First Buy High; Then Sell Low

On Monday last week, Old National Bancorp bought back the warrants it had granted Treasury as part of its participation in TARP, after buying back its preferred stock on March 31. Today, the New York Times ran a story saying that Old National only paid $1.2 million to buy back the warrants, while the warrants were almost certainly worth more.

The main authority cited by the Times was Linus Wilson, a finance professor at the University of Louisiana, Lafayette and a sometime commenter on this blog, so let’s go straight to the source.

Linus’s blog post is here (from May 14, I’m embarrassed to say) and his paper is here. Basically, he runs three different valuation models on the warrants (pages 14-16 in the paper), each with three different sets of assumptions. The assumptions have to do with volatility, dividend yield, and probability that half the warrants would be canceled.

  • Volatility matters because the value of an option depends on its volatility, and volatility has increased recently, so you will get a different estimate depending on the length of time you estimate volatility over.
  • Dividend yield matters because higher future dividends reduce the value of warrants (since when you exercise the warrant, you only get the share, not the share plus the dividends paid while you were holding the warrant), and again the dividend yield depends on whether you look at historical data or at current dividends.
  • Finally, the warrant terms include a provision that half the warrants will be canceled if the bank makes a qualifying stock offering before the end of 2009. So the assumptions include subjective estimates of the likelihood of the bank making such a stock offering.

You can look at the paper to see how Wilson came up with these assumptions. My guesses would be that the most likely assumptions are the volatility assumption of the middle valuation, the divided yield assumption of the high valuation, and the warrant cancellation probability assumption of the low valuation.

Wilson’s preferred model (page 14) produces the lowest estimates of warrant values – from $1.5 million to $6.9 million. Traditional Black-Scholes (page 16) produces estimates from $4.1 million to $8.5 million.

(For those wondering, warrants have a positive value even though the exercise price of the warrant exceeds the market value of the common share you get by exercising the warrant, because there is a significant chance – given the length of the warrants – that at some point the share price will exceed the exercise price.)

OK, so that’s the calculation. The question is, since Treasury undoubtedly has many smart economists who know all about derivative pricing, why did they end up getting only $1.2 million? That question is left as an exercise for the reader.

Correction: I changed “Treasury” to “Old National” in the second sentence; thanks to Proofreader for catching that.

Update: There are some good comments, starting here, on different assumptions for the warrant pricing and what values you get in that case.

By James Kwak

43 thoughts on “First Buy High; Then Sell Low

  1. I have a simpler question. Why didn’t Treasury simply auction off the warrants? Then they would not even need any “smart economists” to calculate the prices, and the bank could overbid everybody else, if they were so inclined.

  2. Obviously, both coming and going – taxpayers are to get the short end of the stick.

    Everyone with a modicum of intelligence and following what is going on with the Treas/Fed should expect this by now.

    It will not stop until the country is a land of serfs and barons.

  3. I struggle to maintain objectivity on the matter, but this administration has charted, time and again, a course that benefits the banks, their shareholders, and their creditors over the taxpayer.

    Credit where credit is due: they have succeeded, for the time being, in stopping the patient from bleeding out. But in nearly every decision, they have chosen, among many options, the one that benefits the banks. (Full coverage of AIG obligations to GS, a rescue plan that focuses on asset values and bank profitability, etc.)

    This is another example of such awful behavior. TARP was sold with the idea that the taxpayer MIGHT EVEN profit from their ‘investment’. Yves Smith would have a field day with this.

    Also, an auction would indeed have been a good idea. Many participants would probably have been using a modified Black-Scholes model anyway, so the taxpayer would have come out far ahead. This is obnoxious and infuriating.

  4. All (hope) is lost. Whatever is not lost, goes to the banksters. Taxpayers be damned. Your fate is sealed.

  5. I am sure Dr. Wilson has already done more work in valuing the warrants than the Treasury has.

    I can’t say I ever believed that taxpayers would fare well from the financial assistance we have provided the banks, etc. since this crisis began, but I am still pretty disturbed by the manner in which everything is… negotiated.

    How does the Treasury “negotiate” with an institution that Treasury has already determined it will save? It doesn’t. Why do they even bother to pretend like some legitimate process is taking place?

