Hi everybody,Essentially I would like to talk about the difference between two types of asset pricing models.On the one hand:Structural bond pricing models that specify stochastic processes for a firm's asset value and the short rate, both driven by observable state variables. Default occurs when the asset value falls below the value of the liabilities. The processes are formulated in terms of the risk-neutral measure, and a bond's price is given as the present discounted value of expected future payments. Returns are calculated using changes in prices.On the other hand:Asset pricing models in the spirit of the CAPM that view an asset's expected return as compensation for systematic risk, as measured by market beta (in the case of the CAPM) or other risk factors as well, such as SMB (Fama-French).It seems to me that any discussion of the relationship between these two types of models is thoroughly avoided in asset pricing books and the academic literature!I'd be glad if anybody with more experience could comment, or suggest answers to some of my questions:-Do these models compete in applications? What would be examples of applications where either one would be used?-Are there any studies that compare these models empirically?-Do the two types of models conflict in terms of their implications?Cheers a lot!Alfred

I reckon this is chalk and cheese

Dave,Thanks for your comment! You're probably right that they are quite different in their approch.But they talk about the same things, namely how the price of a security will change from one period to the next. That's why I am surprised to not find them ever mentioned in the same book! Let alone paper or paragraph...I was just wondering if anybody else had thought about that and can give me a reason. Or a succint description of the difference between the models that would help me understand.Cheers!

are you saying that nobody has tried to reconcile the CAPM with option pricing ?

QuoteOriginally posted by: alfreduxDave,Thanks for your comment! You're probably right that they are quite different in their approch.But they talk about the same things, namely how the price of a security will change from one period to the next. That's why I am surprised to not find them ever mentioned in the same book! Let alone paper or paragraph...I was just wondering if anybody else had thought about that and can give me a reason. Or a succint description of the difference between the models that would help me understand.Cheers!It seems to me Merton's model (the structural model) is mostly about default risk and bankruptcy, which is mostly idiosyncratic, and so part of the noise in CAPM. That might explain the disconnect.If you really want studies with some sort of overlap, google for kitchen-sink regression models that attempt to predict bankruptcy risk, which should contain accounting measures (assets, liabilities, etc) and market factors such as betas as explanatories. Just guessing, though ...

This is actually just mainstream modern finance as developed over the past forty(ish) years. A decent starting point (at a graduate level) would be most recent version of Darrell Duffie's "Dynamic Asset Pricing" book Duffie. Alternatively, you can google terms like "stochastic discount factor" or "growth optimal portfolio" for a rather rich literature that spans the two approaches.

QuoteOriginally posted by: alfreduxHi everybody,Essentially I would like to talk about the difference between two types of asset pricing models.On the one hand:Structural bond pricing models that specify stochastic processes for a firm's asset value and the short rate, both driven by observable state variables. Default occurs when the asset value falls below the value of the liabilities. The processes are formulated in terms of the risk-neutral measure, and a bond's price is given as the present discounted value of expected future payments. Returns are calculated using changes in prices.On the other hand:Asset pricing models in the spirit of the CAPM that view an asset's expected return as compensation for systematic risk, as measured by market beta (in the case of the CAPM) or other risk factors as well, such as SMB (Fama-French).It seems to me that any discussion of the relationship between these two types of models is thoroughly avoided in asset pricing books and the academic literature!I'd be glad if anybody with more experience could comment, or suggest answers to some of my questions:-Do these models compete in applications? What would be examples of applications where either one would be used?-Are there any studies that compare these models empirically?-Do the two types of models conflict in terms of their implications?Cheers a lot!AlfredTo expand on what Bearish suggested, in the Merton model, market return from CAPM will be the 'state' variable that determines the risk-neutral PD and the bond returns. If you write CAPM in terms of a pricing kernel E(return*discount factor) = 1, then you can price anything including bonds. For a zero bond, you'll have E( (1-PD*LGD)*discount factor) =1. Another way to think about this is in terms of the difference between risk-nuetral and real world PDs. In the merton world, you'll have risk neutral PD = F (F^-1(real world PD) + Market sharpe ratio * correlation between firm and market), or something like this. I think Kealhoffer derived this in some paper.

