Idiosyncratic volatility and stock returns: Evidence from the MILA

Research in International Business and Finance 37 (2016) 422–434

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Research in International Business and Finance j o u r n a l h o me p a g e : w w w . e l s e v i e r . c o m / l o c a t e / r i b a f

Idiosyncratic volatility and stock returns: Evidence from the MILA Luis Berggrun a,∗ , Edmundo Lizarzaburu b , Emilio Cardona c a b c

Universidad Icesi, Calle 18 #122-135, Cali, Colombia Universidad ESAN, Alonso de Molina 1652, Monterrico, Surco, Lima, Peru Universidad de los Andes, Calle 21 # 1–20 Ed. SD, Bogota, Colombia

a r t i c l e

i n f o

Article history: Received 19 May 2015 Received in revised form 22 December 2015 Accepted 6 January 2016 Available online 14 January 2016 JEL classification: G11 G14 G15

a b s t r a c t This paper examines the association between idiosyncratic volatility and stock returns in the MILA from 2001 to 2014. Based on portfolio strategies that rely on one- or two-way sorts, we find that idiosyncratic risk is not a predictor of returns in the whole period or during high or low volatility months in the integrated market. We confirm the lack of an idiosyncratic volatility effect in a multivariate setting conducting errors-in-variables-free panel regressions. Overall, unsystematic risk is not a priced factor in the MILA, in line with predictions of several pricing models and recent literature in the U.S. market. © 2016 Elsevier B.V. All rights reserved.

Keywords: Idiosyncratic risk Emerging markets Latin American Integrated Market Mercado Integrado Latinoamericano Portfolio performance evaluation Panel regression

1. Introduction Since the pioneering work of Fama and MacBeth (1973), which showed that idiosyncratic volatility (IVOL) is not a priced factor in the U.S. (in line with predictions of the CAPM model of Sharpe (1964) and the three-factor model of Fama and French (1993)), several studies have attempted to understand the role of IVOL (if any) in explaining one-period ahead returns. To date, findings are mixed, pointing to a negative, positive, or a non-existent association between IVOL and future returns. Ang et al. (2009) show evidence of a negative (perhaps puzzling) relationship between lagged IVOL and future excess returns using monthly data for a sample of stocks from developed countries. This finding is similar to one reported by the same authors for the U.S. (see Ang et al. (2006)). Peterson and Smedema (2011) also find a negative relationship between lagged (or realized) IVOL and returns (for all months except January) in the U.S. Furthermore, Chen et al. (2012) document that the negative (and significant) alpha for a value-weighted portfolio, long on high past IVOL and short on low IVOL common stocks, tends to be quite ubiquitous. The negative spread is present for a subsample of both large and small stocks as well as

∗ Corresponding author. E-mail addresses: [email protected] (L. Berggrun), [email protected] (E. Lizarzaburu), [email protected] (E. Cardona). http://dx.doi.org/10.1016/j.ribaf.2016.01.011 0275-5319/© 2016 Elsevier B.V. All rights reserved.

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for subgroups of stocks determined by prices ranges (e.g., the negative alpha is shown to be highly significant for portfolios of stocks with prices that range from $5 to $10 USD). In addition, the authors find that the indirect relationship between IVOL and returns is significant even after controlling for the effect of past (monthly) returns into current month returns. In the same vein, Guo and Savickas (2010) find that, controlling for size (usually small stocks show higher IVOL than large stocks), portfolios of high IVOL stocks underperform in risk-adjusted terms portfolios of low IVOL stocks. Furthermore, the authors show that in pricing regressions, a factor related to idiosyncratic risk (returns of a portfolio long in low IVOL stocks and short in high IVOL stocks) appears, in the cross section, positively related to stock returns. Two recent papers provide possible explanations for the negative association (or IVOL anomaly) between IVOL and returns. Han and Kumar (2013) show that retail investors tend to hold high IVOL stocks (usually overpriced) due to the speculative features (e.g., high idiosyncratic skewness and low price) of these assets. High retail trading proportion stocks, in turn, tend to significantly underperform stocks that are predominantly traded by institutional investors. Overall, the proportion of retail investing appears to be related to the puzzling negative association between IVOL and return. Furthermore, Avramov et al. (2013) document that several pricing anomalies (in particular, the IVOL anomaly) are more salient in the worst creditrated stocks. In essence, the short side of the IVOL strategy tends to profit around price decreases following credit rating downgrades. When Avramov et al. (2013) exclude low-rated stocks or periods around downgrades, the profitability of the IVOL long-short portfolio vanishes. Thus, financial distress appears to be an important driver of the IVOL anomaly. For emerging markets, the issue of the pricing ability of IVOL has unfortunately attracted less attention. Two studies that also find a negative association between past IVOL and returns are those of Lee and Wei (2012) and Nartea et al. (2013). Lee and Wei (2012) document a negative relationship between lagged IVOL and expected short-run returns for stocks listed in the Hong Kong Exchange. They claim (based on Shleifer and Vishny (1997)) that low idiosyncratic risk stocks are more profitable because arbitrageurs, being risk-averse in the short run, usually tilt their portfolios to low volatility shares, causing an upswing in trading volume and prices for this particular type of stock. Nartea et al. (2013) report a negative relationship between risk-adjusted returns and IVOL (measured as in Ang et al. (2006, 2009)) in China. This negative association might be related to a behavioral tendency of Chinese investors (many of them retail investors) who are prone to overpay for high volatility or speculative stocks that ultimately underperform. A different set of studies reports a direct, perhaps more intuitive, relation between IVOL and one-step ahead returns. Malkiel and Xu (2004) document a positive association between stock returns and past IVOL using the portfolio formation methodology of Fama and MacBeth (1973). Interestingly, the authors show that this association is stronger than the one between returns and beta (or size). In addition, Fu (2009) shows evidence of a positive relationship between expected IVOL (proxied by a one-step forecast from an EGARCH model) and expected (monthly) returns. Also in the U.S. market, Huang et al. (2010) find a positive relation between monthly returns and IVOL (estimated with a rolling window of thirty months of returns and using an exponential GARCH model). The positive relationship between expected returns and idiosyncratic volatility can be understood based on Merton’s (1987) model, which shows that undiversified investors will ask for a premium to hold high IVOL stocks. As a consequence, these high IVOL stocks will bring about higher expected returns. Moreover, Vozlyublennaia (2012) documents an overall positive and significant relationship between returns and lagged IVOL (see Table 3 of her paper). She is able to determine which characteristics are more conducive of a positive correlation between returns and IVOL. In particular, large companies with low leverage and high share turnover and cash are more likely to show a positive association between IVOL and returns. In a recent study, Eiling (2013) presents evidence of a positive risk-adjusted spread between high and low IVOL stocks and argues that the premium is related to human capital. She claims that conventional pricing models by omitting factors (that end up in the residual) associated with industry-specific human capital (proxied by the growth rate in wages of several representative industries) distort the role of IVOL in explaining returns. Overall, a significant portion (e.g., up to 36%) of the IVOL premium appears to be related to a compensation for bearing nontradable human capital risk instead of companyspecific risk (in fact, high IVOL portfolios showed a positive and significant exposure to human capital factors and vice versa). On the other hand, some of the literature supports the idea that IVOL is not significantly associated with future stock returns. For example, Bali and Cakici (2008) are not able to find a significant (and consistent) relationship between IVOL and average returns (or Fama and French (1993) three factor alphas). Even though the authors report a negative and significant relationship between IVOL and average returns under certain portfolio configurations, the association disappears when they omit the smallest, lowest priced, and least liquid stocks. Fink et al. (2012) show that IVOL (out-of-sample) forecasts using returns’ information up to time t − 1 (i.e., using the information that in practice is available to a portfolio manager) are not informative of future (one-month ahead) returns. Controlling for liquidity effects, Han and Lesmond (2011) find that a hedge portfolio long on high IVOL (or residual IVOL calculated after purging the effect on IVOL of both the bid-ask spread and the percentage of zero returns) stocks and short on low IVOL (or residual IVOL) stocks delivers a zero alpha after controlling for market, size, distress, and momentum effects. Furthermore, Jiang et al. (2009) show that controlling for future earning shocks the association between returns and IVOL disappears. Overall, the authors’ evidence points to the fact that IVOL predicts returns through information on future earnings. In addition, Chen and Petkova (2012) argue that the negative relationship documented by Ang et al. (2006, 2009) between IVOL and returns is a byproduct of an omitted risk factor (because the residual captures the effect on an omitted variable). As a first step to identifying this omitted factor, Chen and Petkova (2012) decompose total market variance into average (value-weighted) stock variance and average correlation. Empirically, they show that the omitted factor relates only to the

