“The idiosyncratic risk during the Covid-19 pandemic in Indonesia”

Conservatism in the CAPM and L-CAPM standards often emphasizes systematic risk to explain the phenomenon of the risk-return relationship and ignores idiosyncratic risk with the assumption that the risk can be diversified. The effect of the Covid-19 outbreak raises the question of whether the idiosyncratic risk can still be ignored considering that the risk has a close relationship to firm-specific risk. This study sets a portfolio consisting of 177 active public firms in the Indonesia Stock Exchange before and after the Covid-19 pandemic. On portfolio set, idiosyncratic risk is estimated by the standard CAPM and L-CAPM in the observation range from January 2, 2019, to June 30, 2021. The results of the analysis show that L-CAPM and CAPM produce sig- nificantly different idiosyncratic risks. Empirical evidence shows that the highest firm-specific risk is in the third period and has a stable condition since the fourth period. This condition is confirmed by regression results that idiosyncratic risk together with systematic risk positively affects stock returns in the fourth period as suggested by the efficient market hypothesis. Uniquely, both systematic risk and idiosyncratic risk based on L-CAPM do not show a significant effect on stock returns in the fifth period, so it is a strong indication that liquidity is an important factor that must be considered in making investments. et al. also demonstrate that the risk premium and expected stock returns are correlating positively. Confirming those results, support that firms with higher systematic risks have higher returns as the market risk premium is positive but they will have lower returns as the market falls. that the idiosyncratic or unsystematic holds its role in circumstances of a not well-diversified portfolio.


INTRODUCTION
The capital asset pricing model (CAPM) is the most effective in explaining the risk and return relationship. In the context of CAPM, the risk itself refers to the systematic risk. Tinic and West (1984) prove that the stock return is mostly affected by systematic risk. Lakonishok and Shapiro (1986) provide evidence that systematic risk could be positive to stock return when the market is at normal condition but negative while the market is down. French et al. (1987) also demonstrate that the risk premium and expected stock returns are correlating positively. Confirming those results, Theriou et al. (2010) support that firms with higher systematic risks have higher returns as the market risk premium is positive but they will have lower returns as the market falls. Lakonishok and Shapiro (1986) provide interesting evidence that the idiosyncratic or unsystematic risk holds its role in circumstances of a not well-diversified portfolio. Malkiel and Xu (1997) noticed that idiosyncratic risk arises from specific events and can be diversified. In most cases, it can be assumed that the Covid-19 pandemic is a specific event that influences the capital markets around the world through firm-specific risk such as reported by He  The efficient market hypothesis (EMH) relies on the concept that stock prices fully reflect all available information (Fama, 1970(Fama, , 1991(Fama, , 1998Fama & MacBeth, 1973). Pontiff (2006) states that market efficiency means the stock prices are directly affected by the information. On the concept, the hypothesis posits that under the condition of uncertainty higher risks result in higher returns (Markowitz, 1952;Lintner, 1965). Consistent with Lintner (1965), Fama and MacBeth (1973) find that both systematic and unsystematic risks move linearly with the optimum returns. They propose that most investors shall face the risk for desired returns in terms of the efficient market. However, as a limitation, Borges (2010) suggests not applying the EMH to emerging and illiquid markets, as they are generally not efficient.
Many studies use asset pricing models to explain the risk-return stock relationship in the capital market under the assumption of uncertain conditions with the information provided according to the EMH. The original CAPM assumes that idiosyncratic risk could be ignored in the assumption that the investors set the portfolio at best to diversify this risk (Wei & Zhang, 2005;Bali & Cakici, 2008). However, Fama (1991) emphasizes that the risk of firm business conditions also affects the asset pricing model. According to Malkiel (2003), there is a condition that stock betas tend not to be the main risk if investors tend to compile their portfolios by considering large company sizes with high liquidity levels. Supporting the opinion of Fama and French (1993), Malkiel (2003) agrees that there are other factors (for example firms that have a certain level of financial distress) that are not taken into account by the CAPM so that they tend to justify the systematic risk. Kumari et al. (2017) find that high idiosyncratic risk is relevant to the under-diversified portfolios by investors. Pontiff (2006) argues that idiosyncratic risk is not a myth but it plays a significant role in determining whether the market is efficient or not.  Le and Gregoriou (2021) in the United States market confirms that a portfolio based on the highest level of liquidity can provide the best asset valuation model. In another case, Baker and Stein (2004) demonstrate that a high level of market liquidity reflects positive investor sentiment on securities with high systematic risk but low returns. Their findings seem to support Jacoby et al. (2000) who find that market liquidity cannot be separated from systematic risk. Loukil et al. (2010) explain that the possibility of a positive relationship between illiquidity and stock returns is due to the tendency of investors to prefer stocks with low liquidity levels to get the expected premium or less trade the securities to reduce the impact of liquidity risk. Acharya and Pedersen (2005) develop the further CAPM into liquidity-adjusted capital asset pricing model (L-CAPM), which assumes that the required returns depend on its liquidity factor together with the covariance of stock return and liquidity and the market return and liquidity. Recently, some empirical evidence has used L-CAPM to explain the risk-return relationship. Kumar et al. (2019) demonstrate that L-CAPM explains the risk-return relationship. It was found that liquidity is priced both for the systematic risk and idiosyncratic risk, which means liquidity is an important factor to determine those risks. In similar, Altay and Çalgıcı (2019) also emphasize that low illiquidity means high liquidity that gives higher returns. They also find that the original CAPM cannot explain the stock return behavior in emerging markets. Confirming those results, Grillini et al. (2019) find that negative market risk in L-CAPM depicts a possibility premium by liquidity risk to investors.

