Bailout Math

[Ike]

Did you know:

*That the total estimated value of all outstanding mortgages in the US is about 10 Trillion Dollars.
*That the record rates of foreclosures we are seeing are only in the range of 2%
*That if a foreclosure resulted in a total loss to the lender, then the total loss involved in the current crisis would be about 200 billion....and thats extremely pessimistic.

So why do we need to bail out wall street to the tune of 700 billion?

Anyway, I learnt all that from the following bloggish posts. They are mostly apolitical. In it, a math guy explains in simple terms how we got where we are.
This is a pretty good series of posts:

http://scienceblogs.com/goodmath/2008/09/economic_disasters_and_stupid.php
http://scienceblogs.com/goodmath/2008/09/bad_probability_and_economic_d.php

http://scienceblogs.com/goodmath/2008/09/how_mortgages_turned_into_a_tr.php

[Viking Kitten]

A economist acquaintance of mine, who is very pro-free trade and hates the idea of the bailout but calls it a necessary evil, explained it to me this way:

The math you quoted may be correct, but right now the balance sheets are so bad that foreign investors are not putting any new money in those firms.

That means those financial institutions have no money to lend. If credit markets freeze up, businesses that borrow money on a daily basis cannot expand. That could in turn cause a downward spiral that could very quickly get out of control.

It's kind of a rock and hard place type scenario, but every knowledgeable person I've talked to assures me it's better than doing nothing.

[Vaevictis]

This is something I wrote somewhere else to describe my estimation of what's going on:


Portfolio Theory

First, a description of portfolio theory and how they related to Collateralized Mortgage Obligations (CMO's), which are central to what's going on.

Portfolio theory is one of those central subjects in finance. Essentially, it attempts to model how the returns on assets changes when you group multiple assets into a "portfolio." I'm certain you've all heard (ad nauseum) that a diversified portfolio is critical to your economic future. This isn't just someone talking for the sake of talking. There's real math and real science behind it.

I'm going to talk about the math, and then describe it in layman's terms. If you're allergic to math, I apologize, but it really is important in order to understand what's happening.

Assume you have an asset 'A'. It could be a stock, a bond, a commodity, a house, a car, whatever. It has an expected return 'r'. This is only expected, however. It can vary. You can statistically describe how it varies using something appropriately called the variance -- we'll use 'v' for that.

You can think of the return on this asset as something like:

r +/- f(v)

where f(v) is a function that randomly selects an adjustment to the return based on the size of the variance.

So, what happens if you take two assets and combine them into a 'portfolio?' Well, statistics work out something like this:

Let 'w1' be the proportion of asset one in the portfolio, and 'w2' be the proportion of asset two. Let 'v1', 'v2' likewise be the variance (standard deviations, really, but let's call them 'variance' because for non-math geeks, that's more intuitive as a term), 'r1', 'r2' be the returns.

The portfolio ends up looking like this ('rp' expected return of portfolio, 'vp^2' expected variance.):

rp = r1*w1+r2*w2
vp^2 = w1^2*v1^2 + w2^2*v2^2 + 2*w1*w2*v1*v2*p12

I've neglected the term 'p12' thus far. This is the 'correlation' between the two assets -- how much they 'move together' in value. This is a number between 1 and -1. If when asset one goes up 1USD, asset two goes up $1, the correlation is 1. If when asset one goes up 1USD, asset two goes down $1, the correlation is -1. If the correlation is 0, then a change in one has no predictive value on how the other will change -- it could go up $1, down $1, stay the same -- it essentially means there's no relation between the two.

First thing you note is that the return of the portfolio is the average of the two expected returns. The variance is where the magic occurs.

w1 and w2 are obviously fractional -- they're both less than one. They get squared. This means that the contribution of each asset's variance to the portfolio's variance gets knocked down quite a bit.

Example: w1 = w2 = 1/2. r1=0.05, r2=0.05, p12=0, v1 = v2 = 0.02

rp = (0.5)(0.05)+(0.5)(0.05) = 0.05
vp^2 = (0.5)^2(0.02)^2+(0.25)^2(0.02)^2 + 0 = 0.0002

As you can see, combining these two assets yielded a portfolio with the same expected return but a much, much smaller variance. This is obviously a very good thing, right?

