Inside Goldman’s ABACUS Trade

Today, in the Huffington Post, I posted a document that shows an earlier incarnation of the ABACUS trade (although, not that different from the one that has got the SEC up in arms). I also explained it as well as I could. Head on over and let me know what you think.

Notes and Predictions: The Stress Test

As the results of the stress test start leaking out slowly, it’s a fun exercise to make some educated guesses/predictions about what the future holds and take note of pertinent facts. As we’ve discussed before, there is a lot to take issue with when considering the results of the stress test at all, especially given the added layers of uncertainty stemming form the limited information provided in the scenarios. So, without further delay, let’s get started.

1. The baseline scenario will prove wholly inadequate as a “stress test.” Please, follow along with me as I read from the methodology (pdf).  I’ll start with the most egregious and reckless component of the mis-named baseline scenario (I would rename it the, “if payer works” scenario) : what I will refer to as “the dreaded footnote six.” From the document:

As noted above, BHCs [(Bank Holding Companies, or the firms being stress tested)] with trading account assets exceeding $100 billion as of December 31, 2008 were asked to provide projections of trading related losses for the more adverse scenario, including losses from counterparty credit risk exposures, including potential counterparty defaults, and credit valuation adjustments taken against exposures to counterparties whose probability of default would be expected to increase in the adverse scenario.(6)

[…]

(6) Under the baseline scenario, BHCs were instructed to assume no further losses beyond current marks.

(Emphasis mine.)

Holy <expletive>! In what alternate/parallel/baby/branching universe is this indicative of anything at all? Assume no further losses beyond current marks? Why not assume everything returns to par? Oh, well, that actually was a pretty valid assumption for the baseline scenario. From the document:

New FASB guidance on fair value measurements and impairments was issued on April 9, 2009, after the commencement of the [stress test].  For the baseline scenario supervisors considered firms’ resubmissions that incorporated the new guidance.

(Emphasis mine.)

Thank goodness! I was worried that the “if prayer works” scenario might have some parts that were worth looking at. Thankfully, for troubled banks, I can skip this entire section. (Confidence: 99.9999%)

2. Trading losses will be significantly understated across all five institutions that will need to report them. First, only institutions with over $100 billion in trading assets were asked to stress their trading positions. Second, from the section on “Trading Portfolio Losses” from the document:

Losses in the trading portfolio were evaluated by applying market stress factors … based on the actual market movements that occurred over the stress horizon (June 30 to December 31, 2008).

(Emphasis mine.)

Okay, well, that seems reasonable, right? Hmmmm… Let’s take a look. Here is what some indicative spread movements for fixed income products looked like January 9th of 2009, according to Markit (who has made it nearly impossible to find historical data for their indices, so I’m resorting to cutting and pasting images directly–all images are from their site):

(Click on the picture for a larger version.)

Well, looks like a big move is taken into account by using this time horizon. Clearly this should provide a reasonable benchmark for the stress test results, right? Well, maybe not.

(Click on the picture for a larger version.)

Yes, that’s right, we’ve undergone, for sub-prime securities a massive widening during 2009 already. Also, as far as I can tell, the tests are being run starting from the December 2008 balance sheet for each company. So, if I’m correct, for the harsher scenario, trading losses will be taken on December 2008 trading positions using December 2008 prices and applying June 2008 to December 2008 market movements. For sub-prime, it seems pretty clear that most securities would be written up (June 2008 Spread: ~200, December 2008 Spread: ~1000, Delta: ~800, Current Spread: ~2600, December 2008 to Today Delta: ~1600, Result: firms would take, from December 2008 levels, half the markdown they have already taken).

Also, it should be a shock to absolutely no one that most trading assets will undergo a lagged version of this same decline. Commercial mortgages and corporate securities rely on how firms actually perform. Consumer-facing firms, as unemployment rises, the economy worsens and consumption declines, and consumers default, will see a lagged deterioration that will appear in corporate defaults and small businesses shuttering–both of these will lead to commercial mortgages souring.  Indeed we’ve seen Moody’s benchmark report on commercial real estate register a massive deterioration in fundamentals. That doesn’t even take into account large, exogenous events in the sector. Likewise, we see consistently dire predictions in corporate credit research reports that only point to rising defaults 2009 and 2010.

In short, for all securities, it seems clear that using data from 2H2008 and applying those movements to December 2008 balance sheets should produce conservative, if not ridiculously understated loss assumptions. (Confidence: 90%)

3. Bank of America will have to go back to the government. This, likely, will be the end of Ken Lewis. It’s not at all clear that Bank of America even understands what’s going on. First, if I’m correctly reading Bank of America’s first quarter earnings information, the firm has around $69 billion in tangible common equity. Also, it should be noted that the FT is reporting that Bank of America has to raise nearly $34 billion.  Now, with all this in mind, let’s trace some totally nonsensical statements that, unlike any other examples in recent memory, were not attributed to anonymous sources (from the NYT article cited above):

The government has told Bank of America it needs $33.9 billion in capital to withstand any worsening of the economic downturn, according to an executive at the bank. […]

But J. Steele Alphin, the bank’s chief administrative officer, said Bank of America would have plenty of options to raise the capital on its own before it would have to convert any of the taxpayer money into common stock. […]

“We’re not happy about it because it’s still a big number,” Mr. Alphin said. “We think it should be a bit less at the end of the day.” […]

Regulators have told the banks that the common shares would bolster their “tangible common equity,” a measure of capital that places greater emphasis on the resources that a bank has at its disposal than the more traditional measure of “Tier 1” capital. […]

Mr. Alphin noted that the $34 billion figure is well below the $45 billion in capital that the government has already allocated to the bank, although he said the bank has plenty of options to raise the capital on its own.

“There are several ways to deal with this,” Mr. Alphin said. “The company is very healthy.”

Bank executives estimate that the company will generate $30 billion a year in income, once a normal environment returns. […]

Mr. Alphin said since the government figure is less than the $45 billion provided to Bank of America, the bank will now start looking at ways of repaying the $11 billion difference over time to the government.

(Emphasis mine.)

Right around the time you read the first bolded statement, you should have started to become dizzy and pass out. When you came to, you saw that the chief administrative officer, who I doubt was supposed to speak on this matter (especially in advance of the actual results), saying that a bank with $69 billion in capital would be refunding $11 billion of the $45 billion  in capital it has already received because they only need $34 billion in capital total. Huh? Nevermind that the Times should have caught this odd discrepancy, but if this is the P.R. face the bank wants to put on, they are screwed.

