simple solution: the Beta, explicitly the security marginal contribution to the volatility risk of the market portfolio. In Sharpe, efficient risk-return profiles that strictly dominate all other mean-variance efficient portfolios can be achieved straightforwardly by combining the market portfolio with the risk-free asset, therefore these combinations would represent the optimal solution to the asset allocation problem for all investors. From a theoretical perspective, all financial securities should be located on the same straight line, namely the security market line (SML), that passes through the market portfolio, whose beta equals 1. Following this argument, the CAPM's equilibrium prediction states that a financial security's expected return is beta times the risk premium of the market portfolio.

Despite the CAPM was an appealing and applicable theory it turned out to be highly unreliable in practice. In the last fifty years, several studies attempted to explain such "empirical failure". Hirshleifer (2001) relates the beta inability to differentiate the

cross-section of stock's expected returns either to empirical violations of the two-fund separation theorem or to misspecification of the functional form that describes investor's preferences, which are not well characterized by the quadratic utility function as prescribed by the mean-variance framework. With this regard, two researches it is worth mentioning. Kahneman & Tversky (1979) develop an intuitive and descriptive model that allows investors to have different attitude toward transition probabilities depending on a reference point. According to prospect theory (PT), individuals take investment decisions based on their own subjective probability rather than on true probability, as they empirically tend to overweight (underweight) events with small (high) probability, therefore, being risk-averse for gains and risk-seeker for trades that often offer negative NPV. In order to avoiding the arbitrary non additive probability transformation of prospect theory, Zou (2006) proposes the compounded utility theory (CUT), which is able to reconcile the empirical evidence of non-linearity in probabilities within a rational framework. According to CUT, reference-dependent preferences can be represented in a straight manner by a set of Neumann-Morgenstern-style axioms, where the independence axiom is assumed separately for utility-reward and disutility-risk.

Another strand of the literature has associated the empirical failure of beta to the price impact of psychological biases (sometimes called irrationality) on asset demand and asset prices. It is empirically proved that investors are prone to chase certain assets and that often are subjected to behavioural biases when making investment decisions. There are ample of evidences to support this view. Odean (1998) and Barber & Odea (2000) demonstrate that individual investors trade their position to often realizing gains earlier and losses later than a tax-optimizing behaviour would suggest. Han & Kumar (2008) indicate that retail investors are drawn towards stocks with high skewness and volatility due to their lottery features, and that they build their portfolios under-diversified to fully exploit these stock characteristics. In the same fashion, Falkenstein (1996) advocates that mutual funds have significant preference for stocks with high idiosyncratic volatility and high visibility. Frazzini & Pedersen (2010) support the empirical profitability of a trading strategy that bets against beta, showing that portfolios of low-beta assets have higher alpha and Sharpe ratio than of high-beta assets. This finding can be either related to the investors lack of diversification or to the investors' appetite for high beta stocks. Given their limited market capacity investors demand high beta stocks to leverage their portfolios, this higher demand causes increasing prices of these stocks and lower

subsequent average returns.

All in all, these predispositions are in marked contrast to the well-celebrated equilibrium prediction of neoclassical models of risk: investors are alike and hold a combination of the market portfolio and the risk-free asset. Since this condition rarely occurs in practice, investors’ under-diversification moves prices away from fundamentals and mispricing are often too costly to be arbitraged away even in a world filled with rational traders (Figure 1). Accordingly, the literature grew tremendously in the past years to improve and develop the theory of asset pricing. Novel rational theories that in general assume under-diversification2 have documented that not only market risk, but also idiosyncratic risk plays a role in explaining the cross-sectional difference in expected returns.

FIGURE 1:MISPRICING PROCESS IN THE PRESENCE OF HOLDING COSTS

This Figure depicts the hypothetical mispricing process when holding costs are the only costs faced by rational traders (see Pontiff, 2006). Pontiff states that idiosyncratic risk is the largest holding cost faced by rational traders, who, as long as prices deviate from fundamental values, always take a position, but never large enough to remove completely the mispricing, because they must trade-off the risk of their position against the expected payoff.

2

1.2

I

The role of idiosyncratic risk in asset pricing has been widely studied in the past decades, attracting a bulk of researchers especially after the idiosyncratic volatility puzzle documented by Ang et al. (2006) (AHXZ (2006) hereafter). This puzzle comes from the cross-sectional evidence that stocks with high idiosyncratic volatility earn low future returns and vice versa. When sorting stocks into quintiles based either on total or idiosyncratic volatility, the average return of a trading strategy that buys high volatile stocks and sell low volatile stocks is negative at -1% per month. The average alpha is even wider: -1.2% of the fifth quintile (the most volatile) against 1.4% of the first quintile (the least volatile). According to AHXZ (2006) this finding persist even after controlling for other cross-sectional asset pricing effects such as leverage, size, liquidity, coskewness or momentum and is not circumscribed to the US equity market, explicitly to stocks traded on NYSE/AMEX/NASDAQ exchanges, as Ang et al. (2009) deliver additional evidence as well for all G7 markets.