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pricing of average variance. Importantly, when both average variance and IVOL are included in a pricing model, only the former variable has a significant role in explaining excess returns. We contribute to the literature by expanding the evidence on the association between IVOL and one-month ahead return in the Latin American Integrated Market or Mercado Integrado Latinoamericano (MILA). The MILA is an integrated trading venture between Chile, Colombia, and Peru stock exchanges that began operating in May 30, 2011. The stock market integration allows, for example, Chilean (or U.S.) investors to send market orders to buy Colombian or Peruvian equities without the need to open brokerage accounts in these two foreign markets. MILA is the second largest market by market capitalization in Latin America and the Caribbean after Brazil. According to the World Federation of Exchanges (WFE), the market capitalization (as of the end of November 2014) of listed firms in Bogota, Lima, and Santiago stock exchanges totals 476.4 billion USD. More specifically, we examine the explanatory power of realized IVOL in foretelling future returns. We study an emerging market in which little or no evidence on the subject has been presented before in a period in which the three local markets have witnessed an important increase in their overall size. In particular, the market capitalization of listed shares in the three national markets has more than tripled from January 2005 to November 2014 (according to the WFE). However, the value of shares traded through the integrated market has been low and trading has focused on stocks from a few industries like (Chilean) retail, (Colombian) oil, and (Peruvian) mining companies. Despite the integration effort, trading in the region is mostly concentrated in local investors buying local shares. In all, MILA is far from being a liquid and deep market. Although the integrated market offers investors wider diversification opportunities, MILA may well resemble the setup of Merton’s (1987) model, in which investors are unable to diversify perfectly and may require compensation (in terms of higher returns) for bearing some company-specific risk. In this paper, we begin by exploring the association between realized IVOL (estimated as the standard deviation of the residual of the Fama and French (1993) model using daily data) and monthly returns. We first notice that high IVOL stocks are usually small and illiquid stocks. Examining the performance of a portfolio strategy that is long on high IVOL stocks and short on low IVOL stocks in the integrated market, we find that IVOL does not carry a significant (and direct) ability to forecast in-sample returns. The alpha of the long-short IVOL portfolio is not statistically significant, implying that investors were unable to profit from a non-systematic risk pricing anomaly during the sample period. In one of our robustness checks we extend this result within a conditional framework since we analyze the performance of long-short IVOL portfolios during periods of low and high total volatility (perhaps the lack of diversification opportunities during high total volatility months would lead investors to demand a higher premium to hold high IVOL stocks). In either low or high total volatility months we are not able to document a significant IVOL effect. We then explore whether controlling for several systematic risk factors and firm or stock attributes commonly suggested in the literature affects the association between monthly returns and realized IVOL. Adopting the errors-in-variables-free panel regression methodology of Brennan et al. (1998), we reconfirm that realized IVOL is unrelated to future (one-step ahead) returns. After controlling for systematic risk factors and size, book-to-market, past return, and liquidity effects, the coefficient of realized IVOL is statistically insignificant in a regression that explains monthly returns. We conclude (in line with findings of Bali and Cakici (2008), Jiang et al. (2009), Han and Lesmond (2011), Chen and Petkova (2012), and Fink et al. (2012) in the U.S.) that IVOL has a non-significant ability to forecast future returns both within a univariate (using one-way sorted portfolios) and a multivariate context in the integrated market. A battery of robustness tests lends further credence to our results. The remainder of the paper is organized as follows. Section 2 describes the database of MILA stocks. Section 3 examines the return-realized IVOL association based on one-way sorted portfolios to determine whether an investor can profit from any idiosyncratic volatility anomaly. Regression results used to determine whether a positive, negative, or non-significant relationship between lagged IVOL and return exists are discussed in Section 4. Section 5 offers robustness checks, and Section 6 concludes. 2. Data 2.1. Sample We obtain from Bloomberg the daily prices in U.S. dollars, adjusted for dividends and splits, of all common stocks listed in the Colombian and Peruvian stock markets as well as in Santiago’s (Bolsa de Comercio) stock exchange. The estimation period spans from July 2001 to November 2014 for a sample of listed and delisted stocks. The beginning of our sample period coincides with the merger of the three local exchanges in Colombia into a single (national) stock market. We apply three filters to our sample. We remove (as in Han and Lesmond (2011)) real estate investment trusts (REITs). Next, we exclude stocks with less than two months (42 days) of trading (or number of shares traded) data. We also delete stocks with gaps in the number of traded shares for up to two months.1 In all, our sample includes information of 99, 25, and 36 Chilean, Colombian, and Peruvian stocks respectively for a total of 160 securities.

