A Theoretical Model And Empirical Analysis Of Components Of Spread In Over The Counter Exchange Of India

Abstract

Over the Counter Exchange of India (OTCEI) was established in 1992 mainly to provide a platform for small and medium sized companies to raise money for their capital requirements. It is a well defined dealer market with market makers giving bid and ask quotes. It was established with state-of-the art technology with ringless, scripless trading.

In this study, we develop a theoretical model to decompose spread into its three components in a dealer market. This model is further empirically examined by using OTCEI data. We find that Inventory holding cost to be the highest on OTCEI followed by Adverse Information cost and Order Processing cost. The result reflects market microstructure which is peculiar to OTCEI.

The methodology developed in this study is basically a generalization of S toll's (1989) methodology. . Roll(1984) shows that in a pure order processing world, spread equals the square root of negative of serial covariances of successive differences of transaction prices. Stoll (1989) relates spread to the covariance of successive difference of transaction prices and that of the quotes. Stoll introduces two parameters, 5, which is a measure of magnitude of price change and JI, the probability of reversal of type of transaction, that is, from Bid to Ask or vice-versa, to model the Bid/Ask price movements from one transaction to the next. Thus Stoll, from this model, establishes a theoretical relationship between serial covariances of successive differences of transaction and quote returns and spread. 5 and n are estimated via regression of serial covariances of transaction and quote, returns on average proportional spread square. With these two parameters, Stoll finally decomposes spread into three components.

δ, is the amount of price change between transactions for two reasons- Inventory holding reason and adverse information reason. Stoll explains these price changes due to two reasons with just one parameter, 5. This forms the main motivation of this study. In our study, we let 8 assume two different values, 5i and 82 which attempts to capture the price changes due to the two different causes viz inventory holding and adverse information. It is convenient to think of these two S's being associated with two different states of transactions. However, these states themselves are indeterminate . In other words, the price change could be due to inventory reasons, or due to trading with an informed trader, or due to both. Thus, while Stoll assumes only one 8, in our study, we have two different values of 8. Thus, with three parameters, 81, 82 and n, this study attempts to estimate the relevant parameters and realistically decompose the three components of spread in a dealer market.

Just like Stoll, the developed theoretical model also relates serial covariances of transaction price changes and quoted price changes to spread square. However, unlike Stoll, now there are 3 parameters, namely, 5j, 82 and n. As it is impossible to solve three unknowns with just two equations, it becomes necessary to introduce one more equation relating the three parameters to the spread. It is here that we introduce, for the first time, the serial covariance of the second order differences of the transaction price changes, which is related to spread via an equation. Intuitively, we can explain this relationship using Roll's result. Roll(1984) has shown that spread equals square root of the negative serial covariances of transaction price changes in a pure order processing world. Since the second order difference is nothing but the rate of price changes, it also must be related to spread, since the price change themselves are related to it, empirically, we find that spread square significantly affects the serial covariance of second order difference of price changes as well.

Besides explaining the price changes with just one 5, Stoll's method of decomposition is not realistic. Though his method of decomposition does yield three components of spread, in reality, it lumps Adverse information cost and Inventory holding cost together. In our study, we make use of the state-of-the art Huang and Stoll's (1997) methodology of decomposition of spread. We first embed the developed theoretical price-movement model into that of Huang and S toll's this yields a functional relationship between 5i and 52 and a and |3 of Huang and Stoll, which directly refers to the adverse information and inventory holding components respectively. Thus, in our study, we realistically decompose the components of spread and OTCEI and empirically too, we find that the components estimated from our methodology does reflect the market microstructure of OTCEI.

Apart from developing and empirically testing the theoretical model, we also see if it fits the observed data on OTCEI. We find that the theoretical model does not exactly conform to the observed data in OTCEI, necessitating some empirical fine-tuning. We build an empirical model which is again used to get the three components of spread.

We also estimate components of spread in OTCEI using Stoll's and Huang and Stoll's methodology and we compare them with the estimates obtained using our methodology. We find that Stoll's methodology overstates the Adverse information component of spread and understates the inventory holding component of spread and Huang and Stoll's methodology and Our methodology and model yields estimates of components of spread which is more in tune with the market micros tructure of OTCEI. The estimates obtained from empirical model too conforms to the market microstructure of OTCEI.