Okay, let's do another example:

Example: w1 = w2 = 1/2. r1=0.05, r2=0.05, p12=1, v1 = v2 = 0.02

rp = (0.5)(0.05)+(0.5)(0.05) = 0.05
vp^2 = (0.5)^2(0.02)^2+(0.5)^2(0.02)^2 + 2*(0.5)(0.5)(0.02)(0.02)(1) = 0.0004

You'll notice that the correlation term 'p12' can have a huge impact on the results. In the case of p12=0, we got a 0.0002 variance, but when we increased it to 1, we got 0.0004.

One of the nice things about a portfolio is that you can keep adding assets to a portfolio and the 'wX' weighting terms get smaller and smaller -- which causes their squares to get smaller and smaller, which causes the variance to be smaller and smaller.

But you have to be very careful about the correlation. As you can see, if the assets in the portfolio are highly correlated, it can do a lot of damage in terms of increasing your variance.

So, what does all that have to do with the current situation? Well, Collateralized Mortgage Obligations (CMOs) are portfolios of fractional claims on mortgages. They're much less risky than owning just a single mortgage due to the above effects I just described.

But, as I showed before, there's that niggling little correlation term that can ruin your day. I suspect in the past, when the economy was booming, that correlation coefficient was low. When one mortgage failed, it had very little to do with another failing, so it kept the variance of the portfolio very low.

But what happens when the economy goes south? Suddenly, one mortgage failing does have a lot to do with another failing, because lots of people are having a rough time and defaulting in bunches. The variance goes up. A ton.

And whoever's holding the portfolio has their expected return get creamed.

Derivatives

Derivatives seem to have a bad name with some people. Can they be used for shenanigans? Absolutely. Do they muddy the water with complexity? Yes. Are they useful? Extremely.

The term 'derivative' in this context comes from the fact that a derivative security derives its value from the value of some other security.

We'll go with the simplest example: A call option. A call option gives the holder the right, but not the obligation, to purchase an asset at a specified price (called the strike) before or on a certain date (called the expiration date).

(I now disclose that I'm using American style options here. There are other styles, European, exotics, etc. If you're interested, look them up -- I won't discuss them here.)

This is very simple to understand. If you own a call option on IBM at strike price $100 with a duration of one year, you can exercise the option at any time during the year and receive one share of IBM for a payment of $100. When would you do this? Obviously, when IBM's share price is above $100. Exercise it, sell it, and keep the difference.

There's another option called a put. It's the opposite of a call -- it gives you the right to sell an asset at a certain price. Why would you want a put? Well, you might be speculating that the price is going to drop -- that way, you can buy it below the strike, then exercise the put and pocket the difference.

... or, you might not be speculating at all. You might own a share of IBM and want to set a floor on the amount of money you can lose.

See, that's the key here. Derivatives provide the opportunity to speculate, but they also provide the opportunity to insure.

In AIG's case, AIG was selling 'swaps' on these CMOs. A swap is an agreement to exchange cash flows around a reference point.

For example, if someone holding a CMO was expecting a return of 5%, they could enter into a swap with another party. If the return exceeded 5%, they would have to pay the other party the difference -- but if it fell below 5%, the other party would pay them the difference. In either case, the first party will always receive a 5% return. The other party receives a floating rate return. Obviously, if the return goes up, the second party is happy -- and if it goes down, the second party is unhappy.

Likewise, if you have a fixed return (eg, maybe you have a treasury), you can turn it into a floating return using a swap.

Often times, banks will get two individuals together -- one in a floating rate, one in a fixed. The swap allows them to 'swap' positions, with the floating rate becoming a fixed rate and vice versa.

Derivatives provide flexibility and insurance in the market. They also provide the opportunity to speculate.

I think the main point I'm trying to make here is: Don't assume derivatives are bad just because they're derivatives. They have multiple uses. Some of them are very important and non-speculative, and some of them are just like rolling the dice.

Leverage

Leverage is debt. One of the central results of financial theory is that debt can be used as a 'lever' to increase returns to shareholders. Given that, it should be pretty obvious that leverage is very attractive to executives and shareholders alike.

