# Intro to Econ: Ninth Lecture Aside – The Winner’s Curse

For one last time, I want to come back to the problem of whether you get a loan for your project under the assumption that the risk inherent in your project is stochastically independent of other investment risks. So this was our problem (see also here and here):

$\begin{tabular}{c|ccccc} Scenario & Income & Probability & you get & investor gets \\ \hline good & 200.000 & 80\% & 200.000-x & x \\ bad & -50.000 & 20\% & 0 & -50.000 \\ \end{tabular},$

where $x$ is the repayment amount that you pay back to the investor in case of the project being successful. We argued (in a previous post) that the range of feasible interest rates is 12,5% to 200%. Anything outside that will certainly not be accepted by either the investor or by you.

Suppose that you and the investor are close to agreeing to an interest rate of just over 12,5%. Put yourself in the shoes of the investor for a moment. What might worry you in this case?

There is something I perhaps didn’t emphasize enough. I sort of glanced over the problem of how the various investors come up with their assessment of the risk involved in your project. Clearly most investors will try to carefully assess the risks in a project before they make any investment. I believe that many banks, for instance, use an internal rating system similar to those used be the big rating agencies such as Standard and Poor’s or Moody’s or Fitch. These companies typically rate risks, for instance of countries defaulting on their bonds or other financial obligations, on a letter scale, such as in the case of Standard and Poor’s from AAA (almost no chance of default) to D (has already defaulted). Banks then translate their ratings into probabilities of various outcomes, with special focus on the probability that the entity that they giving their money to will default (i.e., not be able to pay their loan back).

Different banks or other investors will typically not necessarily completely agree in their assessment of the risks in your project. So now put yourself in the shoes of an investor (such as a bank) and imagine that this bank has made you the offer of a 12,5% interest rate and, after you shopped around at other banks, you decide to take up their offer. So, why might this bank now be worried? Well, it seems that they were the ones making the best offer to you. Why did the other banks not make a better offer? Probably because the other banks didn’t assess your project as favorably as this bank did. But if this is so, is it not now possible that this bank has overestimated the likelihood of success of your project? If this is the case, then perhaps this bank should also not offer you a 12,5% interest rate.

This phenomenon, that when you make the best offer you possibly overestimated the value of whatever you are buying, is generally often called the winner’s curse. You can easily imagine suffering from the winner’s curse when you buy a house at what seemed to you a low price only later to find out that it had all sorts of problems. That may explain why you were able to buy it for such a low price in the first place: because you overlooked something. If you worry about the winner’s curse in such cases, as your bank might when giving you a loan, you might ask for an even lower price to compensate for this – or a higher interest rate in the bank’s case.