The relation between stock price volatility and traded volume represents an open and challenging question, from both a theoretical and empirical point of view. The plethora of works appeared in the last decades on the causal relationship between traded volume and volatility achieved inconclusive or even contradictory results. Despite the old adage of Wall Street stating that it takes volume to move prices, a number of empirical works validated also the opposite implication, supporting the view according to which the volume weighs more in bull than in bear markets.
The literature concentrated mainly on two information theories: the Mixture of Distributions Hypothesis (MDH) and the Sequential Arrival of Information Hypothesis (SAIH). The MDH posits that volume and volatility are driven by the same information flow; therefore, they change simultaneously as soon as information is processed. Thus, the basic MDH does not consider effects as the lagged reactions to news or the interaction among types of traders. This simplification is questioned by the SAIH, which posits that the asymmetrically distributed information spreads sequentially from one trader to another and finds evidence of a lead-lag relationships.
The apparently contradiction in signs of the volume-volatility relation is the first motivation of this project, whose main purpose is to re-examine the contemporaneous relation from the perspective of market liquidity (and, ultimately, efficiency). If some our preliminary results confirm the MDH, when we control for the market liquidity, the relationship seems to reverse in illiquid phases. Our findings seem to suggest that when market behaves efficiently a positive correlation appears; vice versa, when market becomes inefficient a negative correlation arises. If confirmed by the research project, these findings could provide a rationale for the dichotomic results achieved by current literature.
The innovativeness of the research lies in several aspects. First, a very recent methodology is used to describe the degree of market liquidity. This aspect is important in itself, since it is clear to everyone the fundamental role that the (lack of) liquidity plays in the explosion of financial crises. Since lack or excess of liquidity are both symptoms of markets that do not work efficiently, the idea of capturing the dynamics of liquidity through deviations of the Hoelder exponent from the case in which the price process is a semi-martingale (and therefore efficient) is in itself an extremely novel aspect.
A reliable dynamic estimation of this exponent represents a first challenge that the project intends to pursue, also thanks to the fact that a large number of works on this subject are now beginning to emerge. The confidence of being able to successfully apply this methodology also to the case of the volume-volatility puzzle is based on the fact that the proponents of the project have been working for years on the topic of estimation of liquidity related to efficiency and are recognized in the international scene as authors of reference for the financial applications of the theory of estimation of the point regularity of multifractional Brownian motion (this is also testified by the fact that just in the last two years the PI has been invited by three international journals as guest editor for special issues on the topic of fractional and multifractional applications to the economic-financial field).
Along with the estimation problem, an element of strong innovation lies in the possibility of analytically deducing a formula that links the pointwise regularity of the process to volatility. This would also legitimize on the theoretical level the use of Hoelder's exponent in the volume-volatility puzzle. The obvious advantage would be to express volatility not in purely relative terms, but in absolute terms with respect to the level of liquidity perceived as physiologically fair for an efficient market.
Finally, a third element of strong originality lies in the decomposition of the volume-volatility relationship with respect to the degree of liquidity, but without requiring a sequential analysis of the data or a decomposition of the time intervals by homogeneous periods. In fact, having a pointwise estimate of liquidity allows for conditional analyses, in which the conditioning event is independent of the temporal proximity of the data itself. This is obviously a strength of any analysis.