For once we’d like to get a fair value when we come into contact with the banking system

TO BE NOTED: From Bloomberg:

"TARP Warrants Show Banks May Reap ‘Ruthless Bargain’ (Update2)

Share | Email | Print | A A A

By Mark Pittman

May 22 (Bloomberg) -- Banks negotiating to reclaim stock warrants they granted in return for Troubled Asset Relief Program money may shortchange taxpayers by almost $10 billion if Treasury Secretary Timothy Geithner’s first sale sets the pace, data compiled by Bloomberg show.

While 17 financial institutions have repaid TARP funds, two have come to terms with the U.S. on the value of the rights to buy stock that taxpayers received for the risk of recapitalizing the industry. The first was Old National Bancorp in Evansville, Indiana, which gave the Treasury Department $1.2 million last week for warrants that may have been worth $5.81 million, according to the data.

If Geithner makes the same deal for all companies in the rescue program, lenders may walk away with 80 percent of the profits taxpayers might have claimed.

“For once we’d like to get a fair value when we come into contact with the banking system,” said Representative Brad Miller, a North Carolina Democrat and chairman of the Investigations and Oversight Subcommittee of House Science and Technology Committee. “We don’t want a ruthless bargain.”

Under the Old National warrants formula, Bank of America Corp. would save $2.03 billion, followed by Wells Fargo & Co. at $1.48 billion and JPMorgan Chase & Co. at $1.46 billion. Morgan Stanley’s benefit would be $983 million, Citigroup Inc.’s would come in at $965 million and Goldman Sachs Group Inc. would have $693 million, according to the data compiled by Bloomberg.

‘Stronger Incentives’

For the 20 largest TARP recipients, the total savings would be $9.985 billion, the data show.

Senator Jack Reed, a Rhode Island Democrat and chairman of the Banking Subcommittee on Securities, Insurance and Investment, said today in a letter to Geithner that warrants were part of the TARP so that taxpayers could be compensated for the risks they took investing in lenders.

“We need to ensure that the financial industry recovers and that banks can start lending again, but taxpayers must be fairly compensated as well,” Reed said.

Geithner wants to move swiftly to sell the TARP warrants, he said on May 20. Their worth depends on assumptions about the chances the underlying stock will go higher than the rights. Depending on the input, different valuation models reach a range of conclusions.

Lenders shouldn’t be trusted to make suppositions that would be to the advantage of taxpayers, said Linus Wilson, an assistant professor of finance at the University of Louisiana at Lafayette.

‘Doing Our Best’

“Bank managers have stronger incentives than Treasury personnel to get a better deal for their constituents,” said Wilson, who has written about appraising warrants.

Because Old National was the first to repay TARP money and buy its rights back, the transaction “sets the price point for the whole program,” said Simon Johnson, a fellow at the Peterson Institute for International Economics in Washington.

“The point of the warrants is that taxpayers participate in the upside,” said Johnson, who testified on the securities before Miller’s subcommittee on May 19. “It defeats the whole purpose if you’re going to sell them way below market price.”

Treasury Department spokesman Andrew Williams declined to comment on Old National.

“We’re doing our best to protect the taxpayers’ interest and make sure we get fair market value,” he said.

Returning $45 Billion

The department has a “robust process” of evaluation, using two modeling systems, consulting with an asset manager and collecting bids from market participants, Williams said.

The U.S. received rights to buy 1.4 billion common shares in exchange for $287 billion in TARP capital, according to data compiled by Bloomberg.

A company that accepted aid had to grant warrants equal to 15 percent of the TARP investment at a strike price equal to the 20-day trailing average of the shares. A strike price is that at which an option can be exercised.

Now that Goldman Sachs, JPMorgan and Morgan Stanley have applied to return the $45 billion they received, they may also reclaim their warrants.

Those may be worth about $4 billion, data compiled by Bloomberg show. If the U.S. followed the Old National formula for the three New York-based banks, taxpayers would receive less than $1 billion.