Even though some critics have questioned the robustness of AHXZ (2006)'s finding, the related literature is far from being conclusive. Early studies on idiosyncratic volatility claim a positive relationship between residual risk and expected returns. One of the first empirical researches is by Douglas (1969) who finds that the variance of the CAPM's regression's residuals carries a statistically and economically significant positive risk premium. Goyal & Santa-Clara (2003) measure the average stock risk as the monthly cross-sectional variance of all traded securities, and confirm the positive trade-off between this measure, essentially idiosyncratic, and the security's return on the market. Fama & MacBeth (1973) (FMB (1973) hereafter) reject the role of idiosyncratic risk in the CAPM based on a more robust methodology, namely the two-pass regressions method. After a careful econometric revision, Lehmann (1990) rehabilitates Douglas’ results warning that the role of residual risk in asset pricing should be carefully interpreted since it may reflect exposure to omitted sources of systematic risk (e.g. non-linear risk), which cannot be described by the coefficient estimates from a simple non-linear ordinary least squares (OLS) regression. In Lehmann, a statistically positive coefficient on residual risk surfaces over the full sample period and in numerous 5-years subsamples.

theoretically motivated by the apparent lack of diversification that characterize some investors3, whose market participation capacity is exogenously constrained. Background risks, leverage constraints, taxation or investors heterogeneity are common justifications of this phenomenon. As indicated by Levy (1978) and Merton (1987), not being able to diversify company-specific variance rationalizes a return premium for bearing this risk. Malkiel & Xu (2006) building an extension of the CAPM in which one group of investors is unable to hold the market portfolio, find that idiosyncratic risk explains the cross-section of asset returns better than either the beta or the market value of equity. Among the studies that attempted to solve the idiosyncratic volatility puzzle, some argues that the negative association between idiosyncratic risk and expected returns is driven by the inadequacy of the statistical procedures employed to measure residual risk, whereas others points out to the misspecification of the expected returns' model. The first argument is by Fu (2007) who shows that idiosyncratic volatility risk, computed in AHXZ (2006) as the standard deviation of daily regression's residuals over the previous month, does represent a biased proxy for expected idiosyncratic risk if the stochastic process of idiosyncratic risk is not stationary. This is indeed the case documented by Fu who accordingly proposes to model idiosyncratic risk by using the exponential generalized autoregressive conditional heteroskedasticity (EGARCH) model developed by Nelson (1991). Similarly, Chua et al. (2007) decompose stock's idiosyncratic volatility into one expected and unexpected component by adopting an autoregressive model (AR) of order 2. After controlling unexpected returns for unexpected residual risk, they infer that expected idiosyncratic volatility is again positively priced. Bali & Murray (2013) claiming the informational value of expected returns constructed on analyst price target, demonstrate that the trade-off between idiosyncratic risk and expected returns is positive. Disregarding a widely used approach of traditional asset pricing theories, which considers systematic and idiosyncratic risk separately, Jiang & Lee (2006) examine the dynamic relation among these variables in different stages of business cycles4 and find that idiosyncratic risk helps predicting positive market risk, mainly in early part of a recession. This is well supported in the literature, which documents how economic

3

Goetzmann & Kumar (2004) document that between 1991 and 1996, based on a sample of 62,000 US household investors, only less than 10% of them were holding more than 10 stocks in their portfolios.

4

Prior studies have documented that the time-series variation of market and idiosyncratic volatility is particularly significant over business cycles (CLMX, 2001 and Fama & French, 1997). That is, these volatilities have been relatively high during phases of market instability like the oil crisis, the technology stock bubble, the recent subprime mortgage crisis and the financial crisis started with the Lehman Brother bankruptcy.

downturns tend to be triggered by some idiosyncratic sectoral shocks. Pastor & Veronesi (2009) illustrate that the nature of the risk associated with new technologies changes over time. This risk, which is initially idiosyncratic, gradually changes to systematic as the new technologies are adopted on a large scale, while remains idiosyncratic for the technologies that are never adopted.

Interestingly, Hou & Loh (2012) provide a complete examination of existing candidate explanations of the idiosyncratic volatility puzzle up to date. Arguments that are based on expected idiosyncratic skewness (Boyer et al., 2010), maximum daily return (Bali et al., 2011), one-month return reversal (Hoang et al., 2009), illiquidity (Bali & Cakici, 2008), retail trading proportion (Han & Kumar, 2012), average variance beta (Chen & Petkova, 2012) together account for 60 to 80% of the negative risk premium.

1.3

I

The role of industries in the asset pricing literature5 has been fairly modest domestically and only weakly relevant in international markets (Caviglia et al., 2000). After the publication of CLMX (2001), a renovated interest in studying volatility risk at disaggregated level emerged. While the majority of researches focused on modelling the behaviour of firm-specific risk, as revealed by the previous section, only few researches extended the analysis of stock returns volatility at the industry level.

Wang (2010) documents the dynamic behaviour of 30 industry specific volatility for the US market finding an upward linear trend in 17 industries over the sample period July 1963 to June 2008. The Business Equipment and Services industry are the most volatile and were responsible for the industry volatility surge in the late 1990s. On the other hand, the industry of Business Supplies, Shipping Containers and Banking are the most important lead indicators of industry volatility, as they use to provide products for other industrial uses.

Despite most studies have examined the unconditional return distribution of industry portfolios, Moskowitz & Grinblatt (1999) document that, after conditioning returns on

5

This might be related to the well-known publication bias. Yet, it is in marked contrast to the pivot role that industry risk play a in the Corporate Finance literature with regard to optimal investment or financial policy decisions.

the information contained in past prices, industries matter and contributes almost entirely to the profitability of individual stock momentum strategies, especially over intermediate trading horizons of 6 up to 12 months. This finding reveals that in practice stocks who performed well (winners) or badly (losers) during the portfolio formation period tend to belong to the same industry. Several behavioural studies provide further insights on this phenomenon. Investors may show overconfidence or conservatisms in certain type of industries, hence, causing industry’s returns to be persistent or to revert with a lag. Rational theories that assume slow information diffusion into asset prices predict lead-lag relationship within and across industries. For example, Menzly & Ozbas (2010) provide evidence of cross-momentum within industries that are related to each other through the supply chain.

