Managerial Economics- Final Exam

Question 2

Part A - Theory

In second-price sealed bid auctions, the optimal bidder strategy when values are private is to bid his personal reservation price, regardless of risk aversion. This is a dominant strategy since it maximizes the total available surplus, defined as the difference between the reservation prices of the two highest valuation bidders.

This strategy is not optimal when considering common-value auctions, where all bidders value the good similarly but the true value of the good is unknown. The bidder in this case can improve his strategy by bidding lower than his best estimate when:

1) He has less information relative to other bidders about the object’s true value 2) The number of bidders increase 3) He is less confident in his estimate of the true value

Winner’s Curse tends to be a problem in price-sealed auctions with common values but not with private values because bidders must estimate the true value of the object without knowing the estimates of others. The graph below1 illustrates that bidders with extreme estimates (right tail of bids distribution) bid values that exceed the best estimate (mean of dotted distribution) and end up paying a price that exceeds the true value, generating negative surplus. In private values, unlike common values, the bidder will not change his valuation when he has knowledge of other bidders’ valuations. The bidder’s reservation price is a function of information and risk -adjusted utility (personal experience) and individuals’ values for the object being auctioned are determined independently of each other.

To help alleviate the winner’s curse, the seller can: 1) Run an ascending-bid auction 2) Provide more information about the true value of the object. 3) Draw as many informed bidders to the auction 4) Share the risk e.g providing warranties

These actions tend to minimize the surprise between the actual bid and the mean estimate value. The seller would be inclined to alleviate the winner’s curse when bidders are aware of it, because the seller’s expected revenue will be low in that all bidders will shade their bids further away from the true value.

Part B - Real World Example

Description

This example pertains directly to my work experience in the Treasury Department at the National Bank of Kuwait. I was responsible for purchasing treasury bills from the Central Bank on a monthly basis. The auction process is a first-price sealed auction, in which the central bank specifies a total volume and 12 local banks bid on lowest yield (highest prices). The auction process had two key features:

1) Discriminatory Pricing – bidder pays his bid 2) Multiple units – multiple bids consisting of price and quantity pairs

The bid that the bank places is contingent on client orders and on estimating the total bid volume of the market (each bank can bid up to the maximum volume issue). I placed a bid of 1.45% on a single tranche of 65 million KWD for issue 1154, confident that the other banks’ demand schedules would follow aggressively as they have been in past issues.

The table below2 shows a sample of the auction market results in 2011 for the 5 largest banks.

Interpretation

Treasury bills auctions are typically common value auctions. In these auctions, all bidders ex-post place the same value on the object; ex-ante this value is unknown to the bidders. In discriminatory treasury auctions, the common value would equal the secondary market price after the auction. Banks can place independent private values on Treasury Bills prices because: 1) Dealers hold all client orders and are able to gauge market demand 2) Securities can be resold in the post-auction secondary market, which can be illiquid at times and demand premiums. Therefore, there may exist a private component in bidder valuations that can alter the rational behavior of the bidder, and bid away from the best estimate of the true yield (affiliated values).

Issue 1154 posed a winner’s curse problem for the bank. The volume/bid ratio of NBK was 0.32, above the historical average of 0.25. In addition, the accepted bank’s bid yield was the lowest. This had implications because the secondary market valued these bills at 1.57%, meaning the bank incurred unrealized losses upon purchase relative to the other banks. In this case the problem wasn’t as severe due to tight spreads, but this illustrates the weakness in the auction process that could be severe for aggressive banks in market disruptions.

Analysis

Post-auction information and higher post-auction trading volatility revealed that competing banks’ client demand orders were dramatically lower than expected. This caused banks to shift their bid on the higher yield ranges, putting NBK at an informational disadvantage at the time of the auction.
At the face of uncertainty, a richer strategy could be employed by dispersing bids by amount and price; win at higher yields when demand is weaker than expected, and conversely win at lower yields when demand is stronger than expected.
The auction process could be improved if the central bank coverts to a uniform price-sealed auction with a maximum allocation percentage. This would generate higher expected revenues for the central bank than discriminatory pricing because they alleviate the winner’s curse by linking the auction price to the lowest winning bid price, regardless of all bidders’ actual bids. There is evidence of strategic behavior that appears in discriminatory pricing that increases the volatility in both bidding yields and post-auction trading. Under a uniform pricing regime, greater pre-auction information flow would lower uncertainty, lower variability of bidding yields during auction and increase selling prices.

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Word Count: 904 words (excludes headlines and graphs)

References

1 London Business School: Managerial Economics notes

2 Central Bank of Kuwait – www.cbk.gov.kw

Journal of Financial economics (1996) 63 -104: Discriminatory versus uniform Treasury auctions, Kjell Nyborg, Suresh Sundaresan

Prices and the Winner's Curse forthcoming, Rand Journal of Economics, 2002 Jeremy Bulow and Paul Klemperer