Now, trying to deal with what little substance there is in the article, along with the FT piece, it seems pretty clear that, if Bank of America needs $34 billion in additional capital, there is no way to get it without converting preferred shares to common shares. There is mention of raising $8 billion from a sale of a stake in the China Construction Bank (why are they selling things if they are net positive $11 billion, I don’t know). That leaves $26 billion. Well, I’m glad that “once a normal environment returns” Bank of America can generate $30 billion in income (Does all of that fall to T.C.E.? I doubt it, but I have no idea). However, over the past four quarters, Bank of America has added just $17 billion in capital… I will remind everyone that this timeframe spans both T.A.R.P. and an additional $45 billion in capital being injected into the flailing bank. Also, who is going to buy into a Bank of America equity offering now? Especially $26 billion of equity! If a troubled bank can raise this amount of equity in the current environment, then the credit crisis is over! Rejoice!

I just don’t see how Bank of America can fill this hole and not get the government to “bail it out” with a conversion. The fact that Bank of America argued the results of the test, frankly, bolsters this point of view. Further, this has been talked about as an event that requires a management change, hence my comment on Lewis.  (Confidence: 80% that the government has to convert to get Bank of America to “well capitalized” status)

Notes/Odds and Ends:

1. I have no idea what happened with the NY Times story about the results of the “Stress Test.” The WSJ and FT are on the same page, but there could be something subtle that I’m misunderstanding or not picking up correctly. Absent this, my comments stand. (Also, if might have been mean.unfair of me to pick on the content of that article.)

2. The next phases of the credit crisis are likely to stress bank balance sheets a lot more. The average bank doesn’t have huge trading books. However, they do have consumer-facing loan and credit products in addition to corporate loans and real estate exposure. In the coming months, we’ll see an increase in credit card delinquencies. Following that, we’ll see more consumer defaults and corporations’ bottom line being hurt from the declining fundamentals of the consumer balance sheet. This will cause corporate defaults. Corporate defaults and consumer defaults will cause commercial real estate to decline as well. The chain of events is just beginning. Which leads me to…

3. Banks will be stuck, unable to lend, for a long time. I owe John Hempton for this insight. In short, originations require capital. Capital, as we see, is in short supply and needed to cover losses for the foreseeable future. Hence, with a huge pipeline of losses developing and banks already in need of capital, there is likely not going to be any other lending going on for a while. This means banks’ ability to generate more revenue/earnings is going to be severely handicapped as sour loans make up a larger and larger percentage of their portfolios.

4. From what I’ve read, it seems that the actual Citi number, for capital to be raised, is between $6 billion and $10 billion. This puts their capital needs at $15 billion to $19 billion, since they are selling assets to raise around $9 billion, which is counted when considering the amount of capital that needs to be raised (according to various news stories). Interestingly, this is 44% to 55% of Bank of America’s needed capital. This paints a very different picture of the relative health of these two firms than the “common wisdom” does. Granted, this includes a partial conversion of Citi’s preferred equity to common equity.

5. I see a huge correlation between under-performing portfolios and a bank trying to negotiate it’s required capital lower by “appealing” the stress test’s assessment of likely losses in both the baseline and adverse scenarios. As I’ve talked about before, not all portfolio performance is created equal. Citi has seen an increasing (and accelerating) trend in delinquencies while JP Morgan has seen it’s portfolio stabilize. So, for the less-healthy banks to argue their losses are overstated by regulators, they are doubly wrong. It’ll be interesting to see how this plays out–for example, if JP Morgan’s credit card portfolio assumes better or worse performance than Citi and Bank of America.

Contrarian View: HR 1586 (T.A.R.P. Surtax Bill) will Create Millionaires

This is  just a  few quick thoughts, but I believe, in a few years, we’ll be able to take this bill and place it’s effects high on the list of unintended consequences. Let’s wonder what a reasonable firm would do in order to protect it’s people as much as possible from this legislation… I would put forth the proposal that a firm would give it’s employees the most “bang for the buck.” This seems to clearly be by paying in options. Now, I don’t know all the technical details behind how finance companies have to account for and value options given as compensation, but, using the CBOE option pricer and volatility from Morningstar, I get around $0.50 as the option price for a strike of $2.50 at the time Citi was giving bonuses out, around the time it was at $1.00. Or, if we use $2.50 for the equity price and the strike price, we get $1.62 option price.

Since those prices are per share for lots of 100 option, we get anywhere between 500,000 and 155,000 options, depending on when Citi’s rules would require it to re-cast it’s payments to employees. That’s obviously a huge range. However, for some context, when Citi was trading at $50 / share, having 500,000 shares would have meant you had $25 million in the bank. And 155,000 shares would have meant you had $7.75 million in the bank. However, let’s look at some more likely scenarios. Citi is currently trading at $3.00. As these options are longer dated (I believe the prices quoted above were for 3 year options), could one see a world where Citi is at $10, $15, or even $20 3 years in the future? I think so. So, 155,000 options would be worth between $1.55 million and $3.1 million.The other option is some combination of cash and restricted stock. As we see above, the total shares one would get, if merely receiving restricted stock (at the current trading level) is approximately half to two-thirds.

Now, obviously there are risks. Citi might not be around in three or more years–that is anyone’s guess! This assumes share price increases quite a bit (although the numbers look good even for more modest scenarios). However, all of these would be issues with restricted shares as well–which Wall St. heavily relies upon for compensation. Also, this is just for Citi, which is clearly in a more precarious position than some of it’s peers. For a firm like Goldman, Morgan Stanley, or even Merrill/BofA, the probability of defaulting is way lower. And, for those firms, volatility is lower, making options less valuable, and increasing the ratio of options to restricted shares. the purposes of comparison, Goldman is currently trading at approximately $100 and it’s two year volatility is around 60%. This yields an option price of around $39, or 3x as many options as restricted shares. So, for every $20 Goldman’s shares go up, one would make 3x as much if they had options.

You see where I’m going with this? Now, I don’t know the specific rules surrounding a firm’s ability to re-cast their payments once they’ve been made, or how they compute strike prices, restricted share award prices, or other details. But, I would bet that these firms go back to their employees and let them re-think some of their options (no pun intended).

Fun Super Irony Fact: HR 1586, in the 110th congress was the “The Death Tax Repeal Act of 2007”!!!