1.4

T

From the literature review discussed in the previous sections it is clear that since idiosyncratic volatility cannot be directly measured (it is not observable), estimates of residual risk may be subjected to several sources of error, which frequently lead to ambiguous conclusion and misleading interpretations about its relevance. In order to reduce the number of potential biases that may characterize any asset pricing research on this topic, this paper proposes to adopt industrial portfolio as base assets. These portfolios have several valuable properties compared to individual stock that can support my empirical decision.

First, it is arguable that return premia on portfolios formed by sorting individual stocks in equal-size groups based on idiosyncratic volatility might arise from stock characteristics rather than from the covariance risk structure of returns. As pointed out by Daniel & Titman (1997) who criticized the Fama and French's size and book-to-market factor, these stocks might be from related business line, industries or from that same geographical area. Furthermore, it is well documented that beta estimates have much lower standard errors when computed at portfolio level rather than at stock level (Fama & French, 1992). Evidently if systematic loadings are estimated with error, any model-dependent measure of residual risk will be distorted as well. Second, Ferson & Harvey

(1991) sustain that stock returns predictability is mainly associated with the time-varying exposure of asset returns to fundamental economic factors. Compared to individual securities, industries should reflect more accurately exposure to these factors over time, given the varying degrees6 at which they experience growth and distress phases. Therefore, to a certain extent an industry risk premium may be rationalized by relying on clearer economic insights. Finally, the relevance of industries is documented in the asset pricing literature on international portfolio diversification, which has shown that as a result of the globalization of business enterprises and capital market integration, industries-diversified portfolios provide greater risk reduction compared to asset allocation strategies that are driven by a countries dimension of diversification.

Therefore, it seems of general interest for all investors to understand the dynamic relationship across industry returns and volatility risk, and to investigate whether investors should require a compensation for bearing country-specific industry idiosyncratic risk.

1.4.1

H

One established feature of aggregate industry volatility is that it fluctuates over time with relative peaks during economic downturns (CLMX, 2001). This implies that innovation in industry volatilities covaries rather cancel out each other, as instead rational asset pricing theories predict. In these circumstances, therefore, more assets are needed to achieve a given level of diversification and there is more of a penalty for not holding well-diversified portfolio, other things being equal. Accordingly, if investors demand a compensation for bearing this risk, then industry volatility should be priced in the cross-section of stock’s returns.

The intertemporal asset pricing model (ICAPM) of Merton (1973) postulates that priced factors other than market risk should hedge against adverse changes in the investment opportunity set. Whilst in the static optimization problem of Markowitz (1952) investors care only about the transition probability for stock returns over the following trading interval, when it comes to make investment decisions over multiple periods investors are

6

For example, some industries are less affected by economic downturns (countercyclical industries), whereas other industries are more affected (cyclical industries).

also concerned to the stochastic7 process of the changes in such probabilities over time, which is here indexed by a general stochastic discount factor (SDF) from a market model (MM):

( ) ( )

( ₎ (1)

Using conventional asset pricing terminology, Equation 1 shows that the risk premium of a financial security, ( ), is negatively related to covariance between the security's excess return and the stochastic discount factor. Accordingly, securities whose returns negatively covary with the SDF require higher risk premium to compensate investors for accepting the risk of holding an asset that is expected to poorly performs in states of the economy when wealth is particularly valuable, that is, during periods in which investors marginal utility (MU) is high8. On the other hand, a security whose covariance with the stochastic discount factor is large and positive tends to provide higher returns when the SDF is high (a bad times proxy). In equilibrium, these heaven assets are highly in demand and might trade at premium because of their hedging properties.

Endorsing this intuition, Campbell (1996) shows that risk-averse agents demand stocks to hedge against changes in market volatility risk, since high market volatility tends to coincide with high market downside risk. This hedging demand increases prices of stocks with positive loadings on innovation of market volatility, thus, lowering their subsequent returns. In the same fashion, Moise (2002)and AHXZ (2006) document that innovations in aggregate volatility are negatively priced for stocks based on past sensitivity to this factor. Accordingly, this research aims to assess whether risk-averse investors demand a risk premium for being exposed to innovation in industry volatility. Specifically, I test the following research hypothesis:

Exposure to industry risk is (positively) priced in the sense that it affects expected returns. The higher the exposure to industry risk, the higher the potential rewards.

If the industry risk factor is orthogonal to existing asset pricing risk factors, I am expecting that the sensitivity of stock returns to this factor times the changes in its level

7

The term “stochastic” in SDF wants to emphasize the uncertainty in time-varying discount rate. Formally, the SDF exists and prices all assets if and if the law of one price holds: that is, strategies that have the same expected payoff should have the same cost today (Arrow & Debreu, 1954).

8

In general terms, high marginal utility environments are periods in which having an extra dollar of wealth is particularly valuable. Periods of high unemployment, high inflation or financial instability are common examples.

should show up in any market model’s error term. If this is the case, adding the industry factor to the traditional CAPM should increase its explanatory power.

To test this hypothesis, I create a factor-mimicking portfolio that captures the risk of industry volatility following a conceptually similar procedure as in Carhart (1997). Each month I sort industries into quintiles based on the volatility of their market beta over the previous 12 months. Then, within each quintile I sort industries based on idiosyncratic volatility, thus, obtaining 25 portfolios. Finally, industries of the same idiosyncratic rank are averaged over the portfolio's characteristic to form five industry risk-sorted portfolios. Hedging portfolio returns comes from the self-financing strategy that goes long in the most volatile portfolio (Q5) and goes shorts in the least volatile portfolio (Q1).

1.4.2

C

This study extends previous empirical research on volatility risk at the level of the industry over the extended sample period 08/1969 to 12/2013 for the US market, thus considering the recent financial crisis and its aftermath. The main contribution of this paper can be summarized as follows.