JPMorgan spokesman Joseph Evangelisti declined to comment.

Black-Scholes

Mark Lake, a spokesman for Morgan Stanley, said the bank “would support any program that is focused on benefiting the U.S. taxpayer.” Goldman Sachs spokesman Michael DuVally said company officials have “always said the taxpayers should benefit from the value associated with these warrants.”

In the case of Old National, each of the 813,000 warrants had a strike price of $18.45.

On May 11, the day the U.S. announced the sale, the stock’s option-implied volatility, derived from market prices of stock options that are traded daily, was 61 percent, according to data compiled by Bloomberg. The risk-free rate of return, or the yield of government debt, was 3.47 percent that day.

Based on that volatility and that rate, the Black-Scholes options valuation tool appraised one Old National warrant at $7.18. The bank paid the U.S. $1.48 for each.

“We were able to reach a deal that was good for our shareholders and Treasury felt was good for taxpayers,” said Old National Chief Executive Officer Bob Jones.

Risk Management

The bank, with more than $8 billion in loans and branches in Kentucky and Illinois, hired an appraiser to evaluate the warrants, Jones said. He said the government rejected his first offer of $600,000.

The second TARP recipient to reclaim stock-purchase rights was Iberiabank Corp., a Lafayette, Louisiana-based lender with $5.6 billion in assets that took $90 million in TARP assistance.

Iberiabank paid $1.2 million to buy 138,490 warrants at $8.66 a share, according to a May 20 filing. They may have been worth $19.78 each, or a total of $2.74 million, according to data compiled by Bloomberg and modeled by Black-Scholes.

The lender was able to slash the number of warrants from 277,000 by selling common stock in December, a reduction allowed under TARP rules.

A risk management device, Black-Scholes was developed in 1973 by Fischer Black and Myron Scholes to estimate the fair market value of stock-option contracts. Williams, the Treasury spokesman, declined to say whether Black-Scholes is one of the two models the department employs.

Serving Taxpayers

At the University of Louisiana, Wilson used Black-Scholes and two other systems to evaluate Old National’s warrants, plugging in three volatility assumptions: 37.1 percent, 59.72 percent and 72.89 percent.

The lowest, calculated from the bank’s stock price movements over the past seven years, yielded the smallest warrant value, ranging from $2.50 to $6.72 per warrant. The highest, based on changes since Jan. 1, 2008, returned a range from $8.88 to $11.05. The middle estimate -- the options-implied volatility -- said a right was worth from $5.93 to $9.69.

Wilson said the government would serve taxpayers better by auctioning off the securities to investors. The law that established the TARP allows for an auction.

Miller, the North Carolina congressman, said the Treasury should have insisted on terms for taxpayers similar to those Warren Buffett secured for Berkshire Hathaway Inc. shareholders when he invested $5 billion in Goldman Sachs in September.

‘A Tough Penalty’

Buffett received 43.5 million warrants valued by Black- Scholes at $3.6 billion, or $82.18 each, on the date of the transaction, data compiled by Bloomberg shows. Taxpayers injected twice as much into Goldman Sachs and got 12.2 million warrants worth $882 million, or $72.33 each.

The American Bankers Association said in an April 16 letter to Geithner that a company that wants to get out of the TARP now faces an “onerous exit fee” because it has held the investment for so little time.

“There is no reason for Treasury to impose such a punitive obstacle to exiting,” said Diane Casey-Landry, the association’s chief operating officer in Washington.

After Shore Bancshares Inc. returned $25 million in TARP money, plus $208,333 in interest, it offered to buy its 173,000 warrants, according to CEO Moorhead Vermilye. He declined to disclose the bid, which he said the U.S. rejected.

The Easton, Maryland-based bank’s warrants were valued yesterday at $12.33, or $2.1 million, according to data compiled by Bloomberg and modeled by Black-Scholes. Paying that to reclaim them would amount to an annual interest rate of more than 30 percent a year.

“It’s a tough penalty for the short time we had the money -- three months,” Vermilye said.