Why Stress Test Really Means Guesswork

Well, we’ve heard a ton about stress tests recently. Want some details on what a stress test entails? The Journal has some details about the tests here. Now, as much as I think GDP and unemployment are fine things to project forward for economists, let’s walk through the way one would use this to actually price an asset. Let’s start with something simple, like a 10-year treasury note (note that treasury bond specifically refers to bonds with a 30-year maturity). Here are all the components one would need to stress test the value of a treasury note.

1. Characteristics of the note itself: coupon, payment dates, maturity dates, etc.
2. What the yield curve would look like at the date you’re pricing the note.

Why would one need to know the shape of the yield curve (term structure of rates)? This is important, in order to “PV” the bond’s cashflows most accurately, one would discount each cashflow by it’s risk–the simplest proxy is to discount each cash flow by the rate of interest one would need to pay to issue a bond maturing on that date. For the government, this rate of interest is the point on the treasury yield curve (actually, the par zero curve) with the same maturity date. An example would be, if I were going to price a cash payment I will receive in two years, and the government can currently issue two-year debt at 5%, I should discount my cash payment (also from the government, since it’s a treasury note) at 5%. Treasuries are the simplest of all instruments to value.

Here’s an example, form the link above, of what a treasury yield curve might look like:

Now, it is completely and totally guesswork to figure out, given unemployment and GDP figures, what the yield curve will look like at any date in the future. Indeed, one can plug these projections into a model and it can come up with a statistical guess… But the only thing we know for sure about that guess is that it won’t be accurate, although it might be close. However, things like inflation will drive the longer end of the yield curve and monetary policy will drive the shorter end, so these certainly aren’t directly taken from the stress test parameters, but would need to be a guess based on those parameters. This is a large source of uncertainty in pricing even these instruments in the stress test.

Next, let’s examine a corporate bond. What would we need for a corporate bond?

1. Characteristics of the bond: coupon, payment dates, maturity dates, special features (coupon steps, sinking funds, call schedules, etc.), where in the capital structure this bond sits, etc.
2. What the yield curve would look like at the date you’re pricing the bond.
3. The spreads that the corporation’s debt will carry at the date you’re pricing the bond.

Oh no. We already saw the issues with #2, but now we have #3. What will this corporations credit spread (interest/yield required in excess of the risk free rate) at the time of pricing? Will the corporations debt, which could trade at a spread of anywhere from 5 to 1500 basis points, be lower? higher? Will the corporations spread curve be flatter? steeper?

Here is a good illustration of what I’m referring to (from the same source as the figure above):

There, the spread is the difference between the purple line and the black line. As you can see, it’s different for different maturity corporate bonds (which makes sense, because if a company defaults in year two, it’ll also default on it’s three year debt.. but the companies’ two year debt might never default, but the company might default during it’s third year, creating more risk for three year bonds issued by that company than two year bonds). It shouldn’t be a surprise, after our exercise above, to learn that the best way to compute the price of a corporate bond is to discount each cashflow by it’s risk (in my example above, regardless of whether the company defaults in year two or year three, the interest payments from both the three year and two year debt that are paid in one year have the same risk).

Well, how does one predict the structure of credit spreads in the future? Here’s a hint: models. Interest rates, however, are an input to this model, since the cost of a firm’s borrowing is an important input to figuring out a corporation’s cashflow and, by extension, creditworthiness. So now we have not only a flawed interest rate projection, but we have a projection of corporate risk that, in addition to being flawed itself, takes our other flawed projections as an input! Understanding model error yet? Oh, and yes unemployment and the health of the economy will be inputs to the model that spits out our guess for credit spreads in the future as well.

Next stop on the crazy train, mortgage products! What does one need to project prices for mortgage products?

1. Characteristics of the bond: coupon, payment dates, maturity dates, structure of the underlying securitization (how does cash get assigned in the event of a default, prepayment, etc.), etc.
2. What the yield curve would look like at the date you’re pricing the bond.
3. The spreads that the debt will carry at the date you’re pricing the bond.
4. What prepayments will have occurred by the date you’re pricing the bond and what prepayments will occur in the future, including when each will occur.
5. What defaults will have occurred by the date you’re pricing the bond and what defaults will occur in the future, including when each will occur.

Oh crap. We’ve covered #1-3. But, look at #4 and #5 … To price a mortgage bond, one needs to be able to project out, over the life of the bond, prepayments and defaults. Each is driven bydifferent variables and each happens in different timeframes. Guess how each projection is arrived at? Models! What are the inputs to these models? Well, interest rates (ones ability to refinance depends on where rates are at the time) over a long period of time (keep in mind that you need rates over time, having rates at 5% in three years is completely different if rates where 1% or 15% for the three years before). General economic health, including regional (or more local) unemployment rates (if the south has a spike in unemployment, but the rest of the country sees a slight decrease, you’ll likely see defaults increase). And a myrid of other variables can be tossed in for good measure. So now we have two more models, driven by our flawed interest rate projections, flawed credit projections (ones ability to refinance is driven by their mortgage rate, which is some benchmark interest rate [treasuries here] plus some spread, from #3), and the unemployment and GDP projections.

I will, at this point, decline to talk about pricing C.D.O.’s … Just understand, however, that C.D.O.’s are portfolios of corporate and mortgage bonds, so they are a full extra order of magnitude more complex. Is it clear, now, why these stress tests, as they seem to be defined, aren’t all that specific, and potentially not all that useful?

Another “Holy Shit!” Moment in Compensation: The P.A.F.

Wow. Seriously, wow…

This year, up to 80% of the stock portion will come via what Credit Suisse is formally calling a “Partner Asset Facility,” of the illiquid assets, largely corporate loans.

Bankers won’t receive a return on the PAF program for eight years, although they can start to collect some of the principal in 2013. If the firm finds outside buyers for the assets, it will pay the proceeds to itself first, then provide the rest to employees.

The PAF applies only to senior bankers within the firm’s investment bank, which includes merger advisory, capital markets and leveraged finance. Those in Credit Suisse’s private bank and asset-management division aren’t subject to the PAF.

I’m going to play both sides of this one… But, how do you know it’s a good move? Hiede Moore’s post, in the next line, offers the proof:

The announcement elicited livid reactions from senior bankers, many of whom questioned whether it was legal. Many said they believed they were being unfairly punished for risky assets bought by colleagues in distant parts of the firm.