1 Some stocks (most of them thinly traded) presented considerable discontinuities in the number of shares traded so we decided to exclude these stocks by applying this screen. Nevertheless, we reach qualitatively similar conclusions (to those reported below) if we abstain from using this filter.

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Table 1 Descriptive statistics of variables (2001–2014). Exc. returns

IVOL

Alpha

Beta

SMB

HML

CAP

BM

MOM

Illiq.

0.007 0.001 0.100 0.439 2.148 −0.138 0.173

0.070 0.063 0.037 1.560 4.621 0.029 0.136

0.000 −0.000 0.005 0.585 3.188 −0.007 0.009

0.670 0.629 0.671 0.646 4.280 −0.260 1.720

0.091 0.080 0.887 −0.029 2.786 −1.242 1.477

−0.021 0.006 1.184 −0.177 2.907 −1.856 1.738

1.525 1.414 0.882 0.422 −0.457 0.355 2.966

1.039 0.884 0.558 0.990 1.118 0.514 2.213

0.066 0.023 0.290 0.700 0.787 −0.313 0.599

0.054 0.013 0.340 4.999 36.014 0.002 0.100

Panel B. Colombia 0.014 Mean 0.013 Median 0.097 S.D. 0.229 Skewness 0.483 Kurtosis −0.123 5% 0.170 95%

0.071 0.064 0.031 1.034 1.026 0.038 0.126

0.001 0.001 0.005 0.415 0.581 −0.006 0.009

0.745 0.719 0.694 0.295 0.566 −0.161 1.783

0.115 0.114 0.922 0.453 3.360 −1.163 1.318

−0.091 −0.041 1.114 −0.125 1.201 −1.672 1.445

2.725 2.492 1.466 0.096 −1.023 0.737 5.025

0.870 0.819 0.230 0.652 0.387 0.612 1.268

0.126 0.072 0.309 0.799 0.908 −0.258 0.657

0.003 0.003 0.005 2.976 13.259 0.001 0.008

Panel C. Peru Mean Median S.D. Skewness Kurtosis 5% 95%

0.095 0.083 0.051 1.102 1.516 0.041 0.178

0.002 0.002 0.008 −0.088 1.960 −0.007 0.013

0.590 0.558 0.813 0.287 1.160 −0.514 1.826

−0.078 −0.079 1.365 0.130 1.886 −1.783 1.716

0.068 0.021 1.620 0.184 1.925 −2.155 2.349

1.194 1.078 0.844 0.435 −0.829 0.187 2.650

1.061 0.829 0.770 1.361 2.140 0.420 2.578

0.143 0.054 0.411 0.968 1.408 −0.334 0.875

0.008 0.005 0.010 2.869 12.800 0.002 0.023

Panel A. Chile Mean Median S.D. Skewness Kurtosis 5% 95%

0.022 0.010 0.127 0.598 2.052 −0.141 0.232

Exc. stands for excess and SD. for standard deviation. Alpha, beta, SMB, and HML are estimated regression coefficients from Eq. (1). Market cap (CAP) is measured in USD billions. BM (book-to-market ratio) is the ratio of the book value per share over the market value per share. MOM stands for six-month momentum returns and Illiq. (illiquidity) for Amihud’s (2002) illiquidity measure. The rows 5% and 95% show the 5 and 95 percentiles of the variables.

The S&P MILA Index (a value-weighted index of the 40 largest and most liquid stocks in the integrated market) in U.S. dollars serves as our proxy for the market index, and the interest rate for U.S. Treasuries with one-month maturity is our proxy for the risk-free rate. We also gather information on the number of outstanding and traded shares as well as bookto-market ratios for our sample of MILA stocks. Moreover, to obtain Fama and French (1993) factors, we proxy the SMB (“small minus big”) factor as the return difference between the MSCI small cap index for Latin America (Bloomberg ticker: MSLUELAN) and the MSCI large cap index for the region (Bloomberg ticker: MLCUELA). In a similar manner, we proxy the returns for a HML (“high minus low”) portfolio as the return difference between MSCI value and growth indices for Latin America (Bloomberg tickers: MVUEEGFL and MGUEEGFL).2 Following Ang et al. (2006, 2009), we estimate IVOL for a month as the standard deviation () of the residuals of the Fama and French (1993) pricing model. Every month, we estimate for each stock i the following regression with daily (i.e., intra-monthly) data: Rt − Rft = ˛i + bi (Rmt − Rft ) + si Rsmbt + hi Rhmlt + et ,

(1)

where Rt and Rft are the daily return (R) for stock i and the risk-free rate for a daily horizon, respectively. We refer to the difference between the two as excess returns for stock i (on the left-hand side of Eq. (1)). Rmt is the return on the market index, whereas Rsmbt is the return of the SMB portfolio. Rhmlt indicates “high minus low” book-to market portfolio returns, and e indicates the residual. To prevent biases arising from infrequent trading (Dimson (1979)), we expand the right-hand side of Eq. (1) with one-period lagged values of Rmt , Rsmbt , and Rhmlt . A stock must trade for at least 80% of the days in a month to apply the (augmented) regression model of Eq. (1) and thereby obtain an estimate of  e . We then convert the daily IVOL estimate ( e ) to a monthly estimate by multiplying by the square root of the number of trading days in a month. 2.2. Descriptive statistics Table 1 presents descriptive statistics of our variables for each country. We winsorize all variables each month at the 1 and 99 percentiles to mitigate the impact of outliers. In our calculations, we first estimate the statistics per firm and then

2 We adopt the recommendation of Cremers et al. (2012) who advocate the use of index-based instead of Fama and French (1993) factors to improve portfolio performance measurement. Cremers et al. (2012) show that by equally-weighting all six (2 by 3) size and book-to market portfolios to obtain SMB and HML portfolio returns under the Fama and French (1993) methodology, one is in fact overweighting stocks in the small and value portfolio (given the substantial differences in terms of market capitalization of each of the six size and book-to-market portfolios). Nevertheless, we also estimated market, size, and distress factors for the MILA following Fama and French (1993) methodology with qualitatively similar results (available upon request) to those reported next.

