Julia Giese and Charlotte Grace
In response to the global financial crisis, the Bank of England (BoE) began using Product-Mix Auctions (PMA) to provide liquidity insurance to financial institutions. The PMA, designed by Paul Klemperer, allows the quantity of funds lent against different types of collateral to react flexibly to the economic environment and market stress. It maximises overall surplus, or ‘welfare’, assuming bidders bid their true values for loans. Mervyn King, the then BoE Governor, described the BoE’s use of PMAs as ‘a marvellous application of theoretical economics to a practical problem of vital importance‘. In this post, we describe a staff working paper that shows that the PMA generates welfare gains relative to simpler alternative auction designs, which cannot achieve such fine-tuned responses.
The BoE’s design: A Product-Mix Auction
The PMA jointly determines the quantities of funds lent against different types of collateral. In the period that we study, June 2010 to January 2014, collateral was grouped into two sets: Level A, which includes gilts, sterling Treasury bills and certain sovereign and central bank debt, and Level B, which includes less liquid sovereign debt and certain asset-backed securities. Ahead of the auctions, the BoE announces a maximum quantity of loans to supply. The BoE also privately commits to a ‘relative supply’ curve which expresses the minimum spread the BoE is willing to accept for Level B collateral relative to Level A. (In the most recent update of the PMA, participants have the option to use a third ‘Level C’ collateral set and the BoE’s total supply depends on the bids received.)
The PMA implements the competitive equilibrium prices and quantities and therefore maximises welfare, assuming – as we will throughout our analysis – that the BoE’s supply curves express the optimal relationship between price and quantity and that bids express bidders’ true values for loans. This bidding behaviour is approximately optimal under reasonable assumptions and is demonstrated empirically by forthcoming research.
Figure 1 provides an illustrative example of the PMA: for the demands shown, 50% of total supply is allocated against each of Level A and Level B collateral. Total bidder surplus is the sum of differences between bids and auction prices, summed across the quantities allocated. BoE surplus is measured by the difference between welfare and total bidder surplus.
Marginal welfare is 3 basis points (bp) for both sets of collateral at these allocations: the marginal bid on A is 3bp and the marginal price the BoE is willing to accept for A is 0bp; the marginal bid on B is 16bp and the marginal price the BoE is willing to accept for B (equal to the relative supply curve evaluated at 50%) is 13bp, giving a difference of 3bp. This allocation maximises welfare because the marginal welfare is the same for both collateral sets, so the sum of the surpluses cannot be improved by choosing a different allocation.
In response to a different set of bids, corresponding to a different pair of demand curves, the PMA would automatically adjust the shares of the maximum supply lent against each collateral set in order to maximise welfare.
Figure 1: Illustrative example of surpluses in the PMA at clearing prices,
𝒑𝑨 = 3𝐛𝐩, 𝒑𝑩 = 16𝐛𝐩, and 50% of total supply lent against each of Level A and B collateral
Comparing the PMA to alternative auction designs
We use a data set of all bids submitted in the Indexed Long-Term Repo (ILTR) auctions in our sample period, as well as the BoE’s private supply curves. Under our assumptions, the data correspond to the prices the bidders are willing to pay, and the BoE is willing to accept, for liquidity provision. Given this information on underlying preferences, we can estimate outcomes under different alternative auction rules, with welfare and surpluses calculated in the same way as for the PMA.
The first alternative is a pair of separate simultaneous auctions (SSA), in which the quantity of funds the BoE is willing to lend against each set of collateral is fixed across the whole period. We compare the PMA to a range of possible SSAs, in each of which the sum of the fixed quantities of funds lent against the different collaterals is equal to the BoE’s maximum supply.
The second alternative design is a ‘reference price auction’ (RPA), in which the BoE fixes a pair of notional prices for the two collateral sets, ie ‘reference prices’, and the highest bids relative to their reference prices are accepted. We also compare the PMA to a range of possible RPAs, in which the reference prices are fixed across the whole period.
These two comparators are simpler, reasonable alternatives, used both historically and by other central banks. For example, the BoE used a somewhat related design to the RPA in LTR auctions prior to the implementation of ILTR auctions.
In the SSA and RPA, marginal welfare may differ across the collateral sets because the designs do not permit quantities and the price difference, respectively, to adjust to the participants’ or BoE’s preferences. The SSA and RPA therefore can create welfare losses relative to the PMA.
Welfare results
We find that the PMA increased welfare by approximately 2bp per loan, or 50%, relative to almost all the alternatives. Because the optimal price difference, and therefore the optimal reference prices, varied over the sample, the RPA could not have maximised welfare with any fixed reference prices. One particular SSA would have almost maximised welfare because the optimal quantities across auctions turned out to be almost constant in our particular time period. However, this would not be the case in less stable periods. Moreover, selecting this best-performing SSA would have required the BoE to accurately forecast the optimal quantities to supply against each collateral set, which seems unrealistic, and the welfare losses of other SSAs would have been large.
Distribution of surplus
A second finding is that, in the period studied, the PMA always gave the BoE more (or occasionally the same) surplus relative to if the BoE had run any possible SSA or RPA, but the effect on the bidders, in aggregate, was ambiguous.
Three features, specific to the period, can explain why the bidders did not always gain. First, there was no significant stress so there was never very large demand for loans secured by Level B collateral nor ever very large net surplus to bidders from borrowing against Level B. Second, the demand curve for loans secured by Level A was flat, so bidders could not make substantial gains on this collateral, regardless of the design. Third, there was little use of the ‘paired bidding’ option in the design, which allowed bidders to express their preferences across collateral sets. Absent any one of these three features, the bidders, as well as the BoE, might have benefited more from the use of the PMA.
Welfare and surpluses in periods of stress
We expect, and confirm in simulations using data that we generate for a hypothetical stress scenario, that the welfare gain, as well as the benefits to the BoE, of the PMA would be qualitatively similar, but quantitatively larger in absolute terms, in a less stable period than the period studied. This reflects the scaling up of the benefits of the PMA’s flexibility in the allocation and its sensitivity to the BoE’s preferences, relative to the alternatives.
Conclusion
The PMA automatically adjusts the amount of funds loaned, and the interest rate premium charged, to market conditions. Our analysis shows that this flexibility significantly increases welfare relative to alternative designs, as measured by the difference between the spreads that participants were willing to pay and the spreads that the BoE was willing to accept for loans.
More importantly, neither the SSA nor the RPA would have achieved the BoE’s main objectives in setting up the PMA. The auctions were intended to improve the availability and flexibility of liquidity insurance to the banking system as a whole, while mitigating potential moral hazard (ie avoiding distorting banks’ incentives for prudent liquidity management), and informing the Bank about stress in the market (see Fisher 2011). First, any SSA is simply setting a quantity for funds lent against the less liquid Level B collateral. The SSA therefore would not allow for a substantial increase in the quantity of funds allocated against Level B in the event of stressed conditions. Second, any RPA is simply setting a fixed spread between loans secured by collateral assets with different liquidity levels. So while the RPA’s allocation against Level B might increase in a period of stress, the RPA would not allow the interest rate premium on Level B to adjust in line with the BoE’s supply preference. Paul Fisher (then Executive Director at the BoE) described the design as ‘potentially a major step forward in practical policies to support financial stability‘. The automatic adjustment to market conditions of both the amount of funds loaned in the PMA, and the interest rate premium charged, improves welfare not just on our measure but also in this broader sense.
Julia Giese works in the Bank’s International Surveillance division and Charlotte Grace is a DPhil student at Oxford University.
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