I’m not crying for these bankers, exactly, but they missed the point. To be honest, it’s a tremendous incentive for everyone to work together for the good of the firm. These same “livid” investment bankers, I’m sure, have been pushing transactions onto their counterparts in capital markets and trading for years. I know this, specifically of C.S.F.B. Their investment bankers would constantly use the “relationship” reason for doing a given transaction that resulted in real estate exposure for their firm (or leveraged finance commitments). So bankers, as a whole, shouldn’t say they are being unfairly punished for their colleagues decisions to make loans that they asked them to make. Now those bankers will not push loans they think might make it into their compensation! (There was a rumor that something like this happened a long time ago at Salomon Brothers.)

Now, why might this be a bad ideas? Honestly, all the reasons are highly technical. First, the investment is much longer dated than normal equity: first principal distributions come in 2013 and the investment will be zero-return for 8 years. This is a bit unfair, as the vesting and return of cash should be similar to normal equity plans if employees are given no notice. It’s only polite as it concerns things like paying college tuition. That being said, this is a program for senior employees and, thus, they should have planned for bad times and not gambled with their entire lifestyle. The two largest issues, though, are where the firm is using this to their advantage instead of being “just” about it. First, Credit Suisse pays itself before employees. That seems tacky.. pro-rata, maybe? Even pro-rata withe the firm counted more… Second, this makes C.S.F.B. employees much less mobile. When a bank is trying to figure out how to make the bankers being recruited from C.S.F.B. whole on what they lose when they depart their current firm (standard practice), it’s likely that their P.A.F. holdings will be valued at, or near, zero.

Now, despite the problems, I think this is a great lesson and a fair mechanism. And, unlike the clawback, if the firm loses money on the investment, so are the people getting paid in P.A.F. units… So you don’t have to worry about going after an employee, they get reduced along with shareholders.

How We Got a Corporatocracy

With all these bailout (banks, A.I.G., Bear Stearns, and, coming soon, autos!) it’s a wonder how we got to this point. Well, I found an interesting statistic. Taken from the history of the S&P 500’s top components and G.D.P. data we find out that the growth rate of the largest companies (A.I.G. and Citi were part of this group in 2006) has outpaced our economy by 6% annually. Stated another way, the market cap of the top 10 components of the S&P 500 has grown by, on average, 9.4% per year and the economy, as measured by G.D.P., has grown by around 3% per year. This data covers 27 years.

Now, I’m no math genius, but when you have a subset of the economy growing much faster than the economy, it points to a super-concentration of risk. Especially when the system is so inter-connected, perhaps the issue is that some companies became too big, ya think?

This sort of growth is a perfectly natural as a corollary to pay issues and other things. If I’m an executive, and I make money based on earnings, and I get paid in stock, then why not buy my competitors to enlarge my company and increase earnings, eliminate competition to expand margins and create more room for error in execution of business strategies, and use my newly-created larger company to invest even more in the business lines that are producing the best quarterly results? Well, I would! And they did.

But, if we are looking for stability in the system, and we really want the market to work wonders, then we want something different. We want lots of smaller, nimble competing businesses that are constantly keeping margins low and product innovations high. We do not want two or three super-sized businesses that are stable in their market share and merely looking to increase earnings through incremental improvements, and not innovation (G.M.? Ford? Chrysler? I’m looking at you). We don’t want an entire industry to consolidate to the point where they all start following each others innovations so that they can all go down with the ship if any one of them is wrong (Investment banks? Bear? Lehman? I’m looking at you now). And, as a taxpayer, I wouldn’t want a decline in the economy, when all businesses suffer, to jeopardize a set of companies that are too big to fail and not drag the economic state down with them–I would have to bail them out when I’m hurting most.

Those of you that are math geniuses know what comes next …  “=><=” (or “⊥”).

I guess we know who won out now. Maybe our leaders should figure out how to prevent this kind of consolidation. They do it with banks (obviously they took a very narrow view there).

Detailed Causes of the Crisis and Post-Crisis

Since this is a political season, and with the economic crisis, I think everyone in finance understands there is a sort of “silly season” that ensues. We certainly noted the sort of irrational behavior that would immediately make an economist question their beliefs. To me, though, the most offensive form of this stupidity comes from those who believe the Community Reinvestment Act and Fannie and Freddie sparked the whole crisis. Mr. Ritholtz rails against this notion over and over again. Oddly, I haven’t seen anyone else tackle this issue… Of course, I’m also way behind on reading my feeds. I even wrote Mr. Ritholtz an email (something I always tell myself is useless afterwards, since I don’t ever get a response, but is usually cathartic) noting that he was being very informative by setting the record straight. Well, maybe I expressed this sentiment with a tirade…

Every time I hear a Republican talking head on a news program saying Fannie and Freddie caused the problem I want to jump through my T.V., explain that the answer “betrays not even a modest understanding of the contributing factors to the current crisis, it’s scope, and magnitude” and begin to rattle off about flawed ratings agencies, excessive leverage (for investment banks and funds), over-reliance on models, a flawed compensation model for Wall St., managements needs to one-up their own earnings and those of competitors, explosive year over year growth of unproven financial technologies, over-reliance on “fast money” to distribute risk, fund’s need to earn outsized returns to attract assets, funds’ need to buy crappy bonds to build a “relationship” that would allow them to get “good” bonds from banks, poor disclosure from companies (specifically investment banks, as I’ve discussed on my blog), and extremely low rates for a very long time. Of course I’m just a normal guy who actually knows what’s going on, I don’t get invited onto these shows.

(Emphasis added, mine.)

Let’s tackle these, shall we?