To contact the reporter on this story: Mark Pittman in New York at mpittman@bloomberg.net.

Last Updated: May 22, 2009 15:43 EDT "

From Kevin Rubash:

Myron Scholes and Fischer Black

"The Black and Scholes Model:

The Black and Scholes Option Pricing Model didn't appear overnight, in fact, Fisher Black started out working to create a valuation model for stock warrants. This work involved calculating a derivative to measure how the discount rate of a warrant varies with time and stock price. The result of this calculation held a striking resemblance to a well-known heat transfer equation. Soon after this discovery, Myron Scholes joined Black and the result of their work is a startlingly accurate option pricing model. Black and Scholes can't take all credit for their work, in fact their model is actually an improved version of a previous model developed by A. James Boness in his Ph.D. dissertation at the University of Chicago. Black and Scholes' improvements on the Boness model come in the form of a proof that the risk-free interest rate is the correct discount factor, and with the absence of assumptions regarding investor's risk preferences.

In order to understand the model itself, we divide it into two parts. The first part, SN(d1), derives the expected benefit from acquiring a stock outright. This is found by multiplying stock price [S] by the change in the call premium with respect to a change in the underlying stock price [N(d1)]. The second part of the model, Ke(-rt)N(d2), gives the present value of paying the exercise price on the expiration day. The fair market value of the call option is then calculated by taking the difference between these two parts.

Assumptions of the Black and Scholes Model:

1) The stock pays no dividends during the option's life

Most companies pay dividends to their share holders, so this might seem a serious limitation to the model considering the observation that higher dividend yields elicit lower call premiums. A common way of adjusting the model for this situation is to subtract the discounted value of a future dividend from the stock price.

2) European exercise terms are used

European exercise terms dictate that the option can only be exercised on the expiration date. American exercise term allow the option to be exercised at any time during the life of the option, making american options more valuable due to their greater flexibility. This limitation is not a major concern because very few calls are ever exercised before the last few days of their life. This is true because when you exercise a call early, you forfeit the remaining time value on the call and collect the intrinsic value. Towards the end of the life of a call, the remaining time value is very small, but the intrinsic value is the same.

3) Markets are efficient

This assumption suggests that people cannot consistently predict the direction of the market or an individual stock. The market operates continuously with share prices following a continuous Itô process. To understand what a continuous Itô process is, you must first know that a Markov process is "one where the observation in time period t depends only on the preceding observation." An Itô process is simply a Markov process in continuous time. If you were to draw a continuous process you would do so without picking the pen up from the piece of paper.

4) No commissions are charged

Usually market participants do have to pay a commission to buy or sell options. Even floor traders pay some kind of fee, but it is usually very small. The fees that Individual investor's pay is more substantial and can often distort the output of the model.

5) Interest rates remain constant and known

The Black and Scholes model uses the risk-free rate to represent this constant and known rate. In reality there is no such thing as the risk-free rate, but the discount rate on U.S. Government Treasury Bills with 30 days left until maturity is usually used to represent it. During periods of rapidly changing interest rates, these 30 day rates are often subject to change, thereby violating one of the assumptions of the model.

6) Returns are lognormally distributed

This assumption suggests, returns on the underlying stock are normally distributed, which is reasonable for most assets that offer options. "

"Quants have ruled the financial roost. But this might just be the time for actuaries to fight back. "

Via Alea, Paul Wilmot on Actuaries Vs Quants:

"Those working in the two fields of actuarial science and quantitative finance have not always been totally appreciative of each others’ skills. Actuaries have been dealing with randomness and risk in finance for centuries. Quants are the relative newcomers, with all their fancy stochastic mathematics. Rather annoyingly for actuaries, quants come along late in the game and thanks to one piece of insight in the early ‘70s completely change the face of the valuation of risk. The insight I refer to is the concept of dynamic hedging, first published by Black, Scholes and Merton in 1973. Before 1973 derivatives were being valued using the “actuarial method,” i.e. in a sense relying, as actuaries always have, on the Central Limit Theorem. Since 1973 and the publication of the famous papers, all that has been made redundant. Quants have ruled the financial roost.

