Posted tagged ‘GDP’

Why Stress Test Really Means Guesswork

March 15, 2009

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:

Normal Yield Curve

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):

Credit Spread

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?


How We Got a Corporatocracy

November 17, 2008

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).