I want to explain the Geithner Put for those without a finance background who want to understand how FDIC is going to get looted. (Warning: Will contain graphs, and be long and boring even by normal standards here.) Recap: Banks have “toxic waste” assets, which they want to sell. Geithner has created a public/private partnership, where FDIC will provide leverage, and government officials and hedge funds will provide some cash and set a bid on this waste. Self-evident has a useful follow-up to his “Geithner Put” post, which I blogged about yesterday. Nemo argues that the FDIC leverage provides a “put option” on the asset. He assumes a uniform distribution of values, and plays around with results. His results confirmed what he did on the back of the envelope – FDIC will be holding the bag.
Put option? What the hell is that? From Taibbi’s argument that we need more financial engineering literacy among the angry populists, I want to graph out what is happening – since I am a financial engineer and an angry populist. The Geithner plan will allow hedge funds to buy large chunks of bank toxic waste, and we’ll use denominations of $100 for each unit. How much to bid?
The problem for markets is we don’t know what these “toxic waste” assets are worth. If I was a hedge fund whiz-kid, or even a normal ho-hum banker worried about credit defaults on my portfolio of regular mortgages, I’d be assuming the value would look like a lognormal distribution (to be fair, at the end I’ll cover this, I’d normally assume that the losses, not values, look like a lognormal distribution – but these are not normal times). Just guessing, the “toxic waste” assets have a mu of 3.3 and a sigma of .5 – made-up, but reasonable. Hedge funds will use historical data to fit a distribution, and then play around with macroeconomic projects and other correlation matrices to fit it to the instruments at hand…it’ll look like what we have, except shifted a bit perhaps. But let’s go with these made-up numbers. Let’s draw one so you can visualize it:
As you can see, as with all lognormal graphs, the mean (red line) is larger than the median (green line). This will become important. So for every original $100 in toxic waste loans, it’ll have a distribution like above, where it is half likely than it will be less than $27. Some loans will be worth more than $100, so they get capped at $100 – this represents pre-payment risk, the idea that someone holding your liar’s loan won the lottery and paid off his mortgage in full.
So we believe that the toxic waste will have an average value, or its mean, of $30.65 – we should bid less than that. In a perfect market, we’d have to bid that. However let’s be crazy and bid $35 for this toxic waste. What would happen if we were a normal investor, who couldn’t leverage off FDIC? I’d have to actually pay $35 if I bid $35. Insane, right? Our payoff would look like this:
(Nerd disclaimer: The distribution is no longer in any kind of units on the y-axis, but is still to scale on the x axis.)
So that blue line is our profit. So if the asset is worth $35, our profit should be $0. It’s exactly what we paid. Note that blue line is at $0 at x = $35. If asset is worth $0, which it could be, we would lose our entire $35. If it was worth $100, we’d make $65. Make sure you follow this before moving on.
Now with the Geithner Plan, the FDIC provides 6-to-1 leverage. Which means we place a bid, and then only have to provide 1/7th of that bid. The FDIC leverage is non-recourse. So if we lose that 1/7th of the bid, we don’t lose any more money. FDIC takes care of the rest. If it goes up, we get the profit. Leverage!
Now what did I just say? Since we are bidding $35, we only need to place $5. This $5 is our “skin in the game”, as people are saying. FDIC covers the other $30. If it is worth $32, we lose $3. If it is worth $30, we lose all $5. If it is worth $10….we just lose our $5. FDIC is on the hook for the other $20. Look at the profit lines on this chart, which is the plan going forward:
Again: If the value of the asset is $30, we only lose our $5. What if the value is $29? We only lose $5 – however someone has to lose that extra $1 – and that is the FDIC. If the asset is $28? We only lose our $5 – that additional extra dollar is covered by the FDIC. If it is worth zero, someone still has to lose $35, and they do – we lose $5, the FDIC loses $30.
The Greenspan put was always a metaphor – the Geithner Put is an actual put option. If it goes up, we get it. Fantastic! If it goes down, our losses are capped. This is what having a put option looks like – under a certain point, we gain a dollar for every dollar we lose, so it nets equal. No value is created with options, so if we gain a dollar there then someone else must be losing a dollar, and that is FDIC. (note: I just fixed that graph so it is correct.)
Aside: If you think about it above, you may ask why would someone every sell a put option like that above? It is crazy – it always loses money and can never make money. Normally you sell it for some value – say $3 above. So if the asset is $30 or above, you make $3 ($30 is the “strike price” here). If it is $27, you break even. So giving away an option is the same as giving away money, in this case. Lots of fancy formulas have been written about how to calculate the value of an option – feel free to read the wikipedia linked above for a quick primer.
So what happens if we bid $35? Running that chart through some monte carlo math programming we expect to make $1.28. When I say expect, I mean on average. FDIC is expected to lose -$5.64.
Let’s look at a bunch of scenarios:
HF is for hedge fund. FDIC losses are in terms of total loan, not its leverage value – so it should actually be higher.
The $35 bid we just covered. But we are a mysterious and wise hedge fund, who has correctly figured out the average price – and with the government’s backing, we are “risk neutral”, and can bid the straight average. What if we bid the average? If we bid the average, we should expect no profit. If we agree to flip a coin a million times, and heads you get $1 and tails you get nothing, and you pay 50cents for each flip, over a million times you should end up with $0. Paying the average balances out. However, looking at the second line, since our downside is covered, we transfer out $3.66 for putting up $4.38, a nice 83% profit transferred straight out of the FDIC, which loses exactly that $3.66.
