Inventory costs models presented by Stoll (1978), Ho and Stoll (1981, 1983), O’Hara and Oldfield (1986) among others, describe dealers as having two functional roles in the market. First, dealers are providers of immediacy (they stand ready to trade in a security at any time); and second dealers act also as optimizers of their own portfolio. Under this framework, dealers try to choose the best possible portfolio, the one that maximizes their utility (for more details see Chapter 2). While a dealer is performing the above two functions the role of volatility in trading volume in determining dealers spreads becomes relevant. When a dealer provides immediacy his portfolio will deviate from what he considers optimum, hence he will adjust his bid-ask quotes to deter more
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transactions on the side of the non-optimum portfolio direction and make sure that the bid-ask spread is at least enough to compensate for the further utility losses. This implies that larger transaction sizes in the order flow expected will lead to larger spreads. However, if trading volume is expected to come in many smaller, independent orders, then increased (predictable) volume could decrease spreads through an opposite inventory cost effect. Taking in to consideration that larger volume is not necessarily driven by larger transaction sizes since dealers may break down large transactions in several smaller ones, it is unlikely that inventory cost effects can be identified though daily volumes and spreads.
To summarise we can say that models that explain bid-ask spreads in terms of inventory costs establish a link between bid-ask spreads, volatility and trading volume. One determinant of inventory costs is the cost of maintaining open positions. Therefore, exchange rate volatility will increase price risk and thereby push spreads up.
Another determinant of inventory costs is trading activity. Empirical research shows that trading volumes can have different impacts on spreads depending on whether they are expected or unexpected. Black (1991) introduces a theoretical approach to estimate the impact of volume on bid-ask spread. In particular, the author is using a model of transactions costs in the interbank foreign exchange market and a model of vehicle currency use to explore the interaction between transaction costs and vehicle currency use.
Chakrabarti (2000) builds a model of bid-ask spreads in the foreign exchange market based on the idea that dealers learn in a Bayesian fashion about the excess demand situation from one other’s quotes and their inventory positions (their overnight costs). He develops a dealer’s objective function and is assumed that the dealer task is to maximize this function. The function includes the expected gains during the day, the cost of bearing the risk during the day and the cost of expected overnight exposure. The assumptions built in to the model are
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that trading takes place for a few hours each day, that individual dealers are risk averse, and that two currencies are traded at a particular financial centre (DM and US dollar). The objective function of a representative dealer at the beginning of a trading and the model are presented in Appendix 3.
The dealer is faced with two inventory risks. The risk of taking a position at any point in a day until he receives or succeeds in making another call and the risk of holding an inventory position overnight. Obviously, the risk of holding inventory overnight is much higher due to the longer time period; therefore, the dealer will set a higher price.
To study the extent to which dealers behave according to this model, the author created artificial traders and provided them with beginning positions in DM as well as beginning prior beliefs about the end-of-day value of DM and made them to act according to the model in a virtual market. The results from the simulations show that trading according to the model in many cases produces a U-shaped pattern in spread, spread volatility, and return volatility. This is in line with empirical research [Hsieh and Kleidon (1996), Bollerslev and Domovitz (1993)]. In particular, from the simulation they find that the spread in the morning is about 138% higher than the average spread, excluding the beginning and end, during the day. At the close of the trading the spread is about 95% higher than the spread measured in the rest of the day. Similar results are obtained for spread volatility. The return volatility at the beginning and close of a trade exceed the daytime average by about 7% and 38% respectively. Therefore, we conclude that the theoretical model presented by Chakrabari provides a more than acceptable framework to explain the U-shape pattern observed in most intra-day trading data.
In an empirical paper, Bessembinder (1994) used regression analysis to examine the relationship between spreads and inventory costs. To investigate whether spreads depend on inventory costs he uses three proxies for inventory costs:
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forecasts of price risk, interest-rate based measures of liquidity costs, and a non- trading indicator to capture Fridays and the last trading day before holidays. Results are generally consistent with the implication that currency bid-ask spreads widen with inventory carrying costs. In particular, the estimated coefficient for the effect of forecasted risk on currency bid-ask spreads is positive and significant for all currencies examined and end-of-day spreads are positively related to the anticipated riskiness of holding a position in the currency over the next trading day. Finally, the results are also consistent with currency bid-ask spreads varying positively with the opportunity costs of maintaining a liquid inventory. The estimated coefficient of the interest-rate based proxy for opportunity cost of liquidity is positive for all currencies considered.