But leverage has a downside -- it multiplies your returns, but it also multiplies your losses. If you're highly levered up, you are a superstar when things are good. But when things go bad, you're bankrupt. That's what you're seeing here.

But it's worse than just that. A lot of these investment banks were probably leveraging on 'margin', and this is (in my opinion) a big part of what precipitated their collapses. It's not the first time something like this has happened. Long Term Capital Management was a superstar hedge fund, and leverage killed it.

So, how does leverage kill, other than the obvious magnified losses?

Simple: Margin calls. Buying on margin is a kind of leverage -- essentially, you borrow money from an investment counter-party. They require you to put up and maintain a certain amount of equity in this margin account. You buy assets with this combined debt and equity account.

As the assets increase in value, your equity in the account increases, increasing the equity ratio. But when the assets decrease in value, your equity decreases, decreasing the equity ratio. When the ratio gets too low, you get a 'margin call'. This means you have to deposit more equity to increase the ratio to an acceptable level, or your counter-party closes out the position, which means selling the assets at market liquidation price.

Imagine you're an investment bank. You want to buy CMO's. Being someone who knows about finance, you know leverage multiplies returns. CMO's look pretty low risk. So you lever the hell out of them.

What do you post as equity? Why, your stock and other assets.

You're chugging along just fine until one day, CMOs drop in value. You have to post more equity. You do so -- maybe cash, maybe stock, maybe other assets. But you're heavy in these CMO's -- it took a lot of equity to maintain the ratio, and it hurt.

Someone on the Street hears about it. Your stock price goes down. But wait, your stock is part of the equity! Now you have to post more. Folks hear about this -- and your stock price goes down further. Now you have to post even more!

This sort of thing happens over and over again -- CMO value drops, stock price drops, margin calls, etc. It's an endless loop. Eventually you can't post margin, and the position gets closed.

Your counter-party tries to liquidate the position -- but finds there are no buyers. So they sell at a massive discount.

But guess what? You and a bunch of other banks have highly leveraged CMO holdings too. This massive discount sale hammers their value. Result? More margin calls, and loops throughout the sector.

This process repeats until say, you have all five major banks go bankrupt, merged, or changed business model to no longer be investment banks.

Interlude

Okay, so the above can be used to give you an idea of what's happening to the banks and why they're in such deep trouble. You misuse the above tools, and you're toast. And boy did they misuse them.

Now, on to why the Treasury and the Fed are scared out of their minds.

The Money Multiplier

This one is rather short and sweet. Deposit accepting banks only have to keep a fraction of the amount of money you deposit on hand. They can loan out the rest. This is called the 'reserve rate.' Banks keep this rate very low when they're bullish, and raise it when they're scared or in trouble.

If I recall correctly, the statutory minimum is 10%. This means that for every $100 you deposit, $90 can be loaned out. But this $90 gets spent, and deposited elsewhere -- that bank can now loan out $81.

This process repeats until you have $100 in deposits and $1000 in loans. This is called the money multiplier. Because of the fractional reserve system, deposits multiply the amount of money in circulation.

But what happens when banks get spooked (like they are now) and they raise their reserve requirements? Let's assume they raise it to 25%. Doesn't seem like a lot, does it?

The impact it has on the amount of money in the system is huge. Instead of $1000 in loans per $100 in deposits, you now have $400. That's a 60% decrease.

This sort of contraction in the money supply causes...

Deflation

Deflation is the opposite of inflation -- as time passes, your money becomes worth more. Doesn't sound so bad, does it?

But it is. It was one of the major causes of the Great Depression. It has the nasty effect of lowering prices on goods -- but not lowering costs to produce those goods as fast (like wages).

It has an extremely nasty effect on debtors -- because the dollar is worth more, but your payments are contractually set in advance -- your cost of debt skyrockets.

Deflation is also a self-reinforcing loop. People get scared, so they hold cash. Taking cash out of the money supply causes deflation. This causes more people to get more scared, taking more cash out of the money supply.

The worst part is that the central bank has few options when an economy goes deflationary. Their main tool -- the Federal Funds Rate -- becomes useless. You can't reduce it below 0% -- and because the economy is deflationary, the interest rate charged on debt may actually be 0% or less -- you don't need it to be high when the value of the money is increasing.

