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a blog from young economists at Nova SBE

The Time Traveller’s Choice; Or: How I learned to stop worrying and love the Portuguese Government Swaps

One of the hot-topics of the past few months has been the discovery of a set of damaging   contracts involving the Portuguese State Swaps. These swaps were created with the goal of hedging against a continual rise of the Euribor. As evidenced by the chart, the rise in the interbank market was quickly quenched due to the actions of the ECB to reanimate lending in the European Economy.


As the Euribor reached new lows the costs associated with the swaps continued to rise and eventually led to the public scandal. The government is now trying to reverse these contracts. To achieve this they are expending resources now, be it money with lawyers, reputational costs, among many others, so they can reduce the current losses. In the interest of this article I wanted to create a very simple general deduction regarding what would be a good trade-off between these costs and the gain in interest.

This general problem likens a situation where a theoretical time traveller would pay a cost (T) in order to return to the past and exploit the interest rates with his new found knowledge. Returning afterwards to the future and finding that his investment choices out-performed the market. I reinstate that this is a very simplified deduction, but it may provide some small insight into the choices by the government.


This is a typical budget restriction for a two-period model. To model the so called time travel we must include an additional cost (T) at the second period that will allow the consumer to go back in time and improve their interest rates by (1+phi). We only know that when T=0; phi=0.


This implies that by going back in time, at cost T, the consumer will obtain an additional (1+phi) from their savings.


This implies that the maximum price a consumer would be willing to pay for time travel is the savings interest with the increased knowledge plus the available resources in the first period minus the consumption in the second period. If equality in (3) is verified (commonly through welfare maximizing agents), then:


This means that an increase in f allows the consumer to pay an additional f times the savings in the first period. The value of time travel then increases with savings and decreases if consumers prefer goods in the first period. It is important to also take into account that the existence of this mechanism may allow for extraordinary consumption in future periods. For this analysis it would be necessary to include assumptions regarding the utility function of agents.

What can this tell us about the Swaps? Knowing that the losses the government stands to sustain without any prior agreement are of about €2.000M, with current discussions of a payment of €500M. If the government was working in equilibrium we would understand that these agreements probably give an additional €1.500 M in value to the counterparties, be it in lessening the risk of default or in assuring future contracts between both parties. Another example of a time-travel dynamic is when the stock market cancels orders or effectively reverses it. This cost of time travel is essentially the cost of obtaining privileged information. By obtaining information ahead of the market it is possible to increase future earnings through additional savings and as such it may be possible to improve the agent’s welfare.

– Manuel Costa Reis, 614

Author: studentnovasbe

Master student in Nova Sbe

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