As I discussed in my last post, effective fed fund rate responded to announcement of target rate changes immediately even before open market operation. The most important reason for this phenomenon being that FOMC communicates the new target rate to the market more explicitly. Apparently, expectation about fed behavior has widely formed in the fed fund market, but how does this expectation formed ?
To understand how rational expectation plays a part, it is important to understand that fed fund market know the reaction of fed trading desk towards a change of target rate, and they take this reaction into account when they choose how much funds to buy. So what is the reaction function of the trading desk and what is the trader’s demand for fed balance? In Taylor’s paper, the reaction function is:
where bt stands for the supply of fed balance at time t. r superscript e stands for effective fed fund rate and r superscript t stands for fed fund rate targets. This function means that the supply of fed balance the trading desk trying to manipulate today depends on fed balance yesterday and the deviation of effective fed fund rate from target yesterday. The second part reflect the truth that FOMC directs the trading desk to but and sell securities so that conditions in the federal funds market are consistent with and average federal funds rate near the targets.
This reaction function is known by all the fed fund traders through their day to day interaction with the trading desk.
What does fed fund trader trying to achieve when they participate in the market? They try maximize the banks profit by getting the cheapest fed funds! And they no only try to get the cheapest deal today, but also tomorrow. So if they predict that fed fund rate will change tomorrow, they will react today. For example, if they predict that fed fund rate will rise tomorrow, they will buy more reserve today, and the effect which is that the fed fund rate will rise today!
the demand for fed fund by each trader at a particular day is characterize as:
if we ignore alpha and gamma for now, we can interpret the function as the demand for fed fund depends on the difference between fed fund rate today and the expectation of fed fund rate tomorrow. The expectation of future rate is a forecast by fed fund traders incorporating all the information available today and the rational expectation of fed trading desk’s reaction tomorrow. If they expect the fed trading desk will perform OMO that bring up fed fund rate tomorrow, they will demand more fund today.
Given our two reaction function above, we have enough ingredients to tell a story of how fed fund rate adjust to new target rate even without OMO.
suppose that the fed announced today that the target will rise by 0.5 basis point. What will trading desk do? Unfortunately, trading desk cannot do anything that day because its reaction function depends on yesterdays information, before the FOMC announced the new targets. This is especially credible given the fact that the trading desk typically enter into the market at 9:30 am before the day of trading start. Again, the trading desk increasing or decreasing of the fed balance is based on estimation of last period’s information.
On the other hand, traders in the market know all the information, both the fact that target is changing and that trading desk perform OMO tomorrow to bring fed fund rate up to new target. The trader formed rational expectation given its own demand function and reaction function of the desk. Knowing for sure that the future fed fund rate will rise, traders will try to buy more funds today to avoid higher expense tomorrow. This increase the total demand in the market and eventually, the market move before the trading desk perform OMO the next day, bringing effr jump a huge step, nearly reaching the new target rate.