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average across firms. For every country in the sample, both the mean and the median of our dependent variable (excess returns) are positive. Colombian firms showed higher median excess returns than their peers in Chile and Peru. Focusing on our set of independent variables, the median value of monthly IVOL is higher for Peruvian firms (8.3%) than for Chilean (6.3%) or Colombian (6.4%) firms. The median alpha value is positive (but close to zero) except for Chile, whereas the loading on a size factor is on average positive (except for Peru). Market betas are positive and tend to be lower for Peruvian firms. Moreover, the mean loading on a distress factor is observed to be mostly negative. The last four columns of Table 1 show descriptive statistics of our control variables. Colombian firms, on average, have a higher market capitalization (CAP),3 a lower book-to-market (BM) ratio and are more liquid (Illiq.) than firms coming from either Chile or Peru. We control for liquidity using Amihud’s (2002) illiquidity measure. We take the average over the whole month of the absolute daily return over the dollar traded volume (and multiply this ratio by 10,000 for presentation purposes). It is evident that our illiquidity variable shows a considerable degree of kurtosis. We also control for past returns (as in Han and Lesmond (2011)) using six-month momentum (MOM) returns. This control variable (in t) is the return from month −2 to month −6. For example, we use the period from January to May to estimate a six-month momentum return for July. Mean momentum returns tend to be positive regardless of the country considered and of a higher magnitude for Peruvian companies (followed by Colombian and Chilean companies). 3. Idiosyncratic volatility and stock returns: portfolio analysis In this section, we study whether lagged idiosyncratic risk is priced. The lack of diversification opportunities in the individual (national) markets and in the integrated market given the low number of stocks and industrial sectors represented may drive investors to require a premium for holding unsystematic risk. In this regard, Miffree et al. (2013) recently documented for the U.S. an inverse association between the price of IVOL and the number of stocks included in the 100 Fama and French (1992) value and size portfolios. As the number of stocks in the portfolios grows, the premium for holding idiosyncratic risk diminishes and even becomes negative (e.g., for portfolios of 70 or more stocks). Although the IVOL premium for individual portfolios is not significant, the authors find a statistically meaningful difference between the premium required for holding less and more diversified portfolios (e.g., portfolios with 20 versus 30 stocks). The authors claim that sectorial concentration (or industry-related factors) might explain the pricing of IVOL for some poorly diversified portfolios. To assess the effect of diversifiable risk into stocks returns, we begin by classifying the available stocks for each month into three (tercile) portfolios. The first portfolio (P1) comprises stocks with the lowest IVOL of all stocks in the month, whereas the second (P2) comprises stocks with medium IVOL. P3 includes the stocks with the highest idiosyncratic volatility. Each stock is assigned an investment weight proportional to its market capitalization during the previous month. In addition to value-weighted portfolios, we also use equally weighted portfolios to gain a clearer view of the impact of IVOL on stock returns. After the ranking and portfolio construction process, we track the monthly returns of the three portfolios in the period after (holding or evaluation period) we formed the portfolios. This ranking and evaluation procedure is repeated until the end of the sample. As a result, we obtain three stacked time series of monthly returns for our IVOL portfolios. With the time series of portfolio returns, we estimate alphas (or intercepts) from the Fama and French (1993) model (see Eq. (1)) using Newey and West (1987) standard errors. Alphas for the three portfolios (j = 1, 2, 3) and for a long-short portfolio become our measures of interest to examine whether bearing higher IVOL commands higher risk-adjusted returns. The long-short (or spread) portfolio invests in high IVOL stocks and takes a short position in low IVOL stocks. We will focus on the sign and significance of the spread (P3–P1) to draw conclusions about the role of unsystematic risk in stock returns. A positive and significant alpha for the long-short portfolio would thus be evidence that investors bearing more IVOL are actually compensated with higher returns after accounting for risk. As a robustness check, we also report alphas for other long-short portfolios (P2–P1 and P3–P2), and obtain similar conclusions. Table 2 shows results for our IVOL portfolios. The first two rows of panel A show that low and medium IVOL portfolios yield positive and significant alphas. On the other hand, the high IVOL portfolio shows a zero alpha. In this initial analysis, we use, each month, the whole sample of stocks with available IVOL to form the three portfolios. In stark contrast to the findings of Ang et al. (2006, 2009) for the U.S. and some developed markets, the alpha for our zero investment cost portfolio (P3–P1) in the MILA is not statistically significant. Our results indicating a zero abnormal return to a zero cost portfolio based on past IVOL are in agreement with recent findings reported by Han and Lesmond (2011) and Fink et al. (2012) for the U.S. market. To check whether our conclusion is sensitive to the presence of small or low-priced stocks each month we restrict our sample to stocks that surpass certain market cap or price thresholds. In particular, we use a similar approach to that of Bali and Cakici (2008), and omit each month the smallest stocks (those in the lowest decile of CAP) to form our IVOL portfolios. In rows 3 and 4 of the upper panel of Table 2 we reach identical conclusions regarding the lack of an IVOL effect in this subsample. In the last two rows of the top panel of Table 2, we exclude in each period the lowest priced stocks (those in the bottom decile of the price distribution) and obtain similar conclusions for this reduced sample.

3

Market capitalization is estimated as the product of the number of outstanding shares and the adjusted share price.

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Table 2 Alphas of lagged IVOL portfolios. P1

P2

Panel A. Value-weighted portfolios Whole sample Excluding small stocks Excluding low-priced stocks

0.006*** [0.008] 0.005*** [0.008] 0.006*** [0.005]

0.004* [0.055] 0.005** [0.027] 0.005** [0.047]

Panel B. Equally weighted portfolios Whole sample Excluding small stocks Excluding low-priced stocks

0.003 [0.109] 0.003 [0.136] 0.003 [0.133]

0.001 [0.573] 0.002 [0.373] 0.002 [0.321]

P3

P3–P1

P2–P1

P3–P2

0.003 [0.501] 0.002 [0.631] 0.003 [0.407]

−0.003 [0.452] −0.004 [0.307] −0.003 [0.540]

−0.001 [0.525] −0.001 [0.755] −0.001 [0.681]

−0.002 [0.665] −0.003 [0.337] −0.002 [0.670]

−0.002 [0.615] −0.001 [0.869] −0.000 [0.994]

−0.005 [0.143] −0.004 [0.263] −0.003 [0.416]

−0.002 [0.327] −0.001 [0.640] −0.001 [0.715]

−0.003 [0.343] −0.003 [0.385] −0.002 [0.498]

P1 (portfolio 1) includes stocks with low IVOL, P2 with medium IVOL, whereas P3 includes stocks with high IVOL. Excluding small (low-priced) stocks is tantamount to omitting, each month, stocks in the lowest decile of monthly market capitalization (the distribution of monthly stock prices). p-Values for two-sided tests of zero alpha using standard errors by Newey and West (1987) reported in brackets below alpha estimates. * Significance at 0.10 level. ** Significance at 0.05 level. *** Significance at 0.01 level.