1. Excessive Leverage — If the plot of the credit crisis had included a deus ex machina it would have been an instant de-levering of troubled investment firms. This didn’t happen and several collapsed. I don’t want to be repetitive, but the Deal Professor says it plainly when he says, “Sometimes, You Can Only Raise Capital When You Don’t Need It” … If a firm is highly levered, as Bear was, Lehman was, Fannie was, Freddie was, and A.I.G. was, then when the market gets bad, losses pile up, and credit tightens it’s a death spiral. There’s a large distance between well-capitalized and insolvent, but once you move from adequately-capitalized to under-capitalized it’s probably impossible not to hit insolvent or bankrupt. Oh, and let’s not forget how this became a problem in the first place … the rules were relaxed in 2004.
2. Flawed Rating Agencies — This is pretty obvious. Moodys errors. Rating agencies noting any deal, even one “structured by cows,” would be rated. And lastly, the smoking gun that seems to be the largest caliber, the fact that … well, I’ll let Mr. Raiter speak for himself:… “Mr. Raiter said that the residential mortgage rating group at S.& P. had captured the largest market share among its main competitors — 92 percent or better — ‘and improving the model would not add to S.& P.’s revenues.‘” Wow! Honesty, stupidity, incompetence … all on display. Now, to be honest, I have no idea what difference these problems made. What I do know is that the rating agencies were used as a means of outsourcing risk management and credit analysis. While it shouldn’t be a huge shock that the rating agencies missed the mark, the magnitude by which they missed is a huge problem if everyone took their ratings as fundamentally true. What these “statistical rating agencies” should have been doing is running securities and mortgage loans through abhorrently conservative scenarios and fixing ratings based on those…. they didn’t. They were argued down to “realistic” scenarios based on past experience. The issues above merely compound the problem.
3. Over-Reliance on Models — Related to the rating agencies’ issues, this one is a great catchall for terrible risk management. Let’s be honest, no one saw the fundamentals in housing getting so bad. That’s not the issue, I didn’t see it so I can’t exactly blame others for not seeing it. What I can do, however, is blame risk management professionals for not preparing for it. When you have, as Citi did, tens of billions of dollars in highly correlated assets, you should know there’s a risk of tens of billions of dollars in writedowns. When you have tens of billions of dollars in commercial mortgages, as Lehman did, you should realize the risks there. Similar lessons for WaMu, Wachovia, and CountryWide. Instead, though, like the rating agencies, there was a push to have “realistic” or “back tested” results. Let’s go to Mr. Viniar, C.F.O. of Goldman, for his take: “Even scenario analysis, which can address some of VAR’s deficiencies, came up short … [This] ’caused us to look at more-extreme scenarios than we used to look at,’ says Viniar. ‘It made us expand out the tails of what we deemed a realistic possibility.'” Logical, concise, and conservative. It seems Goldman didn’t attempt to show lower risk numbers so that they could deploy more capital or be looked upon as safer by the stock market. No, they looked at more extreme scenarios. They reacted quickly. However, in quoting this passage I sandbagged you, dear readers. This quotation is actually much more relevant to this situation than one would think–it comes from 2001! Mr. Viniar, people probably won’t remember (seems like a lifetime ago), but I noted before, was the guy who convened a firm-wide meeting on exposure to the housing markets. The takeaway is that the firm that looked at the most extreme scenarios, not the ones that models said were most likely, weathered the storm the best.
4. Flawed Compensation Model — This one is pretty obvious. Lots of money flowed into people’s P.A.’s (that’s “personal account”) each year based on fees and mark-to-market gains for complex structured products. In many instances these risks were distributed and off the balance sheets of investment banks. However, these businesses were grown, and none of the risks were well understood–the people in the lead, though, lead the charge to increase their compensation. I was personally aware of a senior trader/banker/whatever that pushed a firm, one that has seen tens of billions in writedowns and may or may not still be alive, who pushed for balance sheet commitment of 2-3x the current size in the C.D.O. business. This would have exposed this institution to writedowns larger than most firms equity base. This proposal was shot down, but still… Clearly making eight digits was going to someone’s head. Now, we all know that I believe one should be accountable for their decisions, so it shouldn’t be a surprise that when one has made tens of millions of dollars in bonus and salary, but their decisions lead an institution to take massive losses, reduces shareholder value significantly (keeping in mind shareholders might be woefully unaware of the risks being taken), and leads to thousands of people losing their jobs, merely being fired isn’t enough. Especially since these issues are only beginning to be understood when these people are fired, usually. Becoming an instant millionaire is a huge, huge problem. It’s the “swing for the fences if you’re down” mentality, and it’s also the “worry about the tail events if they happen” mentality. Put simply, there should be the ability to claw-back compensation based on performance for years. Perhaps a ten year lockup of wealth is extreme, but given these issues and famous blowups in the past, and taking into account the tradition of good times to last several years, maybe ten years is harsh but not extreme. Maybe employees should be allowed to hedge exposure to stock prices after a few years, but still have risk if negligence is discovered or things go wrong that were set in motion by that person. Obviously something drastic needs to be done, perhaps merely paying less is sufficient, but I doubt it.
5. Management Pressures — Highly correlated to the flawed compensation model, it’s the case that management was pushed hard to get earnings up. Having seen the “budget” process (an odd name, I thought, since a budget, to me, merely means expenditures) up close, I saw people come up with reasonable numbers, submit them to senior management, and be told, “More!” Well, guess what <expletive>s? If someone tells you they can reasonably deliver something and you always add 10-20% to those numbers, there is more risk taking and less rationality to how that profit is achieved. Maybe the long term effects of pushing the envelope are much worse than not taking those risks to begin with. This is one reason Goldman seems to outperform so often, they understand what they are getting themselves into. They truly work together and achieve revenues through teamwork instead of edict. Now, underperformance is punished, but setting reasonable goals is step one when trying to exceed them. The next generation of management should fight their bosses tooth and nail not to set unreasonable baseline expectations and should figure out objective measures that reflect an employee or business’s effectiveness. The tyranny of quarterly earnings shouldn’t make grown ups act stupidly because they can’t “just say no.” Here’s a hint: if you run a company with a nine- or ten-digit balance sheet and you don’t realize your business is complex enough that you shouldn’t manage to the next ninety days, then you should step aside. Seems simple to me. Maybe that’s why Google doesn’t bother with quarterly guidance.
6. Explosive Growth of Unproven Financial Technologies — Being a bit of a purist I am hesitant to call financial products or methods “technologies,” but I’ll use that word for now. The truth of the matter is, these products had never seen a massive downturn. Sub-prime loans as we know them today hadn’t seen a recession until now. C.D.O.’s backed by structured products hadn’t existed during a protracted period of fundamnetal credit distress before. This was known and talked about often. For as much as this was talked about, it was an observation that was never extrapolated. Hedging and risk management still looked at historical levels of distress and credit problems. The market had grown by orders of magnitude, but that wasn’t part of the equation. Quite simply, the fact that these markets grew so much so fast meant no one had a good handle on the feedback effects of this growth. This is somewhat obvious and very moot, so I won’t dwell on the problems of such massive growth.
7. Over Reliance on “Fast Money” To Distribute Risk — Anyone who knows structured products understand this point. Basically, the fair-weather buyers are “fast money.” This client based is distinct from “buy and hold” or “real money” accounts. Here is where the shell game of wall street really kicked into high gear. Hedge funds would buy bonds with the intention of selling at a profit later. Investment banks would, to show strength of the market, put out “bids” or interest to purchase securities they had just created at a higher price than they had just sold said securities at. Hedge funds would then immediately sell back to Wall St. firms, at a profit, to take advantage of their desire to show the market their securitizations “trade well” or “at a premium.” When firms are making money on the securitization, they can afford this. Speaking more generally, hedge funds just “trade bonds around” more. In recent years insurance companies and banks, the institutions that buy securities and rarely sell them (for a myriad of reasons), went from 70+% of the buying base for structured products to 20-30% of the buying base. This means that in a bad market 70-80% of the bonds that exist can be sold (dumped?) at a moments notice. Add in the fact that during this period there was explosive growth (as noted above) and you see why when the markets hit trouble the huge wave of selling occurred, liquidity dried up, and prices plummeted.
8. The Flawed Model for Relationships Funds have with Wall St. (coupled with Funds’ Needs for High Returns to attract Assets) — The way a bank figured out if a hedge fund was a good customer was, basically, how much a fund helped that bank get out of risk (stupidly, as stated above, since banks were likely to be more hurt by a fund owning assets and were more likely to wind up needing to repurchase those assets, but I digress…). However, when assets were in short supply relative to demand, only the top clients were able to purchase securities banks were creating. So, one might wonder, how did a nascent fund, at the bottom of the food chain, get access to the desirable securities? Easy solution: they purchased the undesirable securities to “help out” a Wall St. firm. These were more risky, although they were generally carried a higher rate of return in the event of no credit problems. These new funds, then, showed higher returns, attracted more money, and bought more securities from banks. Net effect? Most funds had a poor mix of products–higher risk bonds or assets that would get hit much harder than generic securities and more generic securities. Keep in mind that, to get high returns, funds were buying C.D.O. products and other structured products that had higher returns in general, but funds also levered these products and thus funds were much more exposed to moves in the market. Funds, as everyone knows, get paid a percentage of assets under management and returns, so to grow their revenue stream many funds just had to buy lots of securities (and, to establish a strong enough relationship to be allocated enough securities, plenty of lower quality securities). This was the prisoner’s dilemma of the syndicate system–funds cooperated every time. (Just to put some numbers on it, when a fund would try to buy residential or commercial mortgage backed securities it was possible for demand to outstrip supply 2- or 3-to-1. Accounts with strong relationships usually got 100% to 80% of the requested amount of bonds being issued. Weak relationships or smaller firms could receive as little as 10-20% of their desired allocation.) This is a complex process and nuanced point, feel free to email me for more explanation.
9. Poor Disclosure from Companies — This is a point I’ve raised before. I won’t go over it again. The short story is that firms got away with a lot because they didn’t tell anyone what they were doing.
10. Extremely Low Rates for a Very Long Time — I’ve raised this point before as well (between the numbered lists). Rates were very low and, suddenly, a product that trades at 50-100bps over L.I.B.O.R. traded 50-100% higher than L.I.B.O.R. If your benchmark was treasury rates to outperform your benchmark meaningfully you needed to get much higher spreads, and thus take higher risk. This is why C.D.O.’s experienced such explosive growth (see the problems the growth cased above). Low rates also made it more attractive to get a floating rate mortgage, which a huge majority of sub-prime mortgages were. This was part of the ex-post concern with Alan Greenspan’s encouraging people to take out A.R.M.’s.

