Monday, September 10, 2007

CDS Factors In Equity Valuation - Part A

As indicated in the previous post, I have started work on a share valuation model that attempts to integrate Credit Default Swap factors into the equation. This will be done as a series of postings, not only because it would otherwise result into one very long post, but also to allow for timely and helpful comments from readers, as I go along.

Professional colleagues already know that the CDS market has a very big impact on stock prices. There are plenty of models on this correlation, particularly amongst the quant and prop traders. If any of you chance upon this blog it may feel like ...coals to Newcastle. But as will become clear, particularly in later instalments, my idea is not to price stocks based on CDS or vice versa, but to look at the possibility that stocks appear relatively undervalued because a part of the equity risk has been stripped out and is trading separately OTC in the CDS market. It's a bit like creating zero coupon bonds from regular bonds by "clipping" the coupons. Likewise, the stock "corpus" trades on the regular exchange, while its risk "coupon" trades OTC as CDS. To get the proper price we must put both together. I have not personally seen this idea floated anywhere, so if anyone has, please let me know.

A note for those who shudder at mathematical equations: All that will be involved are the four basics: +/-* . Perhaps a Δ (change) and a Σ (sum) here and there but no calculus, I promise. At least not in the first installment... ;)


Part A: The Basics of Equity Valuation

In standard portfolio theory, equity prices can be calculated as the sum of (a) the present value of the series of expected dividends plus (b) the present value of the annual "extra" we expect to receive in the form of capital appreciation and dividend growth, commonly called the Risk Premium.

Price = Discounted Cash Flow + Risk Premium

=> P = DCF + RP
(Equation 1)

The DCF calculation is pretty straightforward: take the series of annual dividends for 30 years, apply a discount interest rate (usually the 30 year Treasury) and arrive at the present value. There may be slight variations depending on the number of years used (30, 40, 50?) and the discount rate, but on the whole that part of the valuation is not volatile, simply because dividends don't change very fast.

When expressed as an interest rate (the usual way) Risk Premium has an inverse relationship to equity pricing: the lower the risk premium, the higher the resulting stock price. The "classical" way to estimate RP as an interest rate (RPi) is through the P/E ratio (PE):

RPi = (Earnings/Price) - (Real 30 year Treasury yield)

=> RPi = (1/PE) - Real Yield (Equation 2)

A way to arrive at the P/E ratio and thus current equity pricing, is to solve the above equation for PE:

=> PE = 1/(RPi + Real Yield) (Equation 3)

This clearly requires that we independently provide the value for RPi, the Risk Premium rate. Keep this firmly in mind as we progress, because it is the window through which the CDS market enters into equity valuation.

We may think of RPi as the "extra" spread above and beyond current dividend return that an investor is willing to accept in order to assume the risk of holding stocks, instead of
risk-free assets (e.g. Treasury bonds). This is partly what Alan Greenspan was referring to when he warned, right before he left the Fed, that prolonged periods of unusually low risk premia commonly end up badly*. Simply put, they indicate a high degree of risk appetite, i.e. speculation.

To put this into perspective, at the recent S&P 500 top of 1555 the present value of dividends (i.e. DCF) came to approx. 400 points, with the rest accounted for by the Risk Premium. Therefore, share buyers at that point were expecting 75% of their returns to come from capital gains and future dividend growth. Today's situation is not much different, with 425 S&P points accounted for by DCF and 1020 points by the Risk Premium, i.e. the split is now 71% - 29%. These are very high imbedded expectations for growth, particularly when one takes into account that corporate earnings as a percentage of GDP are currently at an all time high.

The question thus arises: why are investors willing to accept such low risk premia (when expressed as interest rates)? Has anything changed in the way we calculate or estimate RPi in equation (3) above, to arrive at higher P/Es? The answer is certainly yes and the reason can be found in the explosive growth of the Credit Default Swap (CDS) market, which is functioning as a mechanism for stripping out and trading separately that portion of risk associated with creditworthiness. Naturally, creditworthiness is highly correlated to corporate finances and we can readily perceive how signals from the CDS market quickly find their way to share prices.

That will be the subject of Part B, which I will post in the next few days.

