Now, let's go back to this model, and try to analyze some risks associated with that. Well, first of all, risk one, let's say is greedy investors. Let's say these buyers of red triangles say, you know what dear bank, why wouldn't you give us 135 at point one? Let's say, here, it's the same 185. So, investors push the bank to pay them more at point one. What happens here? Well, at the first glance, clearly, this is better than 125 and 185. It can be shown, with the calculations of expected utility. By the way, I would like to point out that our assignments and their handouts, they allow you to really feel the flavor of that because not only after you did some of these calculations, you'll start feeling what's going on. It all sounds very simple, and very easy to follow, but the only way to do that is to follow through some of the assignments that I offer. Now, see what happens here. Now, we will redo what we did in the previous episode. We will see that, at point one, we have, let's say the saint when the investors come. But they now require not $25 as it was before, but 27. So the bank will have to liquidate at this point 27 black boxes, and instead of 75, it will have only 73 remaining. These 73 remaining will become just 146 at point two. And we remember that we need to pay out 148. So the bank will not be able to deliver on that. So, we can see that greedy investors do pose a huge risk to this model. But that is not it, the main risk comes from the fact that, actually, more people may come. Let's say that, we go back to the model that we had before, we have just 125, so we sort of pushed investors back and said, you know what guys? We cannot unfortunately pay you more. This is the setup of this model. They say fine. But, what if not 20 but 25 people come here. Well, you don't have to be a wizard to realize that here again, the bank has to raise more money than $25, has to liquidate more than 20 boxes, actually many more. And as a result, by the time that the bank faces point two, it will not have enough black boxes to be able to deliver 185 to the remaining deposits. You can say, well, if 25 come here only 75 come here. Indeed. But the problem is that you have to sell sort of disproportionately many black boxes at point one at a loss. Well, it's not a loss, because you paid one for that and you get back one. But, you'll have to pay out 125. So, for each extra arriving depositor, you, in some cases, have to liquidate more than one. You have to liquidate 1.25 of these things, and well, sometimes, let's say if four people come you can liquidate, if five people come, you can sell only four. But you can see that in general, the number of black boxes remaining after dealing with these coming depositors, is insufficient to deliver on these promises. So, this is a key problem. Even more, we can say that this number cannot be known with certainty. In reality, between zero and one something happens. This is not darkness. We just posted that this is darkness to make this model simple. But, now what we can see is, let's say here we made the decision and we expect that 20 people come, but what if something bad happens here, and instead we see 30 people coming. Then the whole scheme collapses. Not only, this is the factor we can no longer make money, but we cannot even deliver on the promises to be deposited at point two. So, this is unfortunately not a great situation. So, we saw the core here that the idea is such; if the probability here is pi, so we can see 100 times pi investors coming here, and 100 times one minus pi there. This is a more generalized problem. We can see that, actually, it is this pi that is a key component of the ability of the bank to deliver on its promises. And therefore, if this pi changes, and changes sort of advertently to the bank, the bank cannot do it. Let's think about the following. What if, at point zero, our assumptions about pi being equal to 20% was great. So, indeed no more than 20 people need money here. But what if some other people woke up this morning at point one, and they saw a nightmare, and they said, damn it. Why wouldn't I go to a bank and get my money back earlier? I don't need it, but I am sort of scared. There is no rational explanation to that, but let's say I don't feel comfortable. So, these people come to the bank and we know what happens. The bank that could easily deliver on its previous scheme of 20 and 80, then starts giving out more money at this point, and that is doomed to fail at point two. Now, let's put ourselves in the shoes of a smart enough depositor who says, well, what if I don't need money at point one, and I don't feel uncomfortable? But someone else does. This someone else comes and takes the money earlier, and that poses a threat to my money at point two. Maybe it's better to me to rush to a bank and get my money earlier. I will save my money, and then later, I'll think what I'll do with it. Now you can see that only the idea that something might prevent the bank from delivering on its promises point two, it pushes the people to come at point one. This classic situation is called a self-fulfilling prophecy. So, if the people expect the bank to fail to deliver on its promises, it does fail. And that makes the whole scheme that we discussed here very vulnerable, with respect to the actions of these people, and it makes the whole banking system extremely vulnerable. Oftentimes people don't get themselves account on that, but that's exactly what's going on. So, what can a bank do? Again, I'm talking about the bank who instead of taking all this money, let's say the bank owners and running away, did invest this money in black boxes. The bank does want to deliver on its promises and to make a positive amount of money as a result of that. But how can a bank prevent the situation that crazy people, who saw a nightmare avail by their actions, force the bank to fail. Well, there are basically two major options. One option has been used for centuries. And that option seems to be temporary and not very efficient but, for