Now we believe markets are good though, right? Since we figured out that we can bid the average and make a profit, some other equally smart hedge fund is going to come along and simply bid a bit higher, making less profit but still some. We know this and do the same. So we both bid to the point where there aren’t any profits (line 3 of the chart). I assume this is what the administration has in mind when they say this will get the banks going again – since we are overbidding, we are giving the banks more money than we expect the asset to give us. And sure enough, we make no profits – and since that red line in the payout charts above has shifted to the right, there is more downside risk. And the FDIC transfers all that money straight to the banks.
Let’s go the other route. Maybe we get lucky! We underbid, the bank takes our bid, and the asset is worth a lot more than we expected. We make a massive profit, however FDIC is still expected to lose some money on some of the assets.
Now maybe you think this distribution is too low. Fine, it probably is. I’ve played around with the mean both higher, much higher, and much lower, and it is still a transfer from FDIC to the hedge funds. However, I’ve kept the variance relatively low; expanding that would increase the transfer, since there would be more tail risk.
So what’s the deal? Now I did a sneak – under normal circumstances, credit modeling usually assumes that the losses are lognormally distributed, not the portfolio value. What? That means that the value of the asset, according to normal credit modeling, should be flipped; the large bell should be around the high end, with a few stray values near zero. More importantly, the mean will be less than the median. This is what banks do when they look at their economic capital. A portfolio of highly rated bond instruments would look like this:
As you can see, almost all assets are above $70, with a small few here and there below, and a few more at $0 if you look really hard.
What happens if this is the case? I called that optimistic in the chart. The hedge fund bids the average, and it doesn’t make a profit (like it should) and the FDIC put option is worthless, since it rarely pays out. This is good for the taxpayers, banks, and the hedge fund. Which is to say, if it did look like this, the market wouldn’t need the government to jumpstart it – people would be lining up to get in on this deal. Holding this portfolio, modeled above, would be a godsend in the current environment. More generally, I’d be very, very surprised if this is what it looked like – because if it did, everyone would want to snatch it up.
I’ve played around with this in matlab for a little bit (I can post the code if anyone is interested); the real issue with determining this in this tail median/mean issue. If you think that all these subprime loans are essentially good, with a few stray bad ones in there, then this is a great deal for taxpayers. This would be surprising, since nobody wants to go near these things. If you think that these subprime loans are shit, and there will only be a few good ones in there, then we are essentially transferring money to banks and hedge funds straight out of FDIC.
Oh – Last two things as a quick update:
1) When I say “hedge fund” above, I mean the public-private half-Treasury, half-Private (hedge funds, private equity, connected insiders, etc.) creation. So technically half the profits go to the Treasury. Unless the bids come in very low, which seems against the idea of what they are doing, half the hedge fund profits above won’t cover the expected losses of FDIC, so it’s a net loss to the Government.
2) And in case you are wondering, FDIC gets its money from taxing banks. Read about the “emergency” fee they are charging all banks in order to recapitalize for 2009, including this move, to supplement the line of credit from the government. Which is it say, we are being joined by medium and small banks, the thousands of them that were responsible with their lending and banking practices, in paying large taxes to bail out their larger, more reckless, and more well-connected competition. You know, those Too Big To Fail Banks, which are necessary because they give us better services at lower risk. Viva crony Financial Capitalism!
Great comments. I didn’t want to dig too much into the microstructure of how these are set up in this post, because I wanted to pitch it at a level of people who are interested in learning about derivatives and put options without any background. A few things.
3) Many people are bringing up that the FDIC sets the leverage. Now if the leverage goes down, all that does is moves the light blue FDIC Put line to the left – it lowers the “strike price”; the dark blue hedge fund line moves appropriately. The option is worth less, as it is strictly increasing in strike price, but it is still a put option.
Now I have leverage exogenous to this above – the distribution sets the bid, and the bid and leverage set the payouts. Will leverage also depend on the distribution? Will the FDIC be able to handle political pressures from Geithner to make sure this works, and will it understand these mortgages better than the private equity and hedge fund folks? As self-evident said “As long as the FDIC has more expertise in evaluating the risk of toxic assets than the entire private equity and banking worlds combined, there is no way they could be taken to the cleaners like this. What could possibly go wrong?” Yup.
4) Some are saying that the assets could/will be more than projected above. True. What didn’t occur to me until I started playing around with this model is how much the FDIC gets hosed even if the assets are great. (I made a lot of charts, but this is already too long). Let’s say the average value is 74.6 out of 100 – very optimistic (mu = 4.3, sigma = .2). The hedge fund knows the distribution in advance, because MBA programs are that good, and bids the average. No profit right? Except they still make $1.63, a nice 15% profit – and that is straight from FDIC.
Wait! Why? The assets turned out fine! Because, without getting too technical, the mean is larger than the median, and the volatility has value in an option. Look at the graph – they are bidding, in that red line, above where most of the values are. So they are chasing all the upside (mean), while the FDIC is left looking after downside, which happens to be where most of the distribution is (median). Also because the volatility here has value to them in the form of the option, regardless of expected value. I will post the matlab code that takes in the leverage, bid, and parameters and gives the estimates and draws the graph, if anyone is interested.
So if you think digging through all these mortgages involves just rooting out a few bad ones (median is greater than the mean) we are fine; if you think it involves trying to find a few good ones among all the crap (mean > median), then the FDIC gets taken to the cleaners.
5) Followups What also surprised me is that the put option, under some assumptions, is more valuable than the banking assets, and I argue the hedge funds may just try to maximize that instead here (somewhat technical, I tried to keep it easy).
For those who say that nationalization is also a put option, and the money comes from the FDIC one way or the other, I talk about how the path dependency does matter for our country.
Thanks for stopping by!