The hypothesis development
Most relevant studies explain the role of idiosyncratic risk based on CAPM. At the first point, Lintner (1965) emphasizes that the relevant risk of firm stocks depends on not only its market risk but also the total variance. The finding of Lintner (1965) can be interpreted as that idiosyncratic risk also affects the stock return significantly. Confirming the result, Goyal Table 1 presents the comparison of idiosyncratic risk between models. The mean difference test shows that models 1 and 3 are significantly different from model 2, which indicates that L-CAPM slightly reduces the effect of idiosyncratic risks rather than CAPM. The results imply that illiquidity risk is a factor causing the difference between CAPM and L-CAPM, which is consistent with Jacoby et al. (2000). On findings, set better portfolio will produce a well-diversified idiosyncratic risk as suggested by Amihud (2002), and Acharya and Pedersen (2005). The test also provides unique results for the first and fifth periods: the idiosyncratic risks based on model 1 and model 3 are significantly different. The first period is the normal period before the impact of the Covid-19 pandemic.

RESULTS
If it assumes that the fifth period has a similar condition with the first period then the portfolio will capture the picture of idiosyncratic risk as the normal conditions. Wei and Zhang (2005) suggest that the idiosyncratic risk is not sustained over time, which means specific-firm risks are random in normal conditions.
Based on the portfolio, the comparison of idiosyncratic risk between periods is examined in Table 2.
On results, the three models show that the third period has the highest idiosyncratic risk, which indicates that there is a higher reaction due to the Covid-19 pandemic comparing to previous or further periods. Another interesting result is that the conditions of the fifth and fourth periods do not have a significant difference. This finding confirms the previous result that the existing portfolio can diversify the idiosyncratic risk in the fourth and fifth periods or in other words, those periods are under stable conditions.
Furthermore, the effect of idiosyncratic risk is tested with systematic risk as a control variable by employing the logistic regression as presented in Table 3. In the first, third, and fifth periods, without systematic risk as a control variable idiosyncratic risk based on L-CAPM and CAPM gives different signs of coefficient. However, adding systematic risk, idiosyncratic risk by L-CAPM (except CAPM) gives consistent coefficient signs. Otherwise, in the second and fourth periods, regression results without control variables show that three models give similar coefficient signs for idiosyncratic risk. Consistently, the regression of the three models after adding the systematic risk keeps giving similar coefficient signs for those periods particularly for the fourth period which is fit with our hypothesis. Overall, the models based on L-CAPM give the same explanations about the picture of idiosyncratic risk together with systematic risk. On results, idiosyncratic risk cannot be ex-plained separately from systematic risk. The results of the analysis also show that market liquidity must be taken into account to set the portfolios in order to diversify idiosyncratic risk.  with firms with lower returns as the reference. The independent variables are idiosyncratic risk (the residuals) and systematic risk (coefficient of determination) as a control variable. *, **, and *** indicate significance at 10%, 5%, and 1%.

DISCUSSION
This section emphasizes the explanation for idiosyncratic risk. This study reports that all systematic risks of all models show a positive coefficient for all periods even though they have different levels of significance. The findings also show that idiosyncratic risks (after including systematic risks) have largely the same explanation in the context of CAPM and L-CAPM. In the first period, the model of Kumar

CONCLUSION
The relationship between risk and return in the context of the EMH is mostly done using the CAPM approach. An understanding of the standard CAPM concept tends to focus only on systematic risk to explain the relationship between risk and return. The background of this understanding is due to the assumption that unsystematic risk or idiosyncratic risk can be diversified by a good portfolio set. Some previous studies developed the CAPM standard into L-CAPM with the consideration that market liquidity risk also affects the total risk of a security in the capital market. The results of the development of the CAPM into L-CAPM indicate that market liquidity also influences the idiosyncratic risks that arise due to company-specific risks. For decades, most empirical evidence still maintains the assumption of idiosyncratic risk until the world finally experienced a shocking outbreak, namely the Covid-19 outbreak. The outbreak of Covid-19 has a bad impact on the capital market around the world including the market in Indonesia that questioned the assumption of idiosyncratic risk in relation to returns still holds true in the concept of asset valuation models.
This study aimed to examine the impact of idiosyncratic risk on stock returns during the Covid-19 outbreak based on the portfolio set of listed firms since 2019. The results of the analysis show that the idiosyncratic risk for each period estimated based on the L-CAPM has a significant difference from the results obtained from the CAPM. These results indicate that market liquidity cannot be ignored in establishing firm-specific risk. In addition, it was found that idiosyncratic risk has the highest value in the third period, which indicates that there are abnormal internal conditions for the firms in this period. However, idiosyncratic risk shows stable conditions in the fifth period for firms on the portfolio basis, which indicates quite encouraging internal conditions in this period. This condition is confirmed by the regression test, which shows that idiosyncratic risk together with systematic risk has an insignificant impact on stock returns in the fifth period. Empirically, these results indicate that there are stable internal conditions for firms that are on a portfolio basis in the fifth period, especially in terms of financial performance when using the L-CAPM approach. On the other hand, the idiosyncratic risk still shows an important problem with stock returns in the fifth period as evidenced by a significant negative when using the CAPM approach. This indicates that the asset valuation model with the CAPM approach does not fully capture changes in market liquidity and its impact on idiosyncratic risk. However, the idiosyncratic risk by the CAPM approach also indicates that the problem of stock returns is not in the firm's internal conditions but by its market liquidity factor.