The Bailout

So, we get to the bailout. One of the things you need to understand is that Bernanke was a respected, tenured finance professor at Princeton. One of his specialties was the Great Depression.

There's a reason he's freaking out right now, and he's behaving the way he's behaving. He knows that a contraction of the money supply was one of the prime causes of the depth and duration of the Great Depression.

He knows that banks are spooked -- they're increasing reserve requirements, they're not lending to each other or consumers, and this has the potential to trigger a deflationary cycle.

Taking these toxic assets off of their hands would loosen them up -- they'd have stronger balance sheets, and they'd know the other banks do too. Hopefully, they'll start lending again, and we'd bypass the deflationary cycle and have a simple recession.

Conclusion (and some editorial content)

Is the current bailout plan the best we can possibly get? I don't know.

I do know that if we don't find a way to stabilize the banking system, we're in deep, deep trouble. I don't think that letting a bunch of banks fail is going to accomplish that.

Are you scared yet? You should be. Some of you need to stop worrying about the fat cats getting paid; there are bigger things at stake here.

For goodness sake, let's not cut off our nose to spite our faces. If a second Great Depression really is in the cards -- and Bernanke CLEARLY thinks there is -- we need to do something. Now. And if that includes a few people taking their pound of flesh or getting unjustly rewarded, well, it sucks. But I think I can live with that much easier than with another Depression.

[mdklatt]

It's kind of a rock and hard place type scenario, but every knowledgeable person I've talked to assures me it's better than doing nothing.

Better for whom?

**** the debtors. They're the reason that savers take it in the ***. Recently, the only way to keep your savings from actually losing value due to inflation is to put it all in the stock market, and oops!, maybe that's not such a good idea either. No good irresponsible negative savings rate-having bitches. :mad:

[AlbqSooner]

For all of you that are opposed to the $85,000,000,000.00 bailout of AIG, please
consider the following.

Instead, let's distribute the $85,000,000,000 to the people of America in
a "We Deserve It Dividend".

To make the math simple, let's assume there are 200,000,000
bona fide (legal) U.S. Citizens 18+.

Our population is approximately 301,000,000 +/- counting every man, woman
and child. So 200,000,000 should be a fair estimate of adults 18 years and over.

So divide 200 million adults 18+ into $85 billon and that equals $425,000.00.

Now, give $425,000 to every person 18+ as a "We Deserve It Dividend".

Of course, it would NOT be tax free, so let's assume a tax rate of 35%.

Every individual 18+ would have a tax obligation of $158,200.00, payable to the IRS.
That sends $29,750,000,000 right back to Uncle Sam.

This will give every adult 18+ a net after tax dividend of $266,800.00 to spend as they see fit.
A husband and wife would have $533,600.00.

What would you do with $266,800.00 or $533,600.00 per family?
Pay off your mortgage - housing crisis solved.
Repay college loans - what a great boost to new grads.
Put away money for kids college - it'll be there when they finish high school.
Save in a bank - create money to loan to qualified borrowers and entrepreneurs.
Buy a new car - save the auto industry.
Invest in the market - capital drives growth.
Pay for your parent's medical insurance - health care improves.
Enable Deadbeat Dads to come clean - or else.
Illegal immigrants will want to get legal - too late for this dividend.

Remember this is for every adult U S Citizen 18+, including the folks
who lost their jobs at Lehman Brothers and every other company
that is cutting their work force. What a nice bonus for our men and women serving in the Armed Forces.

If we're going to re-distribute wealth let's really do it...instead of trickling out
a puny $1000.00 economic incentive stipend that is being proposed by one of our candidates for President.

If we're going to do an $85 billion bailout, let's bail out every adult U S Citizen!!!

As for AIG - liquidate it.
Sell off its parts.
Let American General go back to being American General.
Sell off the real estate.
Let the private sector bargain hunters cut it up and clean it up.

Sure it's a crazy idea that will never happen, but I ask you; don't we deserve it more than AIG?

But can you imagine the Coast-To-Coast Block Party, not to mention the immediate impact on the food and beverage industry.

How do you spell Economic Boom?......"WE DESERVE IT DIVIDEND" !!!

