The cross-section of volatility and expected returns

The cross-section of the volatility and expected returns
The main research question revolves around determining the rank of the stochastic volatility of the marked is in terms of its price within the cross section of expected returns. Basically, the question tries to determine whether the volatility state of the market is priced in a risky manner so that the price of the aggregate volatility risk can be calculated. Frequently, there has been much estimation regarding the possibility of any market to have a negative or positive price risk on the market volatility. Another vital question is examining the cross-sectional relationship between the expected returns as well as the idiosyncratic volatility (Ang et al., 2006). The questions may fall in different dynamics in regard to the context of the market that has to be explained. Despite the fact that volatility is an unknown variable, it is also clear that there are other stock and return market factors that are variable. In order for the question to be addressed properly, it is important therefore to set constant measures.
It is discovered that innovations that occur in aggregate volatility usually carry a comprehensive negative price risk that is usually estimated at -1% per year. There are many reasons according to the economic theory that explains the reason the price of risk of the innovations within the market volatility is negative. It was also found that creating portfolios through mostly sorting the idiosyncratic volatility usually provides no difference in the average returns (Ang et al.

, 2006). Both results were based on the evaluation of variables established for the study to tally the aggregate volatility against the cross-section volatility and expected returns. Most of the study was focused on the volatility components and not the expected returns.

The table above shows the representation of correlations among the entire FVIX factor, STR, VIX and the correlation among these variables and other cross-sectional variables. Daily differences can be noted from VIX whose similar volatility factor can be denoted at a daily frequency having a correlation of 0.91. On the other hand, the correlation between FVIA and VIX is, however, lower on a monthly frequency of 0.70. FVIX and STR, on the other hand, have a correlation of 0.83, indicating no difference of FVIX that was formed from stock returns and STR that was formed from option returns (Ang et al., 2006). However, there is also a negative correlation in tally between FVIX and the liquidity factor LIQ according to Pastor and Stambaugh (2003) which rests at -0.40.
There are many other tables such as the portfolio comparison table that were drawn as a result of the study. Despite the fact that most of the tables use a different logic, they all zero towards the resolution of the two major questions explained at the beginning of the paper. It is also clear from the results that the average returns are mostly associated with the level of sensitivities to the innovations in relation to the aggregate volatility. The Fama and French model are also one of the most vital tools used in the evaluation of the average returns. It is, therefore, clear that there are many aspects that determine the varying nature of the volatility stocks. It is also clear that the returns that result from the calculations also vary depending on the type of theory used to express them.
References
Ang et al. (2006). The Cross-Section of Volatility and Expected Returns. The Journal Of Finance• VOL. LXI, NO. 1
Pastor, L & Stambaugh, R.F. (2003). Liquidity Risk and Expected Stock Return. The Journal of Political Economy