 First, I propose a novel procedure to estimate idiosyncratic volatility by using the dichotomous asset pricing model (DAPM) of Zou (2005) as a market model. Conditioning industry's returns to upper and lower-market regime allows to estimate exposures to market risk, thus, to residual risk with superior accuracy9 than either the traditional CAPM or Fama and French three-factor model (3FF).

 Second, this paper recommends to control for the endogeneity of market returns when estimating betas of portfolios whose index weighting is relatively high, which is a distinctive characteristic of each industrial portfolios. Following Woo et al. (1994) a rather simple procedure is implemented to construct ad hoc industry's instrumental variable that will be used instead of the raw market index to run IV OLS regressions. In-sample tests support the validity of this methodology: industry's IV betas are on average lower than their reciprocals estimated by straight OLS regressions and

9

As a robustness check, I estimate industry betas adopting the 3FF over the full sample period (tables are available upon request). Interestingly, the R-squared of the 3FF and DAPM are almost indistinguishable, however, the 3FF gathered this result by adding two explanatory variables, namely the size and book-to-market factor. This evidence leads suspicious on the consistency of the 3FF's market beta estimates.

coherently reflect the size differential between aggregated industrial portfolios and the market, which by definition has beta equals to 1.

 More importantly, to my knowledge, this paper provides the first empirical asset pricing investigation on industry risk. To examine its cross-sectional relevance under the FMB (1973) testing framework, a factor-mimicking portfolio is used. Moreover, the portfolio construction procedure developed has a characteristic feature that desires to emphasize the importance of considering idiosyncratic and systematic risk as dynamically related, instead that separately as traditional asset pricing theory would suggest. Accordingly, I control for the short-term beta instability that at individual level is due to non-synchronous industry's idiosyncratic shocks, in a sense to be made clear.

The reminder of the paper is organized as follows. In Chapter 2, I describe the data (section 2.1) as well as the econometric methodology adopted to compute idiosyncratic volatilities (section 2.2) and industry betas (section 2.3). Section 2.4 concludes by presenting descriptive statistics of monthly industry variances both over the full period and subperiods. Next, in Chapter 3 I investigate whether exposure to industry risk is priced in the cross-section of stock's expected returns. Section 3.1 presents industrial portfolios' preliminary characteristics, whereas the industry factor-mimicking portfolio is constructed in sub-section 3.1.2. Sub-section 3.2.1 and 3.2.2 reports contemporaneous average returns associated to the dynamic evolution of industry volatilities (here defined as industry migrations) and factor portfolio's characteristics respectively. Section 3.3 presents the FMB (1973) two-pass regressions framework and major empirical results (sub-section 3.3.2). Chapter 4 concludes the paper.

CHAPTER II: ANALYTICAL FRAMEWORK

2.1

D

The sample period of 48 US industrial portfolio returns runs from 08/1969 to 12/201310 and incorporates firms listed on the NYSE/AMEX and NASDAQ, which are grouped according to the industry classification method proposed by Fama & French (1997). From Kenneth French data library I extract monthly returns of portfolios that mimic established risk factors11 such as SMB (small minus big), HML (high minus low), UMD (momentum), STR (short-term reversal) and the one-month Treasury bill, whereas monthly data on the BAB (betting against beta) factor are obtained from Andrea Frazzini personal webpage12. As a proxy for the raw market portfolio the value-weighted CRSP index of all firms incorporated in the US and listed on the aforementioned exchanges is used. Daily returns and level of this portfolio are downloaded from the Wharton Research Data Services (WRDS).

2.2

E

An underlying debate that has attracted many researchers concerns the measurement of idiosyncratic volatility. Most of empirical studies estimate residual risk as the standard deviation of residuals obtained from fitting a market model.

Given the empirical complexity of interpreting regression's residuals from the traditional CAPM as exclusively reflecting idiosyncratic risk and not omitted risk factors, the financial literature for the US has moved toward the Fama and French three-factor model. The common practice consists of regressing individual asset's daily excess return against the Fama and French’s factors. Hence, idiosyncratic volatility is computed as the monthly standard deviation of daily residuals from equation 2.

10

The sample length has been selected in order to allow each industry to have valid daily observations. Industrial portfolio’s return are value-weighted.

11

For a detailed explanation on how these factors are constructed this paper refers to Kenneth R. French Data library. The address is: http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/Data_Library/f-f_factors.html

12

(2)

An alternative model-free methodology is presented by CMLX (2001), who develops a rather intuitive variance decomposition method (sometimes called market-adjusted return model) that allows to estimate idiosyncratic risk without the need of any individual security’s beta. Computing idiosyncratic volatility as the value-weighted sum of squared return differential between stock and aggregate market's returns guarantees that all covariances of individual stock cancel out.

On the other hand, this paper proposes a novel approach to compute idiosyncratic volatility by adopting the DAPM’s as a market model. This decision appears theoretically motivated by several criticisms on the validity of the Fama & French’s size and market-to-book factor (Daniel & Titman, 1997) along with empirical evidence of correlation asymmetry in the US market. Ang et al (2002), Chordia et al (2011) reveal that conditionally on downside market moves, correlations between stock portfolio returns and returns on the aggregate market are significantly different (much higher) than the correlation implied by the bivariate normal distribution. Therefore, holding the gain-loss and mean-variance framework as simple approaches to portfolio selection and asset pricing, the DAPM by optimizing on measures of conditional variance is able to unambiguously improve the CAPM’s pricing accuracy yet retaining its theoretical insight. According to the DAPM, industry's excess returns can be written as follows:

̂ ̂ (3)

where ̂ represents the industry predicted 13 residual at day and ̂ represents the upper and lower-market beta depending on whether the return of market portfolio is positive or negative respectively. Hence, given the central role that value-weighted portfolio plays in asset pricing among with the limited number of industry available, industry realized variance is computed in this paper as follows:

( ̂ ) ∑ ̂ (4)

13

The term "predicted" emphasize the fact that residual are model-dependent, moreover, for computational purposes betas are held constant during the month that follows the rolling estimation period.