I trust my fellow adult Americans will know how to use their $85 Billion
"We Deserve It Dividend" more than the geniuses at AIG or in Washington DC .

And remember, the "We Deserve It Dividend" plan's actual cost is $55.25 Billion, because $29.75 Billion will be returned immediately, in taxes, to Uncle Sam. ;)

[85Sooner]

This is very simple to understand. If you own a call option on IBM at strike price $100 with a duration of one year, you can exercise the option at any time during the year and receive one share of IBM for a payment of $100. When would you do this? Obviously, when IBM's share price is above $100. Exercise it, sell it, and keep the difference.

There's another option called a put. It's the opposite of a call -- it gives you the right to sell an asset at a certain price. Why would you want a put? Well, you might be speculating that the price is going to drop -- that way, you can buy it below the strike, then exercise the put and pocket the difference

And from what I understand, regulations put in place after the Enron fiasco created the ability to put but not call. Also the way assest were valued (the accounting) was changed to prevent the enron thing from ever happening again and in part that is why some people were asking for "DEregulation" of the market to allow it to go back to the pre Enron days and let the market work itself out. Does that make sense?

[mdklatt]

So divide 200 million adults 18+ into $85 billon and that equals $425


Fixed!

[Vaevictis]

So divide 200 million adults 18+ into $85 billon and that equals $425,000.00.


$425, actually.


And from what I understand, regulations put in place after the Enron fiasco created the ability to put but not call.

Nah, you can still buy and write calls. They're important for something called a 'costless collar' which lets a commodity manufacturer set a floor on the price of their production without any initial outlay. (The cost is that they have to sell a call, which puts a ceiling on the price.)



Also the way assest were valued (the accounting) was changed to prevent the enron thing from ever happening again and in part that is why some people were asking for "DEregulation" of the market to allow it to go back to the pre Enron days and let the market work itself out. Does that make sense?

I don't know about this one way or the other.

[Jerk]

Anyone have cliffs notes for what Vaev posted?

[Vaevictis]

Portfolio Theory

When you combine multiple assets with different returns into one portfolio, the variability of the return can be reduced. The degree to which this reduction occurs is dependent on how correlated they are (ie, how similar their variability is.)

Portfolios of mortgages looked like they were uncorrelated when the economy was booming. Then when it turned south a little, suddenly they became highly correlated, and whole slews of CMOs that were safe became very dangerous.

Derivatives

Derivatives are not only used for speculation. They can be used to limit loss or change the behavior of your financial position (eg, they can be used to change a fixed interest rate into a variable one, or vice versa)

Leverage

Leverage can be used to multiply gains, but when you do so, it also multiplies your losses.

Leverage can be created through the use of margin. A margin account consists of a proportion of debt and a proportion of equity. You must maintain a certain ratio.

They constructed these margin accounts in a way that they created an endless loop whereby they were constantly having to deposit equity into the accounts. This caused them to run out of cash and to go under.

It also spread to other banks. Repeat. Now everyone's having issues, and everyone's crashing.

Money Multiplier

We have a fractional reserve system. When you deposit money, the bank keeps a certain percentage, and loans out the rest. This repeats until the whole amount deposited is kept in reserve.

This creates money. When banks get spooked, they increase the reserve percentage. This reduces the amount of money in the system, causing...

Deflation

Deflation is bad. Bad, bad, bad. Horrible. Economists are scared ****less of deflation. Out of their minds terrorized. Especially ones who know about the Great Depression, like current head of the Fed, Bernanke.

Once deflation starts, it's almost impossible to stop. We don't want deflation. It was a major contributing factor to the Great Depression. Avoiding it is worth almost any cost.

The Bailout

Taking these toxic assets off of the hands of the banks should get them to loosen up and start lending money again, so they don't create deflation. It might even prove profitable for the government.

[Jerk]

I can't argue this crap. I don't feel like putting forth the mental effort (i.e. I'm drunk) to dissect it. However, I would like to discuss this with a more philosophical approach. Why would another depression be a bad thing?

Wouldn't it be kind of like burning the house down, and starting all over?

Come on! It will be fun! People will learn new things - like how to hunt and fish (or they won't eat:P)

[Jerk]

mmmmm.....fried squirrel! Just like Grandma ate when she was growing up!