Panel B shows similar patterns for equally-weighted portfolios (nevertheless, now the alphas for the low and medium IVOL portfolios are equal to zero). The P3–P1 spread is negative (regardless of the sample or subsample considered); nonetheless, the spread remains insignificant. Our findings at the bottom panel of Table 2 reinforce the idea that investors are unable to use the information contained in IVOL in a previous period to obtain extraordinary returns in the future. Briefly, using a feasible portfolio approach, we are unable to document an idiosyncratic volatility effect or anomaly in the sample. The alpha difference between high and low (lagged) IVOL portfolios cancels out, pointing to the idea that in practice investors (during the sample period) were not able to benefit from any difference in the level of unsystematic risk of their portfolios. In an untabulated analysis we replicate Table 2 but implicitly assume as if the three national stock markets were not integrated (since this occurs during a fraction of our sample period). To this end we change the risk factors to estimate IVOL in Eq. (1). In particular, we use local instead of regional market factors (the IPSA index for Chilean firms and the IGBC and IGBVL indices for Colombian and Peruvian firms, respectively). To account for size we use MSCI small and large cap indices for each country. Likewise, for local distress factors we use MSCI country indices for value and growth stocks. In short, we do not witness a significant outperformance in risk-adjusted terms of high IVOL portfolios with respect to low IVOL portfolios. Table 3 (using value-weighted portfolios) complements our findings shown in Table 2 and reports factor loadings (applying Eq. (1)) for P1, P2, and P3 as well as for our long-short portfolios using a monthly frequency and the whole sample of available stocks. We observe only one significant difference in factor sensitivities for our long-short IVOL portfolios. Table 3 shows a positive and significant difference between the sensitivity to market movements of the high and low portfolios. The high IVOL portfolio shows a significantly higher beta than that of the low IVOL portfolio (see P3–P1 or P3–P2). The loadings on size (SMB) seem to increase as IVOL rises in line with the idea that IVOL is negatively correlated with CAP. Nevertheless, the size loadings of individual or long-short portfolios are statistically undistinguishable from zero. P3 shows a higher loading to a distress factor (HML). Yet again, neither the distress loadings of individual portfolios nor the loadings of long-short portfolios are statistically significant. Overall, we document insignificant differences in sensitivities to size and distress factors between our high- and low-IVOL portfolios. The last column of Table 3 reports adjusted R2 s of our pricing regressions. For the three IVOL portfolios adjusted R2 s tend to be high and fluctuate from 0.683 to 0.804. The explanatory power of the pricing models decreases when we estimate Eq. (1) for long-short portfolios. To gain some understanding of the characteristics of the stocks that form the three IVOL portfolios, we estimate in each month the median of excess returns for the constituent stocks of each of the three portfolios. With the time series of median excess returns, we then take the average of the series for the whole period to examine any patterns in excess returns. We conduct a similar exercise for other relevant stock characteristics, such as IVOL, alpha, market beta, and the loadings Table 3 Estimated coefficients for value-weighted IVOL portfolios. Alpha P1 P2 P3 P3–P1 P2–P1 P3–P2

Beta ***

0.006 [0.008] 0.004* [0.055] 0.003 [0.501] −0.003 [0.452] −0.001 [0.525] −0.002 [0.665]

***

0.863 [0.000] 0.903*** [0.000] 1.003*** [0.000] 0.140** [0.038] 0.039 [0.250] 0.101* [0.095]

SMB

HML

R2 adj.

0.022 [0.733] 0.068 [0.374] 0.143 [0.290] 0.122 [0.392] 0.047 [0.497] 0.075 [0.599]

−0.033 [0.815] 0.098 [0.536] 0.197 [0.235] 0.230 [0.302] 0.131 [0.363] 0.099 [0.634]

0.759 0.804 0.683 0.038 0.005 0.008

P1 (portfolio 1) includes stocks with low IVOL, P2 with medium IVOL, whereas P3 includes stocks with high IVOL. p-Values for two-sided tests of a zero regression coefficient using standard errors by Newey and West (1987) are reported in brackets below coefficient estimates. R2 adj. stands for the adjusted R2 of the regression. * Significance at 0.10 level. ** Significance at 0.05 level. *** Significance at 0.01 level.

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L. Berggrun et al. / Research in International Business and Finance 37 (2016) 422–434 Table 4 Characteristics of lagged IVOL portfolios. Variable

P1

P2

P3

Exc. returns IVOL Alpha Beta SMB HML CAP BM MOM Illiq. Avg. nr. of stocks

0.003 0.040 −0.000 0.519 0.035 −0.006 1.228 0.735 0.084 0.003 32.3

0.011 0.062 0.000 0.736 0.029 0.001 1.075 0.754 0.104 0.002 31.6

0.021 0.102 0.001 0.849 0.107 −0.049 0.395 1.027 0.089 0.007 32.0

P1 (portfolio 1) includes stocks with low IVOL, P2 with medium IVOL, whereas P3 includes stocks with high IVOL. Market cap (CAP) is measured in USD billions. Avg. nr. of stocks denotes the average number of stocks in each IVOL portfolio.

on SMB and HML, as well as market cap, book-to-market, momentum returns, and Amihud’s illiquidity measure. These characteristics will aid us in the multivariate analysis discussed in the next section. Table 4 shows that the average stock in P3 has an IVOL 155% ((0.102/0.040) − 1) higher than that of the typical stock in P1. The table also shows that the high IVOL portfolio excess returns exceed those of the low IVOL portfolio. Furthermore, the typical stock in P3 has a greater sensitivity to market and size factors and, on average, a higher book-to-market and higher momentum returns. The high IVOL portfolio also usually comprises smaller and more illiquid stocks. The P1 portfolio appears to include stocks with a less negative distress risk exposure (due to the higher HML sensitivity of the typical stock in the low IVOL portfolio). The last row of Table 4 shows that, on average, each portfolio has approximately 32 constituent stocks. 4. Idiosyncratic volatility and stock returns: regression analysis Our portfolio analysis (univariate in nature) suffers from a major drawback because we can only assess the impact of one variable (IVOL) on another variable (returns) without controlling for the effect of other variables that are likely to affect stock performance. To amend this problem, we resort to a regression analysis of our panel of monthly data. We follow the errors-in-variables-free methodology developed by Brennan et al. (1998), which comprises two steps. In the first step, we calculate risk-adjusted returns (Rt∗ ) for each month t as the difference between realized (excess) returns in the month and expected returns using the coefficients related to systematic risk factors estimated from Eq. (1). Risk-adjusted returns are therefore equal to ˆ Rt∗ = Rt − Rft − bˆ (Rmt − Rft ) − sˆRsmbt − hRhml t