But this might just be the time for actuaries to fight back."

First, read this:

"Black–Scholes in practice

Results using the Black–Scholes model differ from real world prices due to simplifying assumptions of the model. One significant limitation is that in reality security prices do not follow a strict stationary log-normal process, nor is the risk-free interest actually known (and is not constant over time). The variance has been observed to be non-constant leading to models such as GARCH to model volatility changes. Pricing discrepancies between empirical and the Black-Scholes model have long been observed in options that are far out-of-the-money, and these correspond to the likelihood of extreme price changes. While these are very rare when price changes are normally distributed, they are observed in practice and can be modeled as a temporary increase in volatility.

Nevertheless, Black–Scholes pricing is widely used in practice ^[1], for it is easy to calculate and explicitly model the relationship of all the variables. It is a useful approximation, particularly when analyzing the directionality that prices move when crossing critical points. It is used both as a quoting convention and a basis for more refined models. Although volatility is not constant, results from the model are often useful in practice and helpful in setting up hedges in the correct proportions to minimize risk. Even when the results are not completely accurate, they serve as a first approximation to which adjustments can be made.

Additionally, rather than assuming a volatility a priori and computing prices from it, one can use the model to solve for volatility, which gives the implied volatility of an option at given prices, durations and exercise prices. Solving for volatility over a given set of durations and strike prices one can construct an implied volatility surface. In this application of the Black–Scholes model, a coordinate transformation from the price domain to the volatility domain is obtained. Rather than quoting option prices in terms of dollars per unit (which are hard to compare across strikes and tenors), option prices can thus be quoted in terms of implied volatility, which leads to trading of volatility in option markets."

Notice the phrases:

"differ from real world prices due to simplifying assumptions of the model."
"nor is the risk-free interest actually known"
"and these correspond to the likelihood of extreme price changes. "
" is widely used in practice ^[1], for it is easy to calculate and explicitly model the relationship of all the variables. It is a useful approximation"
" Even when the results are not completely accurate, they serve as a first approximation to which adjustments can be made."
" which gives the implied volatility of an option at given prices, durations and exercise prices."

Now, unless you want to actually learn how to use these models, these phrases give you enough of an understanding to see that these models are only tools. They are used to model very risky products, in many cases. That should be enough to let a person know that these are very risky models, intended for a very limited number of investors. At least, that's what I see.

For the Central Limit Theorem, I pulled out this graph, which shows that you get a graph telling you how likely various events are:

"Probability mass function of the sum of 1,000 terms

The following image shows the result of a simulation based on the example presented in this page. The extraction from the uniform distribution is repeated 1,000 times, and the results are summed.

Since the simulation is based on the Monte Carlo method, the process is repeated 10,000 times. The results shows that the distribution of the sum of 1,000 uniform extractions resembles the bell-shaped curve very well."

"I am putting the finishing touches to this article a few days after the first anniversary of the “day that quant died.” In early August 2007 a number of high-profile and previously successful quantitative hedge funds suffered large losses. People said that their models “just stopped working.” The year since has been occupied with a lot of soul searching by quants, how could this happen when they’ve got such incredible models?"

Here's a philosophical question: How can a model just stop working?

"In my view the main reason why quantitative finance is in a mess is because of complexity and obscurity."

Neither of these are good. A good result would be simplifying complexity and obscurity, not adding to it.

"Quants are making their models increasingly complicated, in the belief that they are making improvements. This is not the case. More often than not each ‘improvement’ is a step backwards."

Also not good.

"If this were a proper hard science then there would be a reason for trying to perfect models. But finance is not a hard science, one in which you can conduct experiments for which the results are repeatable. Finance, thanks to it being underpinned by human beings and their wonderfully irrational behaviour, is forever changing. It is therefore much better to focus your attention on making the models robust and transparent rather than ever more intricate."