QuoteIt seems to me Merton's model (the structural model) is mostly about default risk and bankruptcy, which is mostly idiosyncratic, and so part of the noise in CAPM. That might explain the disconnect.Default risk is not idiosyncratic. You have huge spikes during recessions: QuoteIf you really want studies with some sort of overlap, google for kitchen-sink regression models that attempt to predict bankruptcy risk, which should contain accounting measures (assets, liabilities, etc) and market factors such as betas as explanatoriesBut that's the real world PD. There is no reason for Beta to explain PDs, eventhough it may important in pricing.

Good critiques of my ramblings, gardener3 and bearish. Am reading some Kealhofer.There is a related conceptual issue that has been bothering me, mostly in terms of volatility modeling.I will try to state it in terms of PD modeling after I am done with my reading ...

OK, here is the issue I alluded to, and I believe on-topic for this thread.Finished reading Kealhofer's "Quantifying Credit Risk II: Debt Valuation" in which he asserts (in 2003)QuoteThe KMV version of the Merton model, which has been extended over the years, has become a de factostandard for default-risk measurement in the world of credit risk As I understand it, the model produces, among other things, an estimate of the real-world default probability (real-world PD) over various time horizons.However, it does so without using directly either bond spreads or credit default swap spreads.It is apparently based mostly upon the equity behavior of the bond issuer.Now this seems to me to be an estimate that would likely be dominated by another estimator that did incorporatesuch market information (bond spreads and CDS spreads). I am just guessing about that, based on my knowledge of a similar issue with volatility estimators. For example, GARCH-style estimators for SPX volatility will be dominated by estimators that include bothGARCH predictions and current VIX. In general, its always suboptimal to ignore relevant market data when makingpredictions, real-world or otherwise. The point is nicely explained in this blog post, in which the author coins theterm "R probabilties" for such suboptimal estimates. My questions/confusions are:1. Why do/did clients pay for such suboptimal estimates, estimates which deliberatelyeschew market information, to use the language of the blogger? 2. How can such suboptimal estimates become the "de facto standard"? 3. Where are things today re the best real-world PD estimators? Again -- apologies if this is nonsense since it's not my area -- I am just extrapolating from the volatility case, where Ithink I understand the issue of failing to include relevant market data. Thoughts?

Alan, No method is perfect, that's for sure. The Merton model is imho more ambitious but fairly dated, probably from before the CDS markets were around or at least noticed. Strictly speaking, the theory assumes the issuer has a stylistically simplistic capital structure, the only debt being a single discount bond. It is not obvious to me how robust the model is to relaxing that assumption, let's hear from the credit specialists please.I agree it is usually a good idea to use market information where available, but using CDS prices also has warts associated with it. For starts, the market convention seems to be to assume a uniform LGD (loss given default) number seemingly pulled out of thin air (or perhaps some more nefarious region) and anything else inferred is affected by this assumption.More significantly, Jarrow and his colleagues at the Kamakura company routinely publish incendiary research on their website that points to significant illiquidity in the CDS markets. They go as far to say that any inferences drawn from CDS prices are highly suspect.