(2)

ˆ sˆ, and hˆ to apply in Eq. (2). We use a fixed-length We use a conditional approach to obtain our coefficient estimates b, rolling window of 24 months (a stock must trade for at least 80% of the months in the window) to retrieve coefficient estimates from Eq. (1). In particular, we use data from excess returns and returns on the market, size and distress factors from July 2001 to June 2003 to estimate regression coefficients and obtain expected returns for July 2003. We repeat this ∗ . process for each month (t) and stock (i) in the sample to obtain Ri,t In the second step, and in the spirit of the approach of Fama and MacBeth (1973), we run the following cross-sectional regression for each month: Ri∗ = 0 + 1 IVOLi,t−1 + 2 CAPi,t−2 + 3 BMi,t−3 + 4 MOMi,t + 4 Illiq.t−2 + εi

(3)

We estimate Eq. (3) with at least 25 firms with complete information in the month. Instead of OLS (ordinary least squares) regressions that assign the same weight on either small or large cap stocks, we perform GLS (generalized least squares) regressions assuming uncorrelated errors and weights equal to the inverse of the market cap of the firm. This weighting scheme reduces the influence of small stocks on the relationship between excess returns and IVOL. Ang et al. (2009) argues that these value-weighted regressions mirror value-weighted portfolios, whereas the standard (OLS) regressions resemble equally weighted portfolios. We use four control variables (motivated by the previous literature and data availability). These four variables control for firm attributes. We use the (two-month) lagged value of the natural logarithm of CAP to account for the fact that the international literature suggests that small companies usually experience higher returns than large firms. The log value of the book-to-market ratio as of the end of the last quarter controls for value or growth effects in expected returns. We also control for past returns (as in Han and Lesmond (2011)) using six-month momentum returns. This control variable (in t) is the return from month −2 to month −6. For example, we use the period from January to May to estimate a six-month momentum return, which in turn serves as a right-hand-side variable for excess returns in July. Han and Lesmond (2011) argue that disregarding microstructure or liquidity-related effects (like the bid-ask bounce) inflates or deflates the estimates

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of IVOL and subsequently biases the sensitivity of expected returns to IVOL. To cancel out these microstructure effects, Han and Lesmond (2011) estimate IVOL using bid-ask midpoint closing prices instead of closing prices and find that lagged IVOL is not a priced factor. Given data availability, we are able to indirectly (and roughly) control for these liquidity-induced effects using the lagged (two-month) natural logarithm of the Amihud (Illiq.) measure. Our choice of two lags (instead of the more often-used one lag) for our size and liquidity controls follows Brennan et al. (1998) to avoid biases from bid-ask effects and thin trading. Nevertheless, we obtain qualitatively similar results if we apply a one-month lag to CAP and Illiq. The objective of the second step is to obtain the values of the  coefficients that are usually interpreted as premia.  1 represents the premium for bearing unsystematic risk, whereas  2 ,  3 ,  4 , and  5 represent size, distress, past returns, and illiquidity premia, respectively. Our main focus is on the sign and significance of  1 to conclude whether idiosyncratic risk is a determining factor of stock returns in the MILA. Next, we average the  coefficients across months. The mean values of the  coefficients are used for inference purposes. To obtain p-values for our coefficients, we use coefficients’ standard errors based on Newey and West (1987) heteroskedasticity and autocorrelation consistent variance-covariance matrix. Nonetheless, our inferences are in a vast majority of cases similar when we estimate standard errors as the (sample) standard deviation of the estimated  (monthly) coefficients. In Table 5, we use seven specifications to analyze the relationship between lagged IVOL and stock returns. In the first three specifications, we use excess returns as our dependent variable (and as a first benchmark) to study whether diversifiable risk commands higher returns. “Errors-in-variables” problems (e.g., coefficient biases) would arise if we were to include in ˆ sˆ, and h) ˆ in the first step the second step of Brennan et al. (1998) panel regression methodology estimated coefficients (b, in Eq. (3) to control for non-diversifiable risk factors. In the following three models, we use risk-adjusted returns as our left-hand-side variable to account for systematic risk factors and to avoid “errors-in-variables” biases. In the first model, we use IVOLt−1 as the sole explanatory variable. In line with our findings shown in panel A of Table 2, IVOLt−1 is unrelated to excess returns of month t. The coefficient suggests that investors perceive a decrease in excess returns when a stock’s idiosyncratic volatility increases. Nonetheless, the coefficient is not statistically significant. Specification 2 expands specification 1 by controlling by firm attributes, which have been shown to affect returns. In particular, model 2 includes size, book-to-market, and momentum effects. To begin, we see that the coefficient of IVOLt−1 remains statistically insignificant. We find a negative although insignificant coefficient for size, and a positive albeit insignificant loading on MOM. Furthermore, BM appears negatively and significantly related to returns. Thus, using unadjusted (excess) returns, we document not a “value effect” but a “growth effect” in the integrated market. The third model augments specification 2 by controlling for liquidity effects. The coefficient attached to illiquidity (proxied by Amihud’s measure) does not attain statistical significance. In short, none of the coefficients attached to control variables (except for BM) yields significant values. Importantly, lagged IVOL remains unrelated to excess returns in month t in our third model. We document an increase in the (average) adjusted R2 as we expand the number of covariates. The final two rows of Table 5 report the number of months in which we conduct cross-sectional regressions and the average number of firms with available information in the monthly regressions. The following three specifications of Table 5 employ the same covariates as in the first three specifications but modify the dependent variable. The coefficient on IVOLt−1 continues to be insignificant in specifications four to six. Using risk-adjusted returns the premium for growth stocks remains significant. Our additional control variables (CAP, MOM and Illiq.) retain their signs and lack of significance. Overall, even after controlling for systematic risk factors and firm or stock attributes, we are unable to document a significant association between unsystematic risk and future excess returns. In untabulated results, we estimate monthly IVOL using a different approach that follows Campbell et al. (2001) and Avramov et al. (2013). IVOL is now the difference between the sum of squared daily returns and the sum of squared daily market’s returns. In short, IVOL remains statistically insignificant under this alternative proxy for unsystematic risk. We also expand our model specifications with country fixed effects with identical (unreported) findings. In addition, we use alternative measures for our two last control variables. Instead of six-month momentum returns, we employ in models (4) to (6) of Table 5 (not shown) lagged (one-month) returns, yielding similar results. Furthermore, we control for liquidity by using turnover (the average within the month of the daily ratio of traded shares over outstanding shares), with the exact same results. The last specification of Table 5 closely resembles the regression model used in the second table of the paper by Ang et al. (2009). As a robustness test, we now regress excess returns on IVOLt−1 , contemporaneous factor loadings (beta, SMB, and HML), and control variables (CAPt−1 , BMt−3 and MOM). IVOL remains an insignificant predictor of excess returns (as in specifications 1–3 of Table 5). The coefficients on the contemporaneous factor loadings turned out to be statistically nil. As for our control variables, we observe a non-significant momentum effect and strongly significant negative BM (or “growth”) and size effects. In summary, using either an unconditional approach (as in section 3) or a conditional approach (as the one of this section), we are unable to verify that investors in the MILA profited from bearing higher idiosyncratic volatility levels in their portfolios. The risk-adjusted returns of low and high IVOL portfolios were basically the same, and any premium from bearing higher diversifiable risk was not distinguishably different from zero. Moreover, we find that the pricing model of Eq. (1) adequately explains stock returns. The intercepts in our regressions with the more complete specifications (i.e., models 3, 6, and 7) were observed to be insignificant, and most of the variables related to stock or firm characteristics (i.e., beyond systematic risk factors) did not achieve statistical significance.