2.2.1

E

By adopting a value-weighted scheme I am able to further point out to the importance of considering estimates of systematic and idiosyncratic risk loadings as dynamically related. Without loss of generality, industrial portfolio's excess returns can be expressed either as in equation 3 or, by imposing unit-beta restriction the industry market model (CMLX, 2001) as follows:

(5)

Comparing equation 5 to equation 3 yields the following definition of industry's predicted residuals and of relative individual monthly volatility:

̂ ( ₎

∑ ̂ (6) By taking the value-weighted average across industry variances produces the following aggregate industry volatility decomposition:

( ̂ ) ∑ ( ) ∑ ( ) ( )

( ) ( _{) (} )

(7)

where ( ̂ ) is the DAPM's industry variance defined as in equation 4, ( ) is the market-return adjusted model’s variance equivalent, ( ) is the volatility of the market portfolio and ( ) is the cross-sectional variance of industry's betas14. From an econometrics perspective, this decomposition shows that at any given time, INDVol is positively related to the level of the true (ex-ante) unobservable industry's volatility and it is negatively to the cross-sectional variance of beta times the volatility of the market index, where ( ) can be interpreted as the slope coefficient from a regression of INDVol on ( ). Testing empirically this expectation, I find that during the period 01/1975-12/2013 the OLS coefficient of market volatility on INDVol is 0.19 (t-statistic = 18.55), whereas the sample monthly cross-sectional variance of beta is 0.07. Apparently, this variable explains a significant share of the endogenous relation between industry and market risk, hence, not taking into account for this issue when constructing an industry risk proxy likely lead to misleading conclusion about its pricing relevance.

14

2.3

E

Although recent developments in this are of research have shown that the cross-sectional variance of stock returns is a consistent and asymptotically efficient estimator of average residual risk (Da et al., 2011 and Garcia et al., 2011), this appealing methodology cannot be applied in this study given the limited number of assets being studied. Therefore, to make the beta estimation procedure more robust, in the following section I preliminarily address one of the most influencing sources of error that might cause my beta estimates to be biased.

2.3.1

E

By studying the Thailand and Hong Kong stock exchanges, Woo et al. (1994) document that beta estimates are biased upwards up to 7% compared to unbiased IV estimates. This issue arises from the relative high index weighting that each security has in these two “small” markets. They further point out that Milan and Amsterdam exchanges may be similar cases in Europe.

Even though the NYSE and NASDAQ exchanges represent the largest stock markets in the world, with a market capitalization of around $25,4 trillion15, the relative high market value of each industrial portfolio raises the possibility that market returns may be endogenous indeed. This suspicious is confirmed by Table 2, which shows high index weightings for all industries, whose weights range from lows of 0.1% of Fabricated Products to highs of 9.16% of Oil. Therefore, regressing industrial returns on the raw the CRSP value-weighted index would likely produce biased beta estimates even in large sample. To tackle this problem I construct 48 instrumental variables (the “instruments”) adopting an intuitive two-stage procedure. In the first step industries daily index weightings are computed from available monthly data, next, 48 market portfolio replicas are constructed.

The first stage proposes to estimate industry daily weights as in equation 8, therefore disregarding an approach that uses a smooth transition between available data such as a simple linear interpolation. Formally, the industry weight in day equals its level in the previous day multiplied by the ratio between the return of the industry and the return of the market portfolio. In other terms, each index weighting increases or decreases over

15

time proportionally to the relative industry's returns on the market. In formula:

(

) (8)

where represents the index weighting of industry , , are the industry and market net excess return respectively. In sequence, the instrument's daily level is determined as follows:

∑ ( )

(9)

where represents the estimated index level in day , whereas and are from equation 8. These computations are iterated once the full time-series of industry’s daily weights is acquired.

In the second stage, daily returns of each index replica are computed as if the performance of the industry for which the instrument is constructed were in line with that of all other industries. Specifically:

∑ ( )

(10)

where is the daily returns of the index replica , ∑ ( ) is the weighted sum of all other industries returns and ( ⁄ ) is an incremental factor. This factor compensates the lower return of the instrument portfolio by increasing its absolute value proportionately to the size of the industry that has been excluded from the numerator of equation 10.

All in all, this procedure controls for the endogeneity issue by removing the effect of industry's returns on the market portfolio, without altering on the other hand the essence of beta, which still measures the covariation of industry's returns to a group of industries of which it is not a part. Testing the relevance condition on each instrumental variable yields correlation coefficients with the raw market portfolio that are higher than 0.9932 (Oil) in any cases. Figure 3, which compares the level of constructed and raw market indexes, supports this finding: over time the two series are almost indistinguishable. Therefore, there is almost no loss of accuracy from using this method.

FIGURE 2:COMPARISON OF RAW AND CONSTRUCTED INDEX RETURNS

This Figure depicts the 12-month moving average of the CRSP index level and its replica constructed according to equation 4 over the sample period 01/1975-12/2013. The level of the index replica is obtained by taking the value-weighted sum over the 48 instruments constructed. Shaded areas represent NBER-dated economic recessions.

2.3.2

B

As stated in section 2.2, this paper estimates industry's best betas according to the DAPM. The term "best" wants to emphasize its role in minimizing potential model's pricing errors (Zou, 2006), whose econometric definition embraces both the intercept and the error terms from a simple OLS regression.