In short, Fannie and Freddie were part of the problem, but not in and of themselves. In fact, if Fannie and Freddie had caused these problems by selling banks their bonds, then we wouldn’t have a problem at all. Why? Because Fannie and Freddie would be “on the hook” for the bonds they guarantee. If these bonds went bad no firms would have taken losses on them (since the government stepped in to keep them solvent and backstopped their obligations). Okay, now that I’m done ranting I’m going to rant on something new. The post-crisis narrative of what went wrong… (don’t you love the rise of the word “narrative”?).

1. The failure of rating agencies, risk managers, and risk management models. This has been getting the most press because it’s easy to explain (not why these things failed, but the fact they failed).
2. Sheer size. This is pretty silly, if you ask me. Bigger doesn’t have to mean riskier. The practices that get a firm to a massive size could be an issue. Super-concentrating the health of the markets with very few players could be a huge problem. The “Too Big to Fail” issue might fit some situations, but didn’t cause this crisis. No one wants to have to rely on the government to save them.
3. Executive pay. This is a limited view on the actual problem. In fact, in most firms, C.E.O.’s aren’t the highest earning individuals.
4. Hedge funds and short selling. Really? Let’s trace the logic here (or lack thereof): a firm runs it’s business poorly and I bet it will decline in value. Clearly I am at fault there. The “free markets at all costs except losses” crowd, like those currently at Treasury, are putting a band aid on an amputated leg here. Especially with the very firms begging to be protected turning around and getting fees from products circumventing the bank on short selling. (What a stupid move, some firms deserve to be in worse trouble.)
5. Everything else. Why get into the details of the actual causes when you can distill down issues to “good” versus “bad” and simple fights? No one has…. so I’m doing it! But I doubt all the other things will make it into the popular understanding of what went wrong.

There you go. My hands are tired, so I’ll stop here. Feel free to comment and ask questions.

In The Year 2010: C.D.O. Edition

In another installment of the series called “In The Year 2010″ I will sit here and guess what will be going on by the end of 2010 with respect to various products. (Inspired by the Conan O’Brian skit “In The Year 2000″). This is a thought experiment, nothing more.

This edition, as the title would seem to suggest, is about C.D.O.’s. Please sit down, because I’m about to argue something very counter-intuitive. C.D.O.’s will be alive and well in the year 2010. Now, I’m willing to claim this victory on a technicality–corporate C.D.O.’s are still being issued. Now, safe in my assured technical victory, I’ll go farther out on the limb

It’s somewhat instructive to understand what have been the various motivations behind the C.D.O. market, historically (some of these obviously no longer exist)…