quite a few hundred years it worked. That's called suspension of a convertibility, see how it works. People start coming at point one, the first I pay him or her 125, the second, the third, then the 20th. Then, the 21st person comes and says, "Well, you know I also would like to get my money today." And I said, "I won't give you money." He say, "How come?" Well, I say, "Only 20 people served at point one, that's it. So you have to wait until point two." Well, the person isn't happy, and clearly if this is the case, then rumors start to travel and then all people rush to the bank and, they say, "Well, you know we have to give us money back." I say, "But I closed my doors and say well, only at point two." So, this is a very aggressive behavior of my side, but it saves me. So these people between point one and two they feel extremely uncomfortable and unhappy and they think that something bad might happen or they will lose their money. But if they live up to this point, I opened up my doors and I pay 185 to everyone. So, this situation can indeed prevent this bank failure, and you know that the actions of the people who rush earlier. There is another great term that is quite well known is called a bank run, when people run on the bank and say, "Well, give me my money back earlier." But clearly, this situation of suspension of convertibility is not very efficient because in reality, there are many more than these two points. And let's say you have to open up your doors some day. Let's say you say, at 6 O'clock pm, you close your doors, and then we're talking about the reality of not the very early days but not now when sometimes all these banks will be operate online and sometimes 24 by 7. But when you reopen your doors, then, the fear of the people will only grow and they will rush in, not only those who wanted to do it now but some other people. And, if all of the people come at point one, if we go back to them all, the bank fails here, because let's say, all 100 people come and we need $125 and we don't have it. So, by suspension of convertibility, we forcefully push the people to arrive only at point two. Now, this suspension of convertibility did work for quite a few years but it's inefficient because, if there's only one bank that has problems, then it can work because the people can somehow either wait or use their other bank accounts, or in case that persists with this bank, the bank can be purchased by another bank and then the situation calms down. And that was the case for many, many, many years. However, the problem here is that this solution, quoted solution to the problem of a bank run, does not uproot the main cause by which people run at point one, because people are still scared. There is another way, and the other way is much more universal. And this is a way that is used right now or has been used for quite a few decades around the globe which this called deposit insurance. This is a situation in which someone else says that if for any reason the bank fails to make payments at either point one or two then, someone else will make these payments to depositors, to the owners of red triangles, and they will go to another place. What is this place? Well, in all the countries where deposit insurance now works, this place is the government, and I will explain why this is the case in the next episode. So for now, we can see that there are two major options to deal with this run, and we will see why the second one namely, the deposit insurance is better than the suspension of convertibility. Now I would like to draw your attention to some episode in a very well known movie that shows to you how the mechanics of the bank run, how it starts, how it develops and how it can be prevented. Well, all of you know the great Christmas movie, it's A Wonderful Life, that was shot in 1946, and the movie tells a story about the good guy, George Bailey, who was actually, yeah and it's a long movie and a very touching movie. Many of you may have seen it, maybe more than once. But there was one episode in this movie that is actually like it was done specifically to illustrate this course. In this movie, when the main hero, George Bailey gets married and then with his newly wed wife, they go to the honeymoon and they have $2,000, and that is during the time of the Great Depression. So that's a significant amount of money. And then they see that someone runs on this guy's Savings and Loan Association. So this is a bank like institution. And he comes back and starts to explain to everyone that they don't have to panic, they have to wait, that everything is going to be fine and people are willing to believe him because he's a good guy, and all of them know, he lives in a in very small town. But one depositor says well, I need my money now. I have to pay the bills, and everyone says that. And at that moment the newly wed wife of George Bailey comes in with these $2000 and she says, "We have the money." And they start paying out their own money. And the first gentleman takes all the money, $242, and clearly of this 2000, you can see that roughly speaking, the eighth person would bring the situation back to the point of an unsolved case. However, the second and the third person, they start to take out not all their money, but only the amount of money that they need to live for, let's say a week, when another bank reopens let's say. And then, by the end of the day they spend all their money but had two bucks left. So, this is a situation that shows that, even if everyone is willing to trust you, the only thing that solves this situation of a potential run or over run, is cash. So, unless and until you start paying out cash, even with some limitations, even with some special terms, then people start to calm down. No cash, no stop over run. So, this is the movie piece, that may sometime show to you how that work. And although this is an old movie, it was shot more than 70 years ago, and it discusses the situation that happened more than 85 years ago, but the mechanics of the run is still the same.
