Now, let's study the model of private information at the act of underwriting. So, I think you've heard this term underpricing, which basically means that when you offer the issue to the public at a certain price, then people are willing to pay less. And here, we would like to analyze why is that so. Well, you can say, "Well, whenever you make an offer, people would always bargain with you." They say, "Well, it's great, but I'm willing to pay less." But the question is, how much less in the first place? And if you offered too low, then there may be other people who jump in and buy out the issue. In order to do so, there is a model that is called the model of Winner's Curse. Now, this model first was studied in the transactions that were dealing with the tenders for oil fields, sometime in the 70s. But then later, it proved very fruitful in the analysis of underpricing in underwriting. Now, the story here deals with private information in an open way, and it specifies two kinds of investors. These are uninformed investors and informed investors. What are these two groups of people? Well, uninformed investors are just people at large, who know little about this company. They might have heard about that, but they do not have any specific knowledge. Now, when you talk about informed investors, there's specifically, and the media have the temptation to say, "Well, these are insiders." And you all have heard that insider trading or insider transactions, they are illegal in United States and in many other countries. So, are we talking about potential criminals here? Well, not exactly. Let's say that if you're the insider or the manager of the company or a vendor, in this case, you might indeed be really working on a very delicate turf. But, what if you are just watching this company? You are just a private individual. Everyday, for quite some time, you would download Bloomberg, and you would see what happened with this company. You would see its financial results, its strategy, because a lot of information may not be public because the company might still be private before, but, let's say, you'll study the industry. You study the public companies in the industry based on the information that is publicly available. So, you are of then more informed than others. And, what if you are an analyst at an investment bank, and you study this industry? Then clearly, you are much more informed than these people at large. Well, you can see that what is likely to happen is that informed investors they do possess superior information, although that is done not in any legal way. So, the story here goes like this. We say that this distinction is putting the model in the following way. Let's say a company offers a share of stock at a certain price. And when it offers that, it does not know the real price. It may be lower or maybe higher and there is some probability there that on average, this is the price of an offer. Now, the informed investors, they are much more likely to know the true value of this issue. And, if they do, then they all participate in bidding if it's a high value, and they refrain from bidding if it's a low value. While uninformed investors, they bid in both situations with the same activity. Now, let's say if the good or the high value outcome occurs, then there are a lot more people who are crowding in to make their bids, and there is oversubscription and therefore, prorationing. So the people if they wanted to buy a certain chunk of stocks, they do not get the full amount. So they have less than that. And, while in the case of a low value when only uninformed investors are in, then they get all the shares of stock for which they bid. So, this is a model that basically gives you a general idea what's going on. We can see that basically uninformed investors are likely to lose on average. That is why Winner's Curse. So the winner is the one who does get the share at the process of an initial public offer or maybe it's only a public offering. So, basically, if you do get these shares, that on average, you're likely to lose. If you bought at an offered price, therefore your normal, your rational behavior would be to bid at a lower price, and there's delta that is called underpricing will compensate you because in the case that you are the high outcome, you will get more. And in the case of a low outcome, you will lose less. So that's basically how this works. Let's see the model in some greater detail. So, let's say I offer a share of stock at $50, and all investors would like to get 10 shares. This is a model. Now, the situation is like this. So I offer at 50. There may be a high value case, that happens with probability of one half. Remember our good old friends want to have probabilities. So here, the actual value issue is 60, and here in the lower case, it's just 40. Because that happens with a probability of one half, you can see that 50 is the correct weighted average. But, in this case, you have both informed and uninformed investors bidding. And as a result, let's say you get only six shares out of 10. In lower case, there are no informed investors, so here you get all 10 shares. Let's see. If you paid 50, what is your expected profit or loss? Well, it's very easy to calculate. So here, you get six shares. And on each share, you make 10 bucks because you paid 50, and you get 60. So it's 60 minus 50. So this is 10 times six. So your overall profit in this case expected is $60. Now, on the lower part, it's different. How much do we get? I'll put it here? You get 10. Now, it's 40 minus 50. And now, you'd expect the loss is minus $100. So, on average, this happens with a probability of one half. This happens with probability of one half. So you add, and you get that your expected, in this case a loss, but I will put profit with a negative sign, is minus $20. 100 minus 60 and multiply by one half. So, see what happened. If you paid the price at which the issuer wanted to place in stock, you on average lose $20. Well, clearly, you can say, why do I know this? Why do I know that? Well, that was the model input, and that is the thing. We know one thing that this is less than 10. It can be shown that whenever it's less than 10, in this setup, this will be a negative number. So I just put this here, six to give you this number of minus 20. We will say just in a few minutes how investment banks send certain signals about these numbers because this is a grossly simplified example. So, we see that if I paid 50, I lose. So, what can I do? Well, I have to pay less. Let's see how much less. I will reproduce this story once again. So this is $50. So, with probability of one half, we arrive at 60. We have probability of one half. We have 40. Now, let's say that now I pay the price P, which is lower, and this will be underpricing. So, what is my expected profit in the upper case? This is now six. This is a number of shares that you've got. 60, that's what you've got, minus P. In this case, it is 10(40 - P). So in order to break even, what should happen? I'll put it here. So, in my expected profit is equal to, with probability one-half, which is in both cases. The upper case is six times 60 minus P plus, in the lower case, I wouldn't change my marker, it's 10 times 40 minus P, and all that should be equal to zero. If I solve this equation, I would get that, now P is equal to $47.5. Now this delta, which is 2.5, this is underpricing. So this is the model, and what do we see here? Well, first of all, we can say that where do these numbers come? Like I said, these numbers six and 10, they are sort of provided by the investment bank in its process. So, the investment bank really sort of ensures the minimum and the pricing given the situation. So it goes to the people, to uninformed investors and sends them certain signals says, "Well, it's likely that numbers are like this, and in the good case you get only six, because of oversubscription," or it may say, "It will be eight," in this case, if it's eight, then this number would be higher, and then the pricing would be lower. Now the question is, why doesn't the investment bank collude with the issuer? Because the investment bank legally is an informed investor here. Remember I told you that the question of who is the client of an investment bank is not such a simple question to answer because issuers are clearly its clients. But at the same time, investors are clients too, and in some cases, these are even more important clients. So, for investment bank to collude with issuers and to screw its base of these bags is a suicidal behavior. Therefore, they are willing to really transmit information to this public and try to alleviate this initial information asymmetry. Now, the next thing is that it's kind of important that an underpricing is an indirect cost of an issue, but there's clearly a direct cost for the issuer, because you pay some fixed commission for the investment bank, and you may pay also some commission depending on the volume of the issue. So, for the issuer, there is some kind of a balance or competition between this. So you pay some direct costs and you pay some indirect costs, and it may be shown that sometimes these indirect costs are much more important. So as you will see in our future episodes, sometimes the issuer purposefully makes the choice of a more expensive investment bank in terms of direct costs, because he believes that this investment banks will do a better job in making this underpricing smaller. And if you do that smaller because of the large volume of shares, then clearly you can make up for some of your expenses that you incur in the form of direct costs. So, this is basically the model of winner's curse that shows the mechanics of how underpricing occurs. And now we see that the key service of an investment bank in the provision of underwriting is the right delta, the right underpricing, and the smaller it is, the better for the issuer.