1. There was the reach for yield. If one could get AAA C.D.O.’s for a higher yield than other AAA bonds, it was a no brainer. Both were AAA, obviously! No extra risk.
2. A highly customized risk profile. If I looked at a pool and thought 6% of the balance was going to written off, but no more, I could buy the 7%-10% tranche and get a higher return. Obviously this higher return would need to match whatever threshhold I established, but that was most likely related to the market anyway. Some people referred to this as taking a position in the collateral with leverage. C.D.O.’s are, in essence, leverage on leverage, but this is a complicated, technical, and largely semantic argument. The surface intuition is that taking a levered position increases your return if nothing defaults, but less has to default for the buyer to lose money.
3. C.D.O.’s were used to finance bonds or other debt positions. “How?” is what I heard you say, in the back? Well, think about it this way: an investment bank requires 50% of the purchase price of a set of bonds and charges LIBOR+100bps on the other 50%. We say that you’ve financed the purchase of the bonds two to one at a rate of one hundred basis points over LIBOR. Now, using our example, let’s say one could issue a C.D.O. and sell enough bonds to get 50% of the purchase price of the underlying bonds up front. Let’s also assume that the liabilities have a weighted average interest rate of LIBOR+10bps. Using the C.D.O. instead of a traditional loan, especially since the C.D.O. can’t be cancelled like a loan can and, most likely, contains much more lax terms than a loan, is much more cost effective. Taking this a step further, it was even possible for C.D.O.’s to be issued that allowed more bonds to be put into the C.D.O. or allow bonds that were sold to be replaced. This effecive made the C.D.O. a credit line with an extremely cheap interest rate. Keep in mind the “equity” or “most levered tranche” or “bottom” of the C.D.O. generally was structured to have a very high return, somewhere in the 15-25% range.

Also, the backdrop of the boom in C.D.O.’s, don’t forget, was a very low rate environment. If one could get LIBOR+10-15bps on AAA bonds when rates were, in 2004 for example, 1% (for USD LIBOR and the Fed Funds), that was a major out performance for a AAA security (AAA, how much risk could there be?!).

Now that the historical context is out of the way, it seems pretty clear that some of these reasons for isssuing C.D.O.’s will not diminish in importance. Funds and money managers will always need more yield. Investors that are smart about credit analysis will always want to take the risks they understand and get paid for taking said risks. Funds and other “levered players” will always need financing. So, let’s examine how the landscape changes rather than disappears.

1. Complexity will die. There are a number of reasons for this. Part of the reason is that buyers of C.D.O.’s will begin to realize that structure adds a layer of complexity that no one really can grasp fully. Why have dozens of triggers and tests at every stage of the waterfall (the way cash is distributed in order of seniority)? In some deals, I’m sure, this complexity helped some tranches of the C.D.O. In some other deals, I’m sure, this complexity hurt some tranches of the C.D.O. The one  constant is that it’s nearly impossible to tell the right levels and specific mechanics beforehand. Hence the complexity will die and structures will simplify. Likely this also means less tranches. Why have a $4 million tranche size in a $400+ million deal when you can’t even predict losses within an order of magnitude (1%, 9%. or 20%? Who knows?!)? This is hardly a new concept, I introduced it already when discussing residential mortgages.
2. Arbitrage C.D.O.’s will reign supreme. This one is controversial, and the term “Arbitrage C.D.O.” almost takes on a different meaning each time it’s defined. The intuition, though, is that a hedge fund taking advantage of a market dislocation by issuing a C.D.O. is an “Arbitrage C.D.O.” Why will these be popular? Well, C.D.O. shops, or firms that are serial issuers of C.D.O.’s, have mostly blown up and are done. Traditional money managers will be shying away from C.D.O.’s for a long time. So, in order to sell the C.D.O. equity, the most levered risky piece, the firm issuing the C.D.O. will need to also be willing to take on the equity–this leaves only hedge funds. Arbitrage C.D.O.’s also come together more quickly and generally are backed by corporate bonds. Funds and other accounts that, as a core competency, already analyze corporate credit won’t have to go “outside the comfort zone” to buy into arbitrage C.D.O.’s.
3. C.D.O.’s or C.D.O. technology will become part of the M&A world more and more. Aha! Maybe too clever for my own good, but while all these specialty finance companies used to be able to issue a C.D.O. for funding purposes on their own, now they will need an investment bank to connect them with hedge funds or take on the debt, and thus the risk, themselves. These C.D.O.’s will likely be simple too (see #1), but will be an efficient way for these companies to finance assets or move them off the balance sheet. Here’s an example: a diversified finance firm, with a large lending presence, for example (most likely with a R.E.I.T. subsidiary, a popular structure of the past eight years) will be looking to sell itself. However, because the assets on it’s balance sheet look risky the leveraged finance groups will need to arrange some financing against those assets. The structure? Most likely a C.D.O. with hedge funds providing the cash and getting a “juiced” return on their money. This is essentially the covered bond product, but with an extra layer of complexity (tranching) on top.

Okay… that’s enough prognosticating for now. Still deciding which product is next. Drop me a line if you have a favorite!

Disclosure? I Call B.S.

Disclosure and financial filings seem to be topical today with the S.E.C. announcing the Investment Banking Analyst Mercy Initiative. So, I’ll play ball. I have read a bunch of things recently making claims about the ability of a diligent investor to know what they are “getting into” and what the risks are for investing in a public company that has disclosure requirements. Actually, I haven’t been doing this for decades, so let’s quote someone that has… Tom Brown:

No one, inside or outside the company, could accurately predict what … ultimate losses would be. But what they could do—and what financial services investors can do now, regarding the banks in general–is make reasonable estimates of ranges of losses, and estimate companies’ future earnings power, then compare that to their market values.

(emphasis mine).

I emailed Tom to clarify a few thing, but never heard back. So, as I am prone to do, I’ll assume I’m correct in my interpretation and move on. I’m assuming that this was also the case in the past–how else would people be able to buy into a financial institution in the past if Tom didn’t think his words were just as true two to three years ago? (Nothing has really changed in disclosure requirements, right?) Surely, in the past, the issue would have been taking a view on the performance of the various financial institutions’ assets as well.

I looked at three firms’ disclosure, from 2006, related to C.D.O.’s … what I could find. Now, in the interest of full disclosure, I’m not trained to do this. I’m just a person, with some financial experience, looking at some S.E.C. filings. I knew i was looking for C.D.O. exposure, especially in the context of figuring out what banks would need to be responsible for if the market had a severe dislocation. Let me explain what I mean by this. Remember all the liquidity put chatter? While mostly related to S.I.V.’s, this is still a relevant concept for C.D.O.’s. As in any syndicated deal, most common for selling bond or stock offerings related to corporations but also relevant for securitized products, when an investment bank agrees to do a securitization they have most likely (call it 80+% of the time) agreed to “take down” or purchase the securities they are unable to sell to investors. Easy enough, right? Those assets are what has generated a huge amount of writedowns. It’s very easy to see the relationship between market share in the C.D.O. and securitized products space and magnitude of writedowns.