In practice, minimizing pricing errors leads to the best beta, which represents the slope coefficient of a linear OLS regression with intercept forced to be zero. The least squares solution can be written as follows:

( )

( ) (11)

The DAPM predicts that the relation between best beta ( hereafter) and expected returns holds separately in the upper and lower market regime and can be characterized by two security market lines (SMLs):

̅ ̅ ̅ ₍₁₂₎

(13)

being positive ( ̅ ) or negative ( ), is the asset’s upper-market beta, is the

asset’s lower-market beta, and ̅ , are error terms. As stated in Zou (2005), the upper-market beta can be interpreted as a measure of asset's upper-market potential, that is: high beta high (expected) gain when the market goes up. On the other hand, the lower-market beta can be interpreted as a measure of lower-lower-market risk, that is: high beta high (expected) loss when the market goes down.

With regard to the beta estimation procedure, I decided to use daily observations due to meaningful reductions16 in standard errors and to their superior accuracy in measuring conditional covariances (Foster & Nelson, 1994). Moreover, to balance the statistical power of large sample against potential problem caused by the non-stationary of beta, I employ a moving estimation window of approximately six years. This decision is supported by several papers, which have stressed the relevance of time-varying betas in discerning the nature risk-return trade-off. For example, Jagannathan & Wang (1996) develop a conditional version of the CAPM where betas are estimated based on the information contained in the past 5-year of monthly prices. This model increases the ability of the CAPM in explaining the cross-sectional difference in expected returns up to 30% compared to the nearly 1% of its unconditional version.

Hence, upper and lower-market industry betas are estimated by rolling the window of 680 conditional daily returns 17 observations ahead. The length of the rolling window is somehow an arbitrary decision. Yet, it is an empirical standard17. Furthermore, it is worth mentioning that even though the length of the estimation window might be not optimal for estimating conditional means, therefore, causing the expected returns and beta trade-off to "fail more often", as means tend to revert over time spans longer than six years, this issue has negligible consequences on my results since estimating conditional mean is out of the scope of this research.

Figure 3 shows the ability of the DAPM to enrich the single security market line prediction of the CAPM as confirmed by the relative steepness of the empirical upper-market and lower-upper-market security upper-market lines. The SMLs’ slope coefficient is 0.7 and 0.78 respectively. Interestingly, I find that the only industry that had negative betas over the estimation period and accordingly negative expected returns in upper-market and

16

As a robustness check, I estimate industry’s betas using monthly data. On average, I find that monthly standard errors are consistently larger than their daily reciprocal (tables are available upon request).

17

positive expected returns in lower-market is Precious Metal, a finding that is not very surprising given the well-known ability of this industry to hedge market risk.

FIGURE 3:DAPM'S EMPIRICAL SECURITIES MARKET LINES

This figure provides a graphical representation of the empirical security market line (SMLs) observed over the sample period 08/1969-12/2013. Industry betas and mean returns are estimated on a 6-year rolling basis. Mean returns are expressed in percentage terms.

Despite the relatively short step-size of the rolling estimation window as well as the high frequency of the data being used, Figure 4 depicts large fluctuation of beta estimates over time. This instability is with small chances driven by changes in fundamental risks, which usually occur over longer periods.

Many studies have attempted to explain such variation. Blume (1975)was one of the first to investigate this topic, documenting a consistent regression tendency for a portfolio with either high or low estimated beta to revert toward one. He also lays down an explanation for this evidence, speculating that firms that undertake risky project in the current period tends to carry out project with less extreme characteristics in the following period, therefore, causing beta to revert toward one. Dejong & Collins (1985) associate higher beta instability to unexpected changes in the risk-free rate or to the level of leverage undertaken by companies. Campbell & Mei (1993) argument that macroeconomic indicators, such as the T-bill yield, the term spread and the default spread, capture most of this variance.

On the other hand, a recent strand of the literature points out to the impact of idiosyncratic shocks that occur during the estimation period on the covariance risk

structure of stocks (Pastor & Veronesi, 2009). Earning announcement, M&A, spin-off are common examples. Whether or not these shocks are related to structural changes in the investment opportunity set or to irrational investment behaviours, once the market moves in the same direction, increasing (decreasing) prices are associated to temporary higher (lower) betas. Providing an unique perspective in undertanding the reliability of the CAPM, Xu & Zhao (2012) document a positive correlation between the level of idiosyncratic risk of a stock in month and its future beta in month . Stocks that have high average volatility tend to be overpriced because of the investors' appetite for this stock's characteristic, accordingly higher prices today are associated to higher betas and lower subsequent returns. Next, if overpricing reverses in the following period, for instance because of short sales constraints, returns tends to drop with a lag, therefore obscuring the CAPM normative prediction: high beta, high expected returns.

FIGURE 4:EVOLUTION OF INDUSTRY BETAS

These graphs plot the 3-month moving average of 11 industrial portfolio betas over the sample period 01/1975-12/2012. Industries are classified into 4 groups: Money (Banking, Insurance, Real Estate and Trading; Panel A), High Tech (Pharmaceutical Products, Communication, Computers, Electronic Equipment; Panel B), Oil & Utilities (Industrial Metal mining, Petroleum and Natural Gas, Utilities; Panel D) and Consumer Durables (Consumer Goods, Automobile and trucks, Business Services, Retail; Panel E). Monthly betas are computed as the weighted average of upper and lower-market daily beta over the previous month, with weights equals to the proportion of upper and lower market trading days respectively. Shaded areas are NBER-dated economic recessions.

Attempting to explain what drives the beta variation depicted in Figure 4, one might wonder whether this apparently cyclical pattern is determined by variations in correlation between industrial portfolios and the market, or by changes in the ratio between their respective volatilities18. Testing empirically these hypothesises, I find that the evolution of industry’s beta is primarily explained by time-variation in the correlation structure: the sample correlation between these two statistics in upper-market regime is 0.63, whereas in lower-market regime is 0.55. Then again, the correlation between betas and the ratio of industrial portfolios’ volatility relative to the market is 0.10 and 0.11 respectively.