QuoteOriginally posted by: DavidJNAlan, No method is perfect, that's for sure. The Merton model is imho more ambitious but fairly dated, probably from before the CDS markets were around or at least noticed. Strictly speaking, the theory assumes the issuer has a stylistically simplistic capital structure, the only debt being a single discount bond. It is not obvious to me how robust the model is to relaxing that assumption, let's hear from the credit specialists please.I agree it is usually a good idea to use market information where available, but using CDS prices also has warts associated with it. For starts, the market convention seems to be to assume a uniform LGD (loss given default) number seemingly pulled out of thin air (or perhaps some more nefarious region) and anything else inferred is affected by this assumption.More significantly, Jarrow and his colleagues at the Kamakura company routinely publish incendiary research on their website that points to significant illiquidity in the CDS markets. They go as far to say that any inferences drawn from CDS prices are highly suspect.The game of quantitative explorations in the credit space is certainly characterized by a lack of perfection. Merton did indeed write his credit paper more than 20 years before the beginnings of the CDS market. And you are right about the most obvious limitation of his paper -- and there are a bunch of others, but to balance this shortcoming there are hundreds of follow-on papers (among the more influential ones would be Black and Cox, Longstaff and Schwartz, Leland and Toft, Duffie and Lando, to mention a few). Market conventions are just that: conventions. If you have any independent view of LGD for a name you are most certainly free to use that along with market quotes for CDS. The good news is that the market quote is actionable and completely independent of any LGD assumption. The main problems with the CDS market are that it is not very liquid (as Don van Deventer of Kamakura points out with alarming frequency - probably correctly despite the fact that he is rather loudly talking his own book) and that the required central clearing house collateral requirements will kill whatever little liquidity that has remained.To Alan -- Peter's blog is funny and largely to the point. He was arguably also talking his book at the time, but I think his arguments will be of a more lasting value than the commercial venture that may have caused him to write it to begin with. I really like the concept of the R rating, and not just because of its alphabetical logic.

Hi Alan,I don't know the answer to your questions but let me through in some relevant thoughts:- There are reduce form credit risk models which take into account additional information. These models usually look like [$]\lambda_{it}=exp(\beta c_{it} )[$] where [$]\lambda[$] is the default intensity and [$]c_{it}[$] are firm specific and/or macro variables.To get to my point, I would like to highlight that one of these [$]c_{it}[$] is usually the distance to default of the company which is a deterministic function of the PD you would get from the Merton model. This means that you can think about these models as extensions of the Merton model with additional information. - The other thing which I would like to highlight is that the Merton model is just an additional measure next to credit ratings. The two sources of information complement each other as ratings are trough the cycle PD estimates and they are lagging behind the "true" PD while KMV is more up to date as they are using market information. - I don't really know any commercial alternative to KMV which would take into account additional information in a reasonable way (Altman Z-score ? but that is really old) There is a nice non-profit initiative to provide daily PDs for listed firms: http://www.rmicri.org/

On 1&2: Both the time series and the cross section of companies that have liquid CDSs or corp bonds is very limited. The former market was almost non-existent when KMV was launched. And merton distance-to-default (given its unrealistic assumptions and the strong functional form it imposes), does a surprisingly good job of explaining the cross-section of defaults. The marginal benefit of adding new variables to improve prediction is fairly low. Also, the difference between P and Q probabilities can be due to market doing a better job incorporating information about future default rates, or it could just be compensation for risk. If it's the latter then you'd just be adding noise to your estimations. Suppose you have two companies. One produces cheap wines the other expensive wines. If there is a boom everybody drinks expensive wines and the cheap wine copmany goes bankrupt. If there is a recession, it is the expensive wine company that defaults. Suppose that a boom will happen over the next year with 10% probability and a recession with also 10% probability. Both companies have the same default rate over the next year. But, since money is more valuable in a recession, the cheap wine company's bonds or CDSs will trade at a discount. Once you control for the real world PD, the spreads on the CDSs or bonds will have zero predictability about future default rates.To see if it's the information or the risk premium, you could try to see if spreads predict defaults after controlling for merton distance-to-default. The problem is you'll have very few defaults with liquid CDSs or bonds, and if you use CDSs you have only one business cycle, which makes it difficult to draw any meaningful conclusions.

That's surprising to hear (from an outsider to those markets), that CDS's don't offer clear prediction improvements.On the general issue of "information or risk premium" in Q-probabilities in general markets (not bonds, but anything) I think you have to assume both are in there and the information content may be significant -- even if it hasn't been so in the past! To take a simple thought experiment, consider actuarial estimates of life-expectancies basedon history. These are a classical example of P-probabilities. But, they are not P-probabilities, but R-probabilities (to use the language of the blog I linked to) if one deliberately ignored market pricing for life insurance. For example, suppose a dramatic medical breakthrough significantly extended life expectancies. This would be quickly reflected in insurance prices. Even though those prices containedhuge risk premiums, it would be a mistake to generally ignore them in estimating the P-probability of death.