These relationships, however, are very complex. Multiple investment banks could be selling an individual deal and each could be responsible for purchasing different parts or different percentages of leftover securitizations. These are individually negotiated for each transaction. As a firm is building up assets (for example, sub-prime mortgage-backed securities), before they have enough to actually securitize and create a C.D.O., the bank/investment bank could have all the risk of those assets losing value or defaulting–if the C.D.O. doesn’t get done then it becomes a big problem. It’s also a big difference what types of assets or structures make up the C.D.O. securities. One sees the problem growing. There is a lot of information that needs to be processed to come up with a reasonable estimation of losses. I would claim that it is completely insufficient for a bank, as they have been, to disclose exposures once they start to become a problem.

So, what did I find? Terrible disclosure. I was able to find almost no information. Certainly no information that would have helped come up with an estimate for losses from these firms based in any sort of logic or fact. Now, I’m not saying one should be suspect of current disclosure–I don’t know what is next to blow up or cause big problems and none of these firms are run by the same regime that decided the previous level of disclosure. What I am saying is that I wouldn’t have been able, even if I had known exactly what was going to happen, to know the magnitude of the losses.

First, I looked at Citi. Citi had a notion of participating or structuring. Those numbers were combined and reported together. This helps to determine market share, perhaps. This does nothing to disclose the risk on the balance sheet. This number ($110 billion) could be made up entirely of bonds were Citi is at risk. It could also be entirely made up of bonds where Citi has no risk and is taking fees. There is nothing I found in the 10-K’s to say anything more helpful. So we know losses, if these C.D.O.’s (named V.I.E. or Variable Interest Entities in the disclosure) were sold at 22 cents on the dollar, as Merrill reportedly did, the losses would have been between zero and $86 billion. Whew! Nailed it down… Now, knowing that, do you buy or sell Citi’s stock?

Second, I looked at Merrill. They state some numbers and then footnote saying they might, potentially, hold a financial interest in some of the securitizations. Same situation as Citi. No disclosure as to what kinds of bonds these are. How much was retained? How much in financing obligations exist related to these? What percentage would have had to be retained by Merrill if unsold?

Last I looked at Bear’s filing. Bear was a slight improvement. They actually stated some of what they retained and have some exposure numbers which one could back out some other information from. Still, if I was modeling the losses I would be asking for a lot more information–while an improvement, in my opinion, it wasn’t enough.

Below are the tables from the various filings. Also, if one was looking for C.D.O.’s, I put the number of instances the term of interest appeared.

Now, since the S.E.C. is mandating and revamping filings and disclosure, perhaps they can do something about this. Maybe financial firms should be forced to disclose risk numbers and sensitivities. I certainly don’t have all the answers, but I think it’s pretty clear that no one had the answers, nor did they have the specific questions, before this crisis occurred.

From the Citi 10-K (2006):

Mentions of the word C.D.O. : Thirteen (lucky!)

From Merrill’s 10-K (2006):

Mentions of the word C.D.O. : Zero

From Bear’s 10-K (2006):

Mentions of the word C.D.O. : Eight

Assume all Bonds are Spheres: Part I

This segment is a regularly occurring feature. It gets its name from a joke that is commonly made about technical people. Usually a very simple problem is presented about horses (or sometimes cows) and a physicist/engineer/mathematician is asked to provide a solution. The solution is made complex because incorporating the nuances of the animals in question is extremely difficult, hence the highly technical person is required. The solution then starts with the technical person saying, “I made two assumptions. The first assumption is gravity. The second assumption I made was that all horses are spheres.” The crux of the joke, which is often found in the markets, is that approximating is both easier and “accurate enough.” Hence the naming of this series on mathematical financial tricks and other interesting tidbits.

Loans are simple enough. I tell you that I would like to originate a loan, which I will securitize, and your interest rate on a loan is going to be 10%. Easy! You just send in 10% of the loan amount every year. Well, not really:

• If I followed convention, I quoted you an Act/360 rate (it accrues yearly based on the actual days, but assumes a 360 day year)–the interest you pay is really 10.14% (~ 365/360 * 10%). (Note that the lower the interest rate, the lower the impact of converting to Act/360.)
• If this was a 10 year loan, those 14 basis points (bps, 1/100th of a percent) are worth about 1.11% of the total notional of the loan (don’t forget, that’s 14 bps extra one pays per year, for 10 years–take the present value of all those cashflows).

Now, let’s look at what happens when I securitize the loan.

• I monetize the 14 bps because the bonds I sell accrue on a 30/360 basis (market convention), so those extra days of interest never get paid to bondholders–I keep it.
• Another nuance: The bonds are priced to the market convention, which is assuming a semi-annual yield. Investors will demand, say, a 10% coupon on their bonds. The bonds, though, match the loan–they pay monthly. What is the 10% worth on a monthly basis? About 9.80% (see below). What do I earn on arbitraging the difference? Well, about 20 bps per year, which, present valued, is worth about 1.59% of the loan amount.

Let’s review: I quoted you a loan at 10%. The 10% tuned out to be more than 10%. I then sold the loan using a completely different set of assumptions and, doing nothing at all, managed to pocket 2.7% of the loan amount. On $10 million dollars that’s $270,000 I made just for arbitraging various conventions and the difference in how bond investors think and how lenders generally think. Would you have been better off to take the 10.05% loan from the insurance company, quoted on a 30/360 basis? Yep. But the rate was lower … and all bonds are spheres.

————————–

The voodoo behind the 9.80% monthly equivalent coupon is easy. The first insight is to recognize that a yield is essentially a discount rate. To find a monthly equivalent to a semi-annual yield one needs only to find the interest rate that, when compounded twelve times a year, equals the yield that assumes compounding twice a year (the semi-annual yield).

We start by saying that an annualized yield, assuming compounding x times a year is

     (1 + i/x)^(x) – 1 = annualized yield       Formula that codifies the above intuition.

For our example of a 10% semi-annual yield, we get the following:

ann. yield (12 pmts.) = ann. yield (2 pmts)
(1 + (r/12))^12 – 1 = (1 + (10%/2))^2 – 1 
1+ (r/12)) = (1+5%)^(2/12)                       Algebra… 😦
r/12 = (1.05)^(2/12) – 1
r = 12 * ((1.05)^(2/12) – 1)
r =  9.79781526%                                       Our answer!

And that’s how I arrived at that solution. I’m sure I’m missing something minor that excel would do for me, but you get the idea.