By definition presented forth by Zhang et al.in their paper of The Cross-Section of Volatility and Expected Returns, in the journal of finance volume 61, idiosyncratic volatility is a risk affecting a small proportion of assets as opposed to the whole market. According to Zhang et al.,(2006), this risk can be done away with or mitigated through the process of diversification. Ansoff (n.d) defines diversification as a strategy whereby the risk factor subjected to a particular portfolio is eliminated through calculated and diversified investments. By investing in a number of assets, a company may reduce the possibility of loss occurrence in case of failure by some assets. In case of failure or underperformance by some asset, the others in the same portfolio cover up the losses. A balance is maintained. Idiosyncratic volatility is interrelated to the expected returns. In theory, the higher the exposure to aggregate risk or volatility, the lower the expected returns would be (Zhang et al., 2006).
Malkiel and Xu (2002) argue that investors will tend to demand compensation if they are not able to diversify their risks. If that happens, then the agents will also demand a premium for holding stocks that have a high idiosyncratic volatility. According to Malkiel and Xu (2002), the stocks of a company with high idiosyncratic volatilities are likely to be mispriced. This is because the investors do not have the capacity to internalize and digest new information in the market. As such, the investors may find themselves investing in stocks and paying a higher price than would normally be due.
Pervasiveness and scope of the anomaly across time and equity markets of different countries
Treating the expected returns and idiosyncratic volatility as having a negative relationship according to Zhang et al.,(2006), this section analyzes how the idiosyncratic volatility anomaly is varied across time schedules. Ross (1976) argue that when investments are varied over time, the risk premiums associated with the covariance between returns on asset and other variables that show the time- variation of the investment in question.
Different countries in the world employ different methodologies in their capital and investment markets to analyze the risks present in a trading strategies. Wang (2009) argue that different investors in different countries in the world are faced with different risks and as such, their modes of dealing with these risks are also different. The following discussion analyzes the effect and pervasiveness of the idiosyncratic risks when subjected to the time and equity factor.
The trading Model â€" Time factor
Here, the main concern is to understand how the idiosyncratic risks vary as the time concept is applied. Zhang et al., (2006) uses an estimation strategy and period in the format of L/M/N. L stands for months, M is the waiting period and N months of holding period. Stocks are sorted into portions based on their idiosyncratic volatility computed using daily returns for the past month. This goes on for every month and the portfolio is rebalanced each month. Afterwards, the portfolio changes each month, where each 1/12 (discounted for the whole year) part of the portfolio contains a value-weighted portfolio. According to Zhang et al., (2006), the first quintile portfolio consists of 1/12th of the lowest value-weighted or highest idiosyncratic stocks from a month ago, 1/12th of the value-weighted or lowest idiosyncratic stocks from 2 months ago and the cycle goes on. This is done so as to level the volatility against a particular time period to get rid of underlying factors.
The equity factor
Idiosyncratic volatility has a substantial effect on the level of future returns of a company. To get the effect of idiosyncratic volatility on expected future returns, Zhang et al., (2006) takes a sample of portfolio and conducts a number of experiments on a number of equities in the portfolio. The average returns per month are taken, bearing the risks involved. The low volatility stocks are sampled and the way they vary when the volatility is increased is observed. After this experiment, Zhang et al., (2006) observes that the average returns drop very rapidly and to very low levels when the idiosyncratic volatility is increased. When the volatility is lowered, the average expected returns increase. According to Johnson (2004) states that firms having a higher idiosyncratic volatility may exhibit a higher current equity value than companies with lower idiosyncratic volatility, but exhibit lower expected equity returns on equity given the fixed terminal value of the company.
This serves to stamp in the connotation by Zhang et al., (2006) that the expected returns of equity are negatively related to the idiosyncratic volatility.
Relationship between the expected returns and idiosyncratic volatility
According to Jian, Xu & Yao (2007), a negative relationship exists between the idiosyncratic volatility and the future returns. The experiment and samplings that were made by Zhang et al., (2006) using equity and different risks, keeping all other factors constant, have shown that the levels of expected returns matched with the idiosyncratic risks keep reducing as the level of risks are increased. Chen & Chollete (2006) stipulate that high volatility relates to the heightened possibility of a firm having financial and agency distresses.
Idiosyncratic volatility anomaly challenged: Does diversification eliminate this volatility?
The notion presented forth by Zhang et al., (2006) that the higher the idiosyncratic volatility or risk that a particular company is exposed to, the lower the level of the expected returns on investment has been put to test by a number of scholars who find this notion not fully abiding or sustainable. According to Zhang et al., (2006), diversification almost eliminates the idiosyncratic volatility.
Frieder & Jiang (2007) argue that the fact that investors can predict future returns on investments based on recognized volatility presents a challenge to the theoretical asset pricing models which were brought to light by Markowitz (1952) and Sharpe (1964). Berrada & Hugonnier (2011) argue that the fact that investors are biased in their notion of the growth rate of dividends and does not institute a reward for risk bearing. This depends on the idiosyncratic volatility and the investors' perception of the growth rate.
Investors do not have full information when it comes to their investment decisions (Xu & Cao, 2010). There exists an information gap, where information dissymmetry may translate to the investors buying stocks at price that are higher than normal, or buying stocks that have a higher idiosyncratic volatility. Investors need to have full information regarding the value of expected returns of some stock, the risks involved and other underlying values which serves to allow them to make informed judgments concerning the investment undertaking they wish to do. Diversification does, to some extent eliminate the risks in a market. However, diversification cannot fully eliminate risks in the market.
Implications of idiosyncratic volatility anomaly on the models of asset pricing and theoretical foundations modern finance
Idiosyncratic volatility anomaly has a substantial effect on the asset pricing models and the modern finance foundations. These models are the Capital asset pricing model (CAP-M) as stipulated by Markowitz (1952), the Sharpe (1966) and the Black-Litterman and they form the basis of modern finance. Players in the finance world today borrow much from these models of asset pricing. According to Berrada & Hugonnier (2011), in the presence of favorable and full information of the market the company with larger idiosyncratic volatility translates into the company producing larger risk-adjusted expected returns and in contrast, in the scenario of lack of information or information dissymmetry, the company will translated into producing low rate returns.
The effect on equity of a firm because of idiosyncratic volatility translates into the profound effect the way the stock is priced. High risks associated with an asset will result into underinvestment or total shun of the stock. Investors will go for the stocks that promise highest returns to investment with the minimal of risks involved.
Conclusion
The idiosyncratic volatility anomaly as presented by Zhang et al., (2006) plays a fundamental role in the development and growth of the modern finance today. The baseline proposition of the anomaly that the level of expected returns of a stock decreases as the level of risk, or volatility is increased provides a key approach to models of investment. If all factors are kept constant, that is, there is information asymmetry, and the information is available to all parties freely in the market, the baseline proposition holds ground. The vice versa is also true. In a normal market economy, the factors that are sidelined by the idiosyncratic volatility anomaly cannot be absent or ignored. Despite these challenges that other scholars have argued against the anomaly, it still retains its viability. With such put into consideration, this anomaly is certainly anomalous.
