## Saturday, March 06, 2010

### Ex Ante & Ex Post Rationality

I have repeatedly written in the last few weeks that I think the current yield spread between Greek and German government bonds of about 300 basis points is too high, given that the probability of default is actually very low.

But wouldn't you agree that the yield spread was too low in the past when it was more like 30 rather than 300 basis points? Previously I might have simply said "yes" to that, and I would indeed agree that 30 basis points would be too low today (Just exactly how high it should be is difficult to say, but 100 basis points would be fairly reasonable), but the issue is somewhat more complicated than that. To understand why, one must understand the difference between ex ante (before the act) and ex post (after the act) rationality.

Everyone makes mistakes, and I've certainly made my fair share of them. However, with regard to most of my mistakes I would still maintain that the decisions behind the mistakes were rational given what I knew then. Had I known what I know now I obviously would have made a different decision, given what I knew then most of the decisions were rational.

To illustrate this, let's compare two lottery tickets. Lottery ticket number one costs \$10, and gives you a 75% chance of winning a \$1 million. Lottery ticket number two costs \$10, and gives you a 10% chance of winning \$12. Assume that you only had \$10, which one would you buy.

I think that just about everyone would choose the first one. But suppose that it turned out later that the first one was actually a blank lottery ticket, while the second was actually a winning ticket. Would you still say that the right choice was the first lottery ticket?

Knowing what we know now, the second ticket was clearly the best choice. But knowing what we knew before the purchase decision, I would maintain that the first ticket was the rational choice. The first ticket was the most rational choice ex ante, while the second ticket was the most rational choice ex post.

Turning now to the issue of whether the German-Greek bond yield spread was too low in the past, I would say that the yield was too low in ex ante terms but far too high in ex post terms.

Given the dismal fiscal track record of Greece in the past, and given that we didn't know with certainty what would happen, a yield spread of 30 basis points was too low.

However, given that we now know that Greece hasn't defaulted during the latest decade, the correct yield spread for all securities that have matured was in fact zero. If there is no default (or other problems like higher transaction costs) than any yield spread above zero is too high, since given that we now know there was no default, the investor in German bonds would earn less for no reason.

Given the knowledge we have now ex post, a 30 basis point yield spread is 30 basis points too high. However, given that we ex ante couldn't know for sure that there would be no default, and given what we knew about Germany and Greece, then 30 basis points was arguably too low, just as 30 basis points would be too low today.