Robust? I agree with this. Human Agency underpins this whole enterprise.

"As I mentioned in a recent wilmott.com blog, there is a maths sweet spot in quant finance. The models should not be too elementary so as to make it impossible to invent new structured products, but nor should they be so abstract as to be easily misunderstood by all except their inventor (and sometimes even by him), with the obvious and financially dangerous consequences. I teach on the Certificate in Quantitative Finance and in that our goal is to make quant finance practical, understandable and, above all, safe."

I hope that it works.

"When banks sell a contract they do so assuming that it is going to make a profit. They use their complex models, with sophisticated numerical solutions, to come up with the perfect value. Having gone to all that effort for that contract they then throw it into the same pot as all the others and risk manage en masse. The funny thing is that they never know whether each individual contract has “washed its own face.” Sure they know whether the pot has made money, their bonus is tied to it. But each contract? It makes good sense to risk manage all contracts together but it doesn’t make sense to go to such obsessive detail in valuation when ultimately it’s the portfolio that makes money, especially when the basic models are so dodgy. The theory of quant finance and the practice diverge. Money is made by portfolios, not by individual contracts."

How about looking at the individual contracts?

"In other words, quants make money from the Central Limit Theorem, just like actuaries, it’s just that quants are loath to admit it! Ironic."

How the hell do you tell who's making the money for you if it's all thrown into a pot and undifferentiated?

"It’s about time that actuaries got more involved in quantitative finance. They could bring some common sense back into this field. We need models which people can understand and a greater respect for risk. Actuaries and quants have complementary skill sets. What high finance needs now are precisely those skills that actuaries have, a deep understanding of statistics, an historical perspective, and a willingness to work with data."

And a penchant for making money and avoiding catastrophes. Good luck!

"Warren Buffett seemed to get a much better deal on his Goldman Sachs capital injection than the Treasury Department did"

Justin Fox argues the following:

"It's already been noted that . It turns out the United Steelworkers union has been kind enough to actually run the numbers on the two deals, using the Black-Scholes option pricing model to value them (steel workers are totally into Black-Scholes; aluminum workers prefer the binomial model). Here's the bottom line, from an analysis the USW sent to Hank Paulson:

I do think Buffett could demand a premium in this case because his investment was seen as an endorsement (albeit it perhaps a premature one) of Goldman Sachs in particular, while Treasury has been offering similar deals to every bank and its brother. And Treasury's goal is to save the banking system while protecting taxpayers, while Buffett's is to maximize returns for Berkshire Hathaway shareholders. So there should be a gap between the two valuations. I'm not sure it needed to be quite that big, though."

Here's my comment:

donthelibertariandemocrat Says:

1. Monday, November 10, 2008 at 11:53 pm

   Justin, I disagree with you. I believe that there is a higher standard for investment returns when the taxpayer's money is spent. As Bagehot believed, the terms of any bailout should be onerous, both in order to deter future bailouts, but also to reward the public for it's largess. There is no such thing as saving a system. There are certain banks that can be saved or not. As such, one has to deal with each bank as a separate entity, and place terms on it that are at least as good as a private investor should get, otherwise they could give the terms to a private investor. In some cases, this simply means giving the government more equity than a private investor would get. Other solutions might also work.

   Reification leads to believing that a system needs to be saved, and that leads to an easing of concrete conditions that should be imposed on actual individual entities. A concrete example is when an individual on a team breaks a rule, and is let off easier than an individual because it would hurt the team. If you let the player continue playing, you should make the punishment harsher in other ways. Otherwise, you're just allowing behavior that will continue forever.

   I'm not sure I believe this, but, I think I do.

Here's his reply:

"Justin Fox Says:

1. Tuesday, November 11, 2008 at 9:00 am

   I think we've moved past the government being lender of last resort to something much more involved and complicated. Because Bagehot only meant for the lender-of-last-resort function to apply in a liquidity crunch, not when institutions may be insolvent.

   That doesn't mean you're wrong that the government should get more equity than it's been taking, though."