430

Dependent variable Intercept IVOLt−1 CAPt−2 BMt−3 MOM Illiq.t−2 Betat SMBt HMLt CAPt−1 R2 T N

Exc. returns 0.018*** [0.002] −0.033 [0.527]

0.035 155 93

Exc. returns 0.006 [0.404] −0.028 [0.553] −0.002 [0.240] −0.012*** [0.000] 0.005 [0.678]

0.138 126 87

Exc. returns −0.002 [0.736] −0.026 [0.591] −0.002 [0.150] −0.012*** [0.000] 0.006 [0.582] −0.001 [0.183]

0.165 125 85

Risk-adjusted returns 0.010** [0.036] −0.051 [0.482]

0.036 137 88

Risk-adjusted returns 0.001 [0.898] −0.081 [0.317] −0.000 [0.819] −0.012*** [0.000] 0.010 [0.477]

0.144 122 81

Risk-adjusted returns −0.006 [0.512] −0.028 [0.713] −0.000 [0.883] −0.012*** [0.000] 0.011 [0.424] −0.000 [0.734]

0.164 117 82

Exc. returns 0.007 [0.215] −0.039 [0.406] −0.013*** [0.000] 0.005 [0.590] 0.005 [0.192] −0.000 [0.969] 0.000 [0.865] −0.006*** [0.000] 0.273 126 85

T is the total number of monthly regressions. R2 stands for the mean adjusted R-squared of the T monthly regressions. N is the average number of firms in the T cross-sectional regressions. p-Values for two-sided tests of a zero regression coefficient using standard errors by Newey and West (1987) are reported in brackets below coefficient estimates. * Significance at 0.10 level. ** Significance at 0.05 level. *** Significance at 0.01 level.

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Table 5 Panel regressions of stock returns on lagged idiosyncratic volatility.

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We conclude (in line with the findings of Bali and Cakici (2008), Jiang et al. (2009), Han and Lesmond (2011), Chen and Petkova (2012), and Fink et al. (2012) in the U.S.) that IVOL has a non-significant ability to forecast future returns both within a univariate (using one-way sorted portfolios) and a multivariate context in the integrated market. 5. Robustness checks In this section, we conduct a series of tests to verify the robustness of our results. In particular, these checks concentrate on whether our main result of the inability of past IVOL to forecast next period returns holds under a different set of assumptions. Due to space considerations, we do not report most of these tests in tables. We first examine whether changing the pricing model to estimate IVOL from a three-factor model to a univariate model (or CAPM model) in Eq. (1) modifies our conclusions. Table 6 shows our findings. We notice patterns similar to those described for Table 5. Under most specifications we do not find a significant inverse relation between size and returns. On the other hand, the negative BM effect holds its significance under all specifications. Additional control variables like momentum and illiquidity remain insignificant. Importantly, the coefficient attached to IVOL is not statistically different from zero. In all, modifying the pricing model does not alter our inference of a zero association between both excess or risk-adjusted returns and realized IVOL. We then examine whether the lack of an IVOL effects holds in periods where total volatility (VOL or standard deviation of returns) is high or low. In consequence, VOL plays the same role of a state variable in our analysis. Perhaps investors are compensated with higher returns for holding high IVOL stocks (as in Merton’s (1987)) when the lack of diversification options (in the portfolio formation month) may affect more negatively investor’s utility (i.e., when the formation month is a high VOL month). Possibly, investors may require a premium for buying high IVOL stocks during high VOL months since the lack of diversification opportunities will render them less able to reduce both the total and unsystematic risk components in their portfolios when total volatility is elevated. We estimate the monthly series of VOL as the mean of the standard deviation of returns of available stocks in a given month. We classify each month as a high VOL month whether VOL during the month surpassed the median of VOL for the whole sample period. When VOL during the month is below median VOL, the month is classified as low VOL. In Table 7 we observe positive and significant alphas for our low and medium IVOL portfolios only when the holding month was preceded by a low volatility month. We then focus (as in panel A of Table 2) on the alphas of hedge portfolios (P3–P1, P2–P1, and P3–P2) that hold a long position on high IVOL stocks and a short position on low IVOL stocks if the previous month was categorized as a low or high volatility month. None of the risk-adjusted spreads was statistically significant. In all, we are unable to document an IVOL effect in the sample even if we restrict our analysis to low or high VOL months.4 We conduct four additional (untabulated) robustness tests. We use OLS instead of GLS regressions in the monthly cross-sectional regressions under the methodology of Brennan et al. (1998). We thus want to verify that our results that use equally weighted portfolios (and coincide with those reported for value-weighted portfolios) in Table 2 (panel B) also hold in a multivariate setting. Assigning the same weight to all monthly observations (regardless of the fact that observations may come from large or small companies) leads us to similar conclusions as those presented in Tables 5 and 6. Next, we use a pooled panel regression (instead of monthly cross-sectional regressions) in the second step of our regression methodology. We obtain qualitatively similar conclusions regarding the lack of an IVOL effect in the sample. We then change the beginning date of our sample to coincide with the launch of the MILA (May 30, 2011). We conduct panel regressions similar to those reported in Tables 5 and 6 using a reduced time span. We find that, with or without controlling for cofounding effects, the coefficient attached to lagged IVOL remains statistically insignificant. In summary, the lack of forecasting power of past idiosyncratic volatility is also a feature at the end of our sample period. In our final robustness check, we study the interrelationship between firm size and idiosyncratic volatility in a portfolio context. We thus use a two-way sorting portfolio strategy instead of one-way sorting (as described in Section 3). Each month, we classify stocks as small and large (whether the stock’s market cap surpasses or not the median market cap) and as low or high IVOL (if the stock’s unsystematic risk exceeds or not the median value of IVOL) and form four portfolios: small and low IVOL (P11 portfolio), small and high IVOL (P12), large and low IVOL (P21), and large and high IVOL (P22). As in section 3, we track the returns of these four portfolios in the month subsequent to portfolio formation and repeat this procedure each month until the end of the sample. We then estimate two alphas: the first in the small cap subsample (P12–P11) and the second in the large cap subgroup (P22–P21). Neither of the two spreads for the long-short portfolios was observed to be significant (the alphas for the two long-short portfolios were −0.006 (p-value of 0.250) and −0.003 (p-value of 0.348), respectively). Thus, controlling for size, the pricing power of lagged IVOL is nil. We also control for book-to-market, momentum and illiquidity (i.e., we first sort stocks by BM, MOM or Illiq., and then by IVOL) and find insignificant spreads for hedge portfolios using bivariate sorting and our control variables. In summary, using univariate (as in Section 3) or bivariate sorts to form portfolios leads to the same conclusions reported in Table 5.