In each of the four cases presented the correlation coefficient is statistically significant at 1-percent significance level, hence, suggesting that on one hand the DAPM industry’s beta correctly reflects “correlation risk”, i.e. exposure to the volatility risk of the market portfolio, on the other hand draws the attention at individual level to the impact of industry’s volatility (which is essentially idiosyncratic) on its own beta estimate.

2.4

P

This section analyses US industry return volatilities for the period 01/1975 to 12/2013. Table A1 provides variable names and compositions of the 48 industrial portfolios. For comparison I also present descriptive statistics for the market portfolio and weighted average of industry variances.

INSERT TABLE 2

Table 2 shows that on average industry volatilities are lower than the market's (16.7% per year, the corresponding variance is 2.80), with the only exception of 10 albeit rather small industries, whose volatilities range from 16.82% of Fabricated Products to 37.28% of Precious Metal. These industries together constitute less than 4% of the total market capitalization. As documented in Wang (2010), I find that size and idiosyncratic risk are negatively correlated (-0.32). Petroleum & Natural Gas, Banking, Pharmaceutical products, Communication, Retail, Utilities, Business Services and Computer are the eight largest industries, each with an average market share greater than 5%. On the other hand,

18 _{A straightforward way of decomposing beta yields the following approximated relation:}

the eight smallest industries have all market share lower than 0.25%. Among the largest industries only Banking, Oil and Computers have been volatile above the industry average (1.67), evidence that is related to the relevant shocks occurred to these sectors during the estimation period.

All in all, volatilities follow similar patterns19 with relative peaks in association to recessions and market corrections, as clearly depicted in Figure 5, which plots 12-month moving average of monthly volatilities for fifteen of the largest industries. These industries are classified into five groups (Money, High Tech, Oil and Utilities and Consumer Durables) for easy of presentation.

FIGURE 5:EVOLUTION OF INDUSTRY VOLATILITY

These graphs plot the 12-month moving average of US market and 11 industry volatilities over the sample period 01/1975-12/2013. Industrial portfolios are classified into 4 groups: Money (Banking, Insurance, Real Estate and Trading; Panel B), High Tech (Pharmaceutical Products, Communication, Computers, Electronic Equipment; Panel C), Oil & Utilities (Industrial Metal mining, Petroleum and Natural Gas, Utilities; Panel D) and Consumer Durables (Consumer Goods, Automobile and trucks, Business Services, Retail; Panel E). Shaded areas are NBER-dated economic recessions.

19

Table 2 indicates that the correlation between the market and industrial portfolios ranges from 0.39 (Tobacco Products) to 0.72 (Insurance) and is averaged at 0.57.

Panel A of Figure 5 compares the market and industry value-weighted average. The correlation coefficient between these two volatilities is 0.65. Interestingly, industry volatility has been almost unaffected by the market crash of October 1987, remaining rather stable from the beginning of the sample to 1998, when it dramatically increased above market level as the Internet bubble busted. During this period all industry volatilities, except that of Real Estate and Industrial-Metal mining, were at their highest. On the other hand, market volatility, which has been suspiciously flat from 2003 to 2007, surged during the 2007's financial turmoil touching its historical maximum in 2008.

INSERT TABLE 3

In the light of the several sectoral shocks occurred over the sample being studied, Table 3 compares industry average volatilities in different subperiods. The first comparison is made between the 10-year average volatilities for the period 01/1975-12/1984 and for the period 01/2003-12/2013. Over time industry volatility has increased by a factor of 2 over but less consistently than market volatility. Industries with high (low) volatility at the beginning of the sample have shown some sort of persistency since they still represent the most (least) volatile industries at the end of the sample.

Additionally, Table 4 compares the 5-year industry average volatility that preceded and followed two of largest recessions ever occurred in the stock market. These are the Internet bubble and the Lehman Brothers' bankruptcy. I find significant differences between the volatility run-up of the early 2000s and the 2008's financial turmoil. During the dot.com bubble, the weighted average change in industry volatility was driven by non-traditional sectors, such as Electronic Equipment, Pharmaceutical Products and Computer, which together added almost 0.8% points to the absolute increase in industry

volatility of 2.65 recorded between 01/2003-12/1997 and 01/1998-12/2003. On the other hand, traditional sectors like Banking, Real Estate and Construction were responsible both for the increase in industry volatility occurred before the bankruptcy of Lehman brothers (15th September, 2008) and for the subsequent volatility reversal observed over the period 01/2009-12/2012, which can be related to their decreased market share.

CHAPTER III: IS INDUSTRY RISK PRICED?

3.1

P

There are numerous papers documenting some sort of predictability in stock returns, whose explanations are either related to rational or behavioural arguments. From a methodological perspective, the simplest approach to test these arguments consists of determining an appropriate trading strategy that is related to the source of expected returns. Each month stocks are sorted into equal-sized bins (e.g. quintiles) by their relative exposure to the risk factor of interest over the previous period. Then, the profitability of a zero-investment strategy that goes long in the quintile with the highest estimated exposure and short in the quintile with the lowest estimated exposure is tested against other risk factors, whose impact on asset pricing has been well documented.

FIGURE 6:NUMBER OF FIRMS

This Figure depicts the 12-month moving average of firms included in the value-weighted CRSP index and into all industrial portfolios over the period 08/1969-12/2013.

3.1.1

P

Given the length of sample scrutinized, it is clear that the number of firms listed in the NYSE, AMEX, NASDAQ (from 1973, Figure 6) exchanges and included into the market or industrial portfolios varied significantly over time, with evident bumps in association

to economic distress phases.

