Auctionettes: Slightly Better Handling of Tied Bids

Julian D. A. Wiseman

Abstract: publishing the scaledown could be a slight leak of information about the distribution of bids at an auctionette. This information should be hidden.

Publication history: only at www.jdawiseman.com/papers/finmkts/auctionettes_tied_bids.html. Usual disclaimer and copyright terms apply.

Contents: Background; The Problem; The Non-Solution; The Solution.

Background

The author has previously suggested a new auction mechanism for the sale of government debt. This would achieve a slightly higher price on average, and guarantees selling the debt at a price close to that prevailing in the secondary market. This essay suggests a very marginal improvement to the new mechanism.

The new mechanism proposed splitting an ordinary auction of, say, £4bn, into forty ‘auctionettes’, conducted one minute apart, and each being uniform price. This is described in detail in Methods for Distributing Gilts: A Reply, being written in response to the consultation published by the UK Debt Management Office on 17^th December 2008. Readers unfamiliar with the proposal described therein will obtain little value from the remainder of this short note.

The Problem

How should tied bids be handled? Previously the author had, rather lazily, proposed continuing with the current practice: bids exactly at the cutoff price to be partially filled, with publication of the proportion of the lowest accepted bids that were filled (the “scaledown”). But part of the purpose of the current mechanism is to protect a ‘lonely bidder’ by hiding information about quantities of bids received and the distribution of prices. Publishing this scaledown number could be a very slight leak of this information.

For example, if the scaledown is rounded to the nearest whole percentage point, a scaledown of 1% or 99% implies a denominator of at least 67. So if bidding is in multiples of £1mn, there were ≥£67mn of bids at the lowest accepted price; and therefore with a auctionette size of £100mn, a scaledown of 99% implies that there were at most £34mn of bids above the lowest accepted price. Probably, a single bidder bought most of the auctionette, having bid at a single price. Similar reasoning applies to a scaledown of 2% or 98%, implying a denominator of at least 40; 49% or 51% ⇒ ≥35; and 3%, 34%, 66% or 97% ⇒ ≥29.

Even though this information is of only little use to other bidders, some bidders might fear that other bidders could use it. As this information can be hidden, it should be.

The Non-Solution

The obvious solution is simply not to announce the scaledown. But some bidders may well have bid for multiple minimum units at the lowest accepted price, and so by observing the proportion of their own bids that were filled, will have an estimate of the scaledown. Even though the information that can be derived is very slight and statistical, there might be merit in reassuring bidders that any loneliness cannot be known by others, even in this probabilistic sense. Hence a better solution is preferable.

The Solution

The recommended course is to change what happens to tied bids. First, gather together bids by the same market maker: multiple bids at the same price being added into a single bid at that same price. Of the bids at the lowest accepted price, one is chosen at size-weighted random. If that bid can be filled in full, it is, and if the whole auctionette is not yet assigned, the process is repeated with another bidder’s cutoff-price bid. And if the chosen bid is for too large a quantity to be filled in full, it is filled as much as possible and no further bids at this price are filled.

So at most one market maker will have a partial fill. Others either have no bids at the clearing price; or all at the clearing price were rejected; or all at the clearing price were accepted. This makes it impossible for a market maker to establish a non-trivial range for the scaledown.

For example, consider a bidder who had bid for £5mn at the cutoff, of which £2mn is filled: what is thereby learnt? It could be that every other participant bid at this price, and was filled in full or not filled at all. And it could equally well be that no other bidder had bid at exactly this price. Nothing is revealed. And if a bid at the cutoff is unfilled, all that is learnt is that there was at least one other bid at this price: again, nothing new is revealed. Thus lonely bidders are protected to the maximum extent possible.

So the new plan is that the only information released after each auctionette would be the clearing price, and, derived from this, the minimum price of the following auctionette. (Though if auctionettes after the first are not of uniform size, then there could be a reminder of the size of the next auctionette.)

But, for emphasis, it is stressed that this is a minor tweak of slender importance.