Now let's proceed with analysis of the cash flows that arrive to the bank.

So we reproduce this matrix once again.

So this is probability 0.64, this is 0.16,

this is also 0.16, and this is,

I will use the red marker here, just 0.04.

And, Remember that the bank

contract with the borrower is this monitored contract, so

the bank gives 6 monitors, but requires back 7.5.

Remember, I told you that borrowers are indifferent.

So before, when the bank did not exist, borrowers engaged

in that contract of liquidation that has a face value of 7.5.

Now we see that for now, and this is important, then the bank charges them

as high a face value as it would if that would be a debt contract of liquidation.

But the bank also monitors and pays some money for that.

Now let's see how this goes.

So in this case, we have 7.5 plus 7.5.

So the bank pockets $15 million.

Now here, we have 7.5.

This is from the project, the high state.

Plus 5, this is from project below state, because we monitor, that's the key story.

So that brings us 12.5, the same story as here, 12.5.

And here we unfortunately have just $10 billion because this is 5 plus 5.

Now, that's what we got.

Now the question is remember I said that

on the side of borrowers and bank, everything is clear.

Now the only sort of unclear thing is that why would borrowers put up

with the fact that the bank monitors them and still charges such a huge if?

But that's another story that we will talk about in just a little bit later.

But for now,

the key story is how to induce these small investors to deposit money with the bank?

So the question is, what, Is this delta?

Delta, remember, is that we take in 100, and

then we pay out 100 plus delta, so let's keep in mind this.

I will say a few words and then I flip over, and then we'll see.

Look, my idea is the following.

In this red square, unfortunately,

we know right away that nothing good is happening there.

Maybe the bank may go bankrupt and

then depositors can get nothing.

Everything goes to the lawyers because this is a debt contract of liquidation.

So we will try to find the situation in which, and also,

we know that in this big box, everything goes fine.

But our job is to make sure that in these boxes,

the bag exists and delivers on its obligations.

Maybe in these areas, the bank does not make money.

But that's alright, if it stays here.

Let's see how that proceeds.

I will say that I pay back to the people 100 plus delta.

And If the bank delivers on its obligations in all these three boxes,

in one big one and these two long ones, with the exception of the small red box,

that happens with what probability?

Let me go back for a moment, 0.64, 0.16, and 0.16.

So these are equivalents, so the probability here is 0.32 plus 0.64.

So the probability of sort of alright cases,

I'll put it here, pi of (okay) is 0.96.

And then over here, the pi of the low is 0.04.

So, we structure our contract with

depositor in such a way that plus delta

times 0.96 is equal to 100.

So, we say that with this delta, we will compensate you for

the loss of money in this small red box.

And then all our cases will be able to deliver, and

you would not lose your money.

So, calculating,

we get that delta is 4.17.

And therefore the contract of depositors,

now I will use a black marker because it's better seen, depositors' bank.

How does that look?

So depositors give 100, and

they receive 104.17.

Now this amount, as you can see, clearly,

the total amount you have to multiply by 100,000.

This is the total number of depositors, and that's exactly $12.5 million.

Now you can see that indeed the key story

is that this amount the bank has here,

here, and there in these long boxes.

This amount is just enough to deliver on the obligations to the depositors.

So the bank makes nothing here, but pays everything to the depositors.

Here, the bank will make money, now let's proceed.

So we have the following situation.

We have the pi of 0.04.

What happens?

The bank is liquidated And no one gets anything, too bad.

Why is that?

Because with this probability, the bank cannot make this payment.

So, the bank defaults on its obligation.

And because this structure in the contract between the depositors and the bank is

the debt contract of liquidation, then depositors liquidate the bank.

They go to the lawyers, and then the bank goes bankrupt, and

all the money goes to the lawyers.

Now with the probability of 0.32,

these are the two long boxes combined.

We can see that the bank does deliver on its obligations,

but expect that cash flow to the bank is just 0.

Because the bank collects exact with this amount, and all the money

is paid to the depositors based on this contract with this small delta.

However, there's another nice thing, and I will put a line here.

And probability of 0.64, this is the big

box of the high and high state, what do we see?

We can see that now, what is the expected cash flow to the bank?

The expected cash flow to the bank now is 0.64 is the probability.

Now, what is the amount that the bank has there?

The bank collects 7.5 plus 7.5, so 15.

Then you have to subtract here 12.5 that it pays to the depositors here.

So this is the expected amount of cash flow that the bank has made.

Now that's not yet it because the bank also paid for two acts of monitoring.

So we have to subtract 2 times 0.02.

This is $20,000 in [INAUDIBLE] and that arrives at $1.56 million.

This is the amount of money that the bank makes, given this setup.

Well, this is a nice amount, given the numbers here.

And now we arrived at another interim stop.

We can see one more local happy end.

The bank engaged in a scheme that we

described, and then the scheme borrowers got financing.

Depositors got a contract that we described here.

The bank made a significant positive profit.

That's great.

Now the problem is, however, that neither the depositors nor

the borrowers improved their contracts a bit.

Because they, in monetary terms,

would have exactly the same if they communicated directly without any bank.

And then the question arises, well, you, dear bank, did great.

Why would you share a bit with us?

Because you made quite a bit of money.

And the key story here is that if the bank did share, let's say,

I will go back to this, paid a little bit more to the depositors.

Now you can see what would happen in these long boxes.

The bank would not have raised enough money, and

therefore, would have gotten liquidated.

By the same token, if the bank charged a little bit less than 7.5, here,

it would make a little bit less money.

That's okay, but here, again, if this is 5 and this is,

let's say, 7.4, it falls short of 12.5.

So the bank would have gotten liquidated with a probability of 0.36,

and this whole scheme would have collapsed.

So we can see that the existence of the bank

as an intermediary that enjoys monitoring and

engages in collecting deposits and

then repackaging them and lending that to borrowers in larger amounts.

This is a great business, but this is fundamentally vulnerable.

And the bank, unfortunately,

does not have any resource to share in the way we discussed.

But then the question is, why the hell would depositors come and

deposit their money?

Because they would like to have something in exchange.

And when it comes to borrowers, that is do-able to discuss that with them somehow.

Because, well, borrowers are multiple, but they're not very many.

But with depositors, you have to create something that will attract

them without the need to engage in lengthy negotiations with each and every one.

And that, as we will see in the future, will be the special way,

how the bank would produce liquidity.

And by doing so, the bank will indeed attract these depositors.

We will do that starting from the next week, but

then we have one more episode here that will wrap up the story of

banking as an intermediary that provides one very important thing.

That is called asset services, or in our more plain vanilla words, monitoring.

We'll wrap this up in the next final episode of this second week.

2.6. Delegated monitoring (1) – the interaction of the parties and bank’s profit

Capital Markets and Financial Institutions – How to Survive Them

Conheça os instrutores