INSERT TABLE 4

Table 4 shows that the average number of firms per industry is 106, whereas the median is 76. Hence, on average industry portfolios are well diversified. The Tobacco Products, Coal, Shipbuilding & Railroad Equipment, Defence, Candy & Soda, Beer and Agriculture industry may represent the exception since they include less than 20 firms in a typical month, nevertheless these industries belong to relatively concentrated sectors: the average firm's size for these group of industries is nearly three-times bigger than the industry standard ($1.25 billion). Therefore, generally speaking these companies should bear lower distress risk.

The top performing industries were Entertainment (1.18%), Tobacco Products (1.14%) and Aircraft (1.09%). On the other hand, Precious Metals (0.42%), Steel (0.47%) and Miscellaneous (0.48%) were the worst preforming industries. Adjusting raw industry20 returns for size and book-to-market effect produce significant positive alphas in 34 cases. Interestingly, among the industries for which the alpha is found insignificant, most of them come from traditional sectors like Automotive, Mines, Textiles, Steel and Construction.

INSERT TABLE 5

Although the market beta, SMB and HML appears to be the most important factors in explaining cross-sectional variations of expected returns, evidences from Table 4 suggest indeed that industry portfolios carry a significant alternative risk premium. To test this hypothesis, I analyse first of all the raw relation between industry volatility and expected returns by a rather simple portfolio sorting approach. Next, in order to be consistent with my cross-sectional regressions in section 3.3, I construct a factor portfolio that mimics innovation in industry volatility risk.

At a first glance, the puzzling "low risk high return” evidence of AHXZ does not persist at industry level. Table 5 documents that, after sorting industries into quintiles based on idiosyncratic volatility, the average abnormal return of the long-short strategy (LS) that

20

To adjust excess returns I employ the 3FF since the aim of this research is to improve its explanatory power by adding the industry risk factor.

buy high volatile industries (Q5) and sell low volatile industries (Q1) is positive at 10-percent significance level (t-statistic = 1.79). Nevertheless, the economic magnitude of the industry volatility premium is abysmally small: 0.6% on a yearly basis disregarding transaction costs.

Panel B offers further insights about these industry risk-sorted portfolios. As expected, the explanatory power of the augmented 5-factor model decreases from the portfolio including low volatile industries to the portfolio including high volatile industries. Portfolio betas are positively related to idiosyncratic volatility, a similar results as in (Koch, 2010). The relationship is monotonic: on average high idiosyncratic industries have higher betas.

Looking at the other risk factors, I find that Q1 has a positive loading on momentum (t-statistic = 1.83), whereas for Q5 the reverse is true. High volatile industries show significant (t-statistic = -2.76) negative exposure on momentum effect. This finding suggests that these industries tend to be, on average, past losers. On the other hand, the size and book-to-market effect is absent at any idiosyncratic level, which is rather surprising given that during a typical month, the market capitalization of Q1 is nearly 3.6 times larger than that of the fifth quintile ($673 billion).

A possible explanation may be related to the value-weighting scheme adopted to compute portfolio returns, which makes the most extreme quintiles exposed to the specific shocks of industries whose equity value is relatively high. The relevance of this phenomenon should be fairly pronounced since the fifth quintile portfolio often includes few smaller industries (e.g. Precious Metal) that are persistently volatile. Interestingly, these dynamic seems to provide a natural hedge against size risk.

Even though Table 5 provides evidence of high idiosyncratic industries outperformance, I do not find a monotonic relationship between industry volatility and expected returns. Then, it is possible that factors other than industry volatility might play a role in explaining such results, explicitly, by affecting the portfolio formation phase. This suspicious is confirmed by panel A, where few distinctive quintile portfolio's characteristics can be observed; industries with higher idiosyncratic risk tend to have higher return volatility and skewness, whereas lower Sharpe ratios.

sorting approach21. Panel C provides the results of this robustness check. First of all, the size factor is scrutinized given its documented high correlation with idiosyncratic risk. After controlling for size, the risk premium on the zero-investment strategy is unchanged at 0.05% per month. Also the R2 of the augmented 5-factor model is rather stable at 0.13. The second asset pricing effect that is considered is the short-term reversal (SRT22), which proxy for the tendency of stock prices to revert over short trading horizons. Da et al. (2011) among the others, document strong evidence of intra-industry reversal during periods that follow phases of market instability.To control for this factor I sort industries based on their previous months excess return and then on idiosyncratic risk. Interestingly, the risk premium on the LS strategy widens to up 3.25% per year, whereas the R2 decreases to 0.09. Nevertheless, even after controlling for those variables, I find that the strategy that buys high idiosyncratic industries and sells low idiosyncratic industries has still significantly positive alpha. This evidence clearly shows that neither size nor short-term reversal (an reversely neither short-short-term momentum) drives substantially the results.

3.2

I

In order to develop a more insightful methodology that is able to disentangle the complicated relation between idiosyncratic volatility and expected returns, in this section an analysis on the determinants of short-term and long-term cross-sectional differences in industry volatilities is presented. The evidences that will be presented in the following paragraphs can be undoubtedly related to the theoretical development proposed in sub-section 2.2.1 and 2.3.2 (the beta instability).

Recalling from equation 4 that industry variance is computed as the weighted average sum of squared residuals, the daily variation in predicted residual can be written as follows:

̂ (14)

21

Specifically, industrial portfolios are sorted into quintiles depending on a characteristic on a monthly basis, then, within each quintile, industries are grouped into equal-size bins based on their volatility over the previous period. Finally, industries of the same idiosyncratic rank are averaged over the corresponding characteristic to form 5 portfolios.

22

To notice that controlling for STR and Momentum (UMD) effect produces opposite results, as expected. Tables are available upon request.