    Perhaps Elizabeth Warren can get them to explain how they arrived at this figure.

  6. Everyone’s out to benefit the banks. It’s that simple.

    It’s disgusting. I never thought this administration would mimic the last. I’m very disappointed.

  7. I think you mean ONB only paid 1.2m to buy back the warrants, not Treasury.

  8. I’m lighting my pitchfork and sharpening my torch … wait, did I get that wrong?

  9. OFF TOPIC…BUT did everyone see the article in bloomberg tonite?

    U.S. Considers Stripping SEC of Power in Rules Revamp

    I guess they are not even considering separating banks from brokerages as one necessary first step to sanity!
    Apparently they are imagining that “too big to fail” continues and combined brokerage/banks/insurance. These have to be busted up BEFORE regulation is imagined.

    We have to do some thing. And to shift more to a PRIVATE BANK (FED) is by itself amazing. Same old game of using A crisis to push thru more privatization of government OVERSIGHT…..we’ve seen this movie!

    Blogg away please….pass the word. This has to be dead in the water.

    (i did not see an obvious way to email James or Simon from this site without posting


  10. i’m sorry to say that the more i read from these blogs, the more clueless the bloggers are. you have no idea what’s going on in this country. james,,,you can only instigate the debate=====>all you can do. but really,,,,this conversation is getting old. the one about gov’t being nice to big banks. if you people are so smart,,,,can’t you read between the lines? why don’t you talk about what this country is headed for with the minorities being the majorities in 20 years. AND how are we to change.that’s just the tip.

  11. If that’s a ‘general paranoia: let’s group increasing diversity together with unscrupulous behavior by the current ruling oligarchy as one undifferentiated phenomenon’ post, please note:

    1) The readers and commenters of this blog are far too rational and intelligent to consider such ideas
    2) One of the bloggers is a prominent ‘minority’ member.

    If not, my apologies.

  12. Sir, break it down real slow for me, as I am not quite sure what you are getting at, but it soundls like it might be interesting.

  13. Reading your post was like watching Elizabeth Warren, Chair of the Congressional Oversight Panel, testify about the findings that treasury overpaid by about33% on the original TARP purchases….the word is out that all this giving away of money is happening, but no one seems to make a motion to do a thing about it… until and unless the complex details of what is going on are understood and once again, the public goes into outrage mode, this theft will go down in history unchallenged.

  14. I don’t know if anyone on here watches South Park. I am reminded of the episode after the election: BO and McCain are actually in cahoots to obtain the oval office only to effect the biggest bank robbery in history. We had an election with a choice between two thieves. Sad.

  15. weren’t the warrants convertible at the option of the bank, not the treasury?

    that’s what i remember from citibank, but i’m not sure if it applies to all the other TARP warrants.

    if that is the case then his entire analysis is bogus.

  16. You’re not going crazy, though. It’s the Capital Assistance Program – the new mechanism for recapitalizing banks – that you’re thinking of. The bank gives Treasury convertible preferred shares that are convertible at the bank’s option, which is non-standard.

  17. Geithner was trained as a cookie-pusher, not a finance guy, and the bankers have been bending him around like a gumby all along. It’s clearer by the day that banks installed him as a dogsbody. I hope that when he goes to feather his nest, the emoluments he gets will compensate him for all the humiliating errands he was made to run.

  18. When in doubt–label and dismiss. The final refuge of paranoiacs, demagogues, and propagandists. I withdraw my tentative apology.

  19. What? How did you jump from a comment on the government favoring the banks (or not…I am confused as to your exact point) to one about minorities? The geopolitics of emotion indeed.

  20. So Treasury put $100M into ONB, and got back $101.2M, or more based on the tarp dividend payment? Wasn’t one of the big worries with TARP that the money was going in a black hole? If we do as well with the money put into BAC, WF, C, & JPM as with ONB, TARP will be viewed positively.

    With regard to the warrants, the post title is misleading because the warrants were kind of a ‘free’ bonus. The dividend payments were the more widely reported cost.

  21. i also think it makes sense given the intent. the intent was to give banks capital and take ownership if they needed it, not to take ownership if the banks did not need it. it also makes sense given that the banks were not able to credibly refuse TARP.

