# Greek Bonds As A Case Of 'Prisoner's Dilemma'

by: Cam Hui, CFA

FT Alphaville posted an analysis from BarCap on whether Greek bondholders should tender to the "voluntary" exchange offer. BarCap concluded that on a probability weighted basis, bondholders should tender to the offer because the probability-weighted payoff is higher if you tender than if you don't.

I beg to differ. It's a little bit more complicated than that. Look closely at BarCap's analysis of the payoffs if a bondholder tender decision under the two scenarios of successful and unsuccessful exchange.

This looks like a case of the Prisoner's Dilemma, which is described by Wikipedia in the following way:

Two men are arrested, but the police do not possess enough information for an arrest. Following the separation of the two men, the police offer both a similar deal- if one testifies against his partner (defects), and the other stays quiet (cooperates), the betrayer goes free and the cooperator receives the full one-year sentence. If both remain silent, both are sentenced to only one month in jail for a minor charge. If each 'rats out' the other, each receives a three-month sentence. Each prisoner must choose to either betray or remain silent; the decision of each is kept quiet. What should they do?

If the exchange is unsuccessful, then the forecast payoff is 40%, regardless of what the bondholder does. If the exchange is successful, then the bondholder gets a higher payoff if he doesn't tender - the higher payoff is the result of being a "free rider".

Wikipedia went on to describe the optimal solution in the Prisoner's Dilemma:

Here, regardless of what the other decides, each prisoner gets a higher pay-off by betraying the other. For example, Prisoner A can, with close certainty, state that no matter what prisoner B chooses, prisoner A is better off 'ratting him out' than staying silent. As a result, solely for his own benefit, prisoner A should logically betray him. On the other hand, if prisoner B, acts the same way, then they both have acted the same way, and both receive a lower reward than if both were to stay quiet. Seemingly logical decisions result in both players being worse off than if each chose to lessen the sentence of the accomplice at the cost of himself spending more time in jail.

How should a bondholder think about the tendering problem? I believe if tender rates are relatively low, then the probabilistic approach is the correct framework as the unsuccessful tender scenario is dominant. However, as tender rates rise and approach threshold levels for a successful exchange, bondholders should start to think about this in game theory terms as there is a higher payoff by being the "free rider".

The bottom line: The probability of an unsuccessful tender is greater than the market might think it is. If you were to assume that the 90% threshold acceptance rate specified by Greece is a bluff, then at current acceptance rates there is little incentive for bondholders to tender. If the 90% threshold isn't a bluff, then it's unlikely that we are going to get there and the tender will be unsuccessful in any case.

Disclaimer: Cam Hui is a portfolio manager at Qwest Investment Fund Management Ltd. ("Qwest"). This article is prepared by Mr. Hui as an outside business activity. As such, Qwest does not review or approve materials presented herein. The opinions and any recommendations expressed in this blog are those of the author and do not reflect the opinions or recommendations of Qwest.

None of the information or opinions expressed in this blog constitutes a solicitation for the purchase or sale of any security or other instrument. Nothing in this article constitutes investment advice and any recommendations that may be contained herein have not been based upon a consideration of the investment objectives, financial situation or particular needs of any specific recipient. Any purchase or sale activity in any securities or other instrument should be based upon your own analysis and conclusions. Past performance is not indicative of future results. Either Qwest or Mr. Hui may hold or control long or short positions in the securities or instruments mentioned.