4 In untabulated results, we used average IVOL in a month as our state variable. For below- or above-median IVOL months, the risk-adjusted spreads of long-short IVOL portfolios were not significant.

432

Dependent variable Intercept IVOLt−1 CAPt−2 BMt−3 MOM Illiq.t−2 Betat CAPt−1 R2 T N

Exc. returns 0.018*** [0.003] −0.029 [0.595]

0.038 155 93

Exc. returns 0.007 [0.339] −0.042 [0.405] −0.002 [0.220] −0.012*** [0.000] 0.006 [0.627]

0.143 126 87

Exc. Returns −0.002 [0.810] −0.036 [0.481] −0.003 [0.136] −0.012*** [0.000] 0.007 [0.523] −0.001 [0.173]

0.167 125 85

Risk-adjusted returns 0.008** [0.015] −0.062 [0.293]

0.040 137 88

Risk-adjusted returns 0.000 [0.935] −0.113 [0.101] −0.000 [0.912] −0.010*** [0.001] 0.006 [0.616]

0.141 122 81

Risk-adjusted returns −0.002 [0.769] −0.065 [0.380] 0.000 [0.998] −0.010*** [0.001] 0.006 [0.630] 0.000 [0.984]

0.161 117 82

Exc. returns 0.009 [0.126] −0.061 [0.265] −0.014*** [0.000] 0.015 [0.138] 0.003 [0.435] −0.006*** [0.000] 0.217 126 85

IVOL is now measured as the standard deviation of the residuals from the CAPM model (including one lag of the market risk premium following Dimson (1979)). T is the total number of monthly regressions. R2 stands for the mean adjusted R-squared of the T monthly regressions. N is the average number of firms in the T cross-sectional regressions. p-Values for two-sided tests of a zero regression coefficient using standard errors by Newey and West (1987) are reported in brackets below coefficient estimates. *Significance at the 0.10 level. ** Significance at the 0.05 level. *** Significance at the 0.01 level.

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Table 6 Robustness check – panel regressions of stock returns on lagged idiosyncratic volatility.

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Table 7 Alphas of lagged IVOL portfolios for low- and high-volatility months.

Low-volatility months High-volatility months

P1

P2

P3

P3–P1

P2–P1

P3–P2

0.010*** [0.001] 0.001 [0.811]

0.007*** [0.001] 0.002 [0.629]

0.006 [0.169] −0.002 [0.603]

−0.004 [0.478] −0.003 [0.540]

−0.004 [0.152] 0.001 [0.739]

−0.001 [0.919] −0.004 [0.360]

We categorize a low-volatility month as one in which mean volatility (or standard deviation of returns) estimated from the sample of available stocks in the month is below the median of the average volatility series. When average volatility in the month exceeds the median of average volatility across all months, we classify the month as a high-volatility month. p-Values for two-sided tests of a zero regression coefficient using standard errors by Newey and West (1987) are reported in brackets below coefficient estimates. * Significance at 0.10 level. ** Significance at 0.05 level. *** Significance at 0.01 level.

6. Conclusion This paper analyzes the association between stock returns and lagged IVOL for a sample of MILA stocks over the period 2001–2014. We examine whether shareholders require compensation (in terms of higher returns) for bearing some company-specific risk in a market (as in Merton (1987)) in which investors are likely to be unable to diversify perfectly. We contribute to the current debate on the role of idiosyncratic risk in shaping expected stock returns and, by and large, on the extent and significance of pricing anomalies in an emerging stock market. We first recreate a portfolio strategy that invests in high IVOL stocks and shorts low IVOL stocks. If investors are compensated for assuming higher unsystematic risk, the alpha of this long-short portfolio should be positive and significant. However, we are not able to document a significant spread for this long-short portfolio, implying that investors in the integrated market were not able to profit by assuming diversifiable risk (in line with predictions of the CAPM or Fama and French (1993) models, in which only systematic risk is priced). Furthermore, in one of our robustness tests, we notice that a high IVOL portfolio is unable to significantly outperform a low IVOL portfolio (in risk-adjusted terms) following months of high or low total volatility. In an additional robustness check, we extend our portfolio strategy to two-way sorted portfolios. This approach allows us to control by one characteristic and then explore the association between IVOL and stock returns. Controlling for size, book-to-market, past returns, or liquidity effects, we confirm the inability of lagged IVOL in forecasting future stock returns. We then move to a multivariate setting using the panel regression methodology of Brennan et al. (1998). Using both unadjusted (excess) or risk-adjusted returns, we do not find a significant coefficient attached to our idiosyncratic volatility proxy. IVOL is not statistically significant in univariate or multivariate regression models that control for systematic risk factors as well as size, book-to-market, return continuation, and illiquidity effects. Overall, we are not able to document any idiosyncratic volatility effect in our sample. Several robustness tests strengthen our conclusion that the association between lagged IVOL and current stock returns is non-existent in the integrated market. For future research, it would be interesting to expand our sample to include stocks listed in the Mexican Stock Exchange (Bolsa Mexicana de Valores, BMV). BMV joined the integrated market in December 2014 (the first trade of a Mexican investor in the MILA took place that month). 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