  22. So. Here’s a way for the taxpayer to recovery their investment. We simply apply the business practices of bankers, insurers and credit card companies who always claim that we must pay more for their services because they have lost money.

    The Treasury and FED should start charging fees to all the participants in their various programs to make up for the money the Treasury has lost. Another way to recoup the losses is to charge a transaction fee on all stock, commodity, and derivative trades. Imagine how much a 2% fee would bring into the Treasury.

    There is no reason for the taxpayers to get stuck with the bill for these bailouts.

  23. not a bad analysis.

    one beef. i would guess his volatility estimates are too high, even in the low case.

    the volatility seems to be pretty high — the low volatility estimate of 37% suggests that this is a volatile stock.

    the high volatility estimate — 80+% is sheer nonsense. no stock in the world is going to have 80% volatility for ten years.

    the methodology for choosing the middle volatility is not correct. he is using volatility from a very short dated option to price a ten year option. the observed (ie implied) volatility of a long dated option is generally much lower than the volatility of a short dated option.

    in reality though there are very very few ten year options in the marketplace, and nobody would know for sure the price through a formula. instruments like these often trade at large discounts to the model. the only way to find out is, like nemo suggested, to sell some of them and see what bids you get.

  24. i looked up the historical vol for ONB US Equity on bloomberg. in the 2000-2006 time period the historical vol averaged 18.17 — far below the 35 used in wilson’s “lowball” estimate. and at no point in the 2000-2006 time period did the 100-day moving average historical vol go above 27.5. based on this, i think he should recompute his results.

    there are other problems with the paper. why is he not using the 10Y treasury as the risk free rate, as opposed to a short dated LIBOR? also, how can he consider the low dividend assumption at all, given that this represents a situation where the bank remains distressed in which case the stock will remain low and the warrants will be worth very little?

  25. Ignore page 16. That model is not adjusting the drift for dividends, which very much matter.

    Let’s just price it up following the div-adjusted model (page 15 model) with the following inputs and see what we get:

    Vol – I agree with q that the low-end vol is nearest to where the market would price these warrants. 35% seems reasonable to me.

    DivYld – I think the high-end div assumption is too low for a long-term div yield. The mid-level div yield (which corresponds to average historic div yield) seems ok to me. 3.93%.

    Likelihood of Cancellation – Wilson’s model assumes that the probability that the company will execute a qualifying equity issuance in 2009 (thus canceling half the warrants) is independent of the stock price. This is probably a poor assumption. But I don’t feel like building a simulation (not to mention making an uninformed correlation assumption), so I’ll roll with this one. Let’s just go with the mid-level assumption that there’s a 30% chance that half the warrants will disappear (deflating the expected number of warrants by 15%).

    Risk-free rate: 3.19%.

    This gives us $3.28 per option, which is twice what Treasury received.

  26. thanks. i didn’t know wolfram alpha could do this.

    i think that 35% vol is very high for a 10 year option. but there is no market for this so who knows. right now the market would price in a very high cost of capital (which would show up as high vol, if you fix the risk free rate) and the treasury could but probably wouldn’t.

    at 25% vol the price is $2.05, which is still higher than the treasury number, but within the debatable level of difference.

    likelihood of cancellation and dilution are not really modelable.

  27. oops — wrong way on the vol. sunny friday mistake.

    strike the third sentence of my second paragraph.

    in any case a private buyer would not pay theory value for it — private buyers would want to be compensated for the risk (taking borrow rate into account is a decent proxy for this).

    what i am thinking is that $1.2M is a low but feasible price for these options.

    i have no idea though why the treasury saw fit to sell them and not hold to maturity.

  28. fair point on borrow cost (which is basically negative drift, just like dividends). And in fact, this option is quite sensitive to drift, so borrow cost would drag-down the value considerably. e.g. a 50bps borrow cost would drop the value under my parameters to a fairly close approximation of what Treasury received.

    In other words, Wilson’s (et al) objections seem like much ado about nothing.

  29. yes and 50 bps would be very cheap now.


    i would like the treasury to explain this publicly and not us.

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