(*) Unlike many in the financial blogosphere, I have great respect for Mr. Greenspan. We can certainly argue bubble creation, but under the circumstances he was probably the best Fed Chairman ever. I point out that he warned against the dotcom madness and even raised rates to contain it, despite then low inflation. The drastic rate cuts he engineered must be viewed through the events of 9/11 and were completely justified, at least up to a point. Don't forget he also had to deal with a mad-hatter fiscal policy designed by the Bush II neo-conservative administration. I also appreciated the merciless way in which he tortured English language syntax when providing congressional testimony. He could speak for hours without anyone understanding a damn thing - he was proud of it, too!


  1. Alright, i've been following this blog for some time, and it's really nice to read. i have some questions now:

    1) could you direct me to an educational site regarding more advanced stock-stuff. i have a little trouble understanding that part

    2) i'm a mathematician, i think the formula's you use are a tad too simple, but again: back to question number one in that regard.

  2. Dear Hellasious,
    yes go ahead ! I suggest that you use nominal earnings yield and not real yields. i think there is no reason at this stage to include inflation in the equation. On risk premium : probably and that is what I am doing rather than taking the T bond yiel, I use the corporate yield as it includes a potential risk spread. assuming this spread was too low it is then easy to move it up and see what it gives on valuation ( a good example is the valuation of asian stock before and after the rise in emerging debt spread in 97.
    best regards

  3. simmu, re simple formulas: Believe it or not, finance is not rocket science. No Dirac equations, no Gauss, no string theory necessary. They keep on toying with chaos theory in market modelling but it keeps breaking down. The whole game is in the assumptions, anyway.

    I recommend you start with Graham and Dodd's book "Security Analysis". It's a classic which will give you the basics and more (just keep in mind that "growth" is more in vogue today than back then, when dividends ruled the roost). I can't direct you to a specific Internet site, sorry. I am sure there are dozens.

    However, is a quick way to get definitions of terms that you may not be familiar with.

    miju: Thanks for the recommendations. I am providing an introduction here and as you will see later on, the terms of the various equations will change to reflect "reality" - from the CDS perspective, anyway.


  4. Anonimo Italiano says...

    yes please go ahead!

  5. Great post...

    I wholeheartedly agree as it relates to AG. As a rule, he was kind enough to talk to us. He was very reesponsive to the caprices of the markets.

    Which only goes to proove the old saying... "No good deed goes unpunished."

    Your conveance of this subject is excellent.


  6. One question, one comment:

    Where can I find the notional about of CDS outstanding for a given security. Bloomberg help claims they don't have that value.

    Assume you have a fund and are writing CDS on company X. Company X has a market cap of $1B. You have written a notional value of $10B against it. Your Hamptons' partners in crime participate in the same writing of CDS against company X until there is a total of $100B notional outstanding. Trouble occurs with X, stock drops 75% to market cap of $250M. Fundamentally, the company is bankrupt, but now the Hamptons crew simply buy X using an extremely complex transaction. The buyers of said CDS were right that the premium was way too low, yet they will never be able to collect.

    That story above is not just a story. Now, which factor does that go in?

    - Shawn H

  7. To: Shawn H

    Don't you just love free markets? Free and opaque... CDS trade completely OTC and there is no central clearing organization. ISDA and BIS do semi-annual market surveys but they do not collect individual names. In the US the Comptroller of the Currency also collects data on CDS but again, I don't believe they have "names".

    As for manipulating outcomes, it's been going on since Eve convinced Adam to buy apples - and she had to worry about a lot more than the SEC.

  8. I think this argument is highly convoluted and erroneous. In the real world of business valuation, the DCF formula measures discounted cashflows over a shorter period (not more than about 15 years) and can add a terminal value at the end of this period. Individual company risk is factored in primarily through a weighted average cost of capital or WACC. It reflects the cost a company is actually paying for a combination of debt and equity. It has nothing (directly) to do with Treasuries. Smaller, newer, or highly leveraged companies pay more to access capital markets. The cost of company capital can increase even when Treasury yields are falling (as has been the case recently).

    If your premise is correct, that CDS accounts for a part of risk stripped out of stock price, then we would be seeing companies with the greatest CDS trading activity showing the lowest risk (highest price) relative to DCF. It's just the opposite. The market is assigning the lowest risk (highest price relative to DCF) to the smallest and most speculative companies, including some without CDS market participation.

    The anomoly of today's stock market is that investors are paying P/Es for putrid little hole-in-the-wall companies that are three times as much as P/Es they are paying for big blue-chips.

    This is mainly due to hedge funds, yen carry, and sheer speculative greed.

  9. Another view of Greenspan. I tend to concur.