The American Academy of Actuaries mag Contingencies this month applied game theory to bidding on reinsurance treaties. The optimal bidding process, it said, was a Vickrey auction, named after the Nobel Prize winner who studied it.
In a Vickrey auction, all bids are secret. The winner is the party who bid highest, but the bidder pays what the second-highest bidder sought. In a bid for a Snickers bar, for example, I might bid $1.05 and you might bid $1.00. I get the Snickers but pay $1.00 for it.
What’s happening here: In a typical auction, each party is guessing what the others will bid and adjusts accordingly. If you think everybody else will underbid, you lower your bid. If you think everyone else will bid strong, you will bid stronger. Sometimes you bid too strong; enter buyer’s remorse.
If the winner pays the second-highest bid, though, the nonsense ends. Everybody submits his best bid, knowing that if the rest of the market underbids, he will get a good deal. If you overbid, he will still get a good deal.
Great theory, I muttered to myself yesterday, but can’t happen. Too much risk of collusion.
Today, David Merkel makes me the fool. He describes how – and why – he actually conducted Vickrey auctions in the bond market:
One of the problems with the auctions was that some investment bank would overbid, and win, and then the salesman would come back to me, confess the error, and say, “Can you show me some love here?” I was taken aback by it the first time I heard this, but came back with a fairly rational solution, giving back one-third of the difference between the winning bid, and the second-place bid.
But I came up with a better way. Here is a Bloomberg post that I made to five of my brokers:
BWIC [Bid wanted in competition] — 1:30PM — 5 dealers only. I am selling these just to raise cash. This is a continuation of my experiment so bear with me. In an effort to reduce buyers remorse (and thus get better bids) I am awarding the bond to the winning bid at the COVER level. In case of a tie, I will award bonds pro-rata at the tie level. If you don’t want to play, let me know. Thanks, David. [Bond list follows]
Everything has meaning here:
- 5 dealers — limit the auction to the dealers who have the most interest, it makes them fell comfortable that they have a shot at getting bonds. I never used more than 6 dealers in an auction.
- Just raising cash — says that you don’t know anything they don’t know. Makes them more willing to bid.
- Cover level is the second place bid.
- You can’t come back begging for love here.
- Ties were particularly valuable, because there was no love and both brokers got half of the bonds, and typically lost money on resale, since they were competing against each other.
- If I did not get enough bids on an auction, typically three, I could cancel it.
I reviewed my auction results and found that it erased the advantages of my brokers. I ended up selling bonds near their ask levels, on average. What was worse, many thanked me for being innovative in creating an auction method that “showed love” in advance of the auction. When I explained this gambit to my wife as we were traveling to prayer meeting one evening, she gave me a hard hit on the shoulder, and said to me, “David Merkel, you are horrible! Not only do you beat Wall Street at its games, but you get them to thank you for it!” Oh well, guilty as charged……..
So the academics got this one right. And this gives me a chance to point you to Merkel’s blog, where he is carrying an excellent series on being a bond manager. It’s an interesting view into an important part of the economy, and if you happen to be considering a trading career, it gives you some insights into the life.