Mortgage Defaults

Came across an interesting paper on mortgate defaults the other day while I was, actually, searching for some models of credit card default.

The authors, Campbell and Cocco, develop a microeconomic model of this important behavior and come up with some interesting results.

In particular, they make a clean connection between negative equity and borrowing constraints when it comes to default. Negative equity increases the default risk, of course, but the degree of negative equity that triggers a default depends on the degree to which the household is constrained in the credit markets. pofoundly constrained households can default at low levels of negative equity.

The other interesting result is the breakdown of the particular risks of the various types of home financing. For example, interest-only mortgages have the highest risk of default waves. Even so, there are ranges of risk events for which they have some clear advantages over other forms of financing. For one, these borrowers are less likely to face borrowing constraints than other types of borrowers. This benefit is generally overwhelmed by the equity risk they face -- interest-only homes are the most exposed to decreases in home value.

The paper is pretty deep and will take several readings to get a handle on the arguments. But the idea of approaching the question with a dynamic micro-model is significant.

New Product Launches -- Tobacco

In the last year or so, I’ve had the chance to monitor several product extension launches in the cigarette industry; all the big players have made some moves. For example, Marlboro has sequentially launched several Special Blend sub-brands, while Newport has successfully launched a non-menthol brand. Despite the different success levels we observe in terms of market share for these launches, all of them share a remarkable similarity in terms of their share diffusion in the market. I want (briefly) to look at some of the implications of this fact as it relates to the cigarette industry.

The basic Bass model suggests that the volume (share) of a new product is determined by the interaction of two effects. The first is the innovation/advertising effect, which is taken to drive people to experiment with the product quickly. The second effect is the imitation/word-of-mouth effect, which is assumed to spread the desire to try the product over time.

The sales as a function of time can be expressed:

Nt = Nt-1 + p(m-Nt-1) + q(Nt/m)(m- Nt-1)

Where N is the number of units sold (or, scaled appropriately, market share), m is the total market size for the product, p is the innovative/advertising effect, and q is the imitation/word-of-mouth effect. Typical values for p are said to be around 0.03 and for q around 0.4.

You might be able to see that the last term on the right hand side is the difference term that we see in simple models of population growth with carrying capacity, used to model the size of a colony of bacteria in a Petri dish, for example. So, the “q” term is the logistic or organic growth and the “p” term is the exponential or advertising-related growth. And overall volume is determined by the balance between these two effects.

So far, so good. But here is where it gets interesting. Below are a pair of simulated new product launches, the first from a product with typical coefficients and the second with coefficients that have been calibrated to yield weekly changes in volume that mimic those of the new products in the cigarette industry. Check out the graphs at the top of the page to see what I mean.

The overriding fact of all the new product introductions was a peak in the share change that happens in week #2, and the share changes generally fell to near zero by week #4 (though I haven’t modeled the drift that some products display subsequently). But the coefficients as calibrated are very far outside what is considered typical: the “p” value is 0.3 (up from 0.03) and the “q” value is 0.8 (as compared to a typical value of 0.4).

Now, these numbers are merely the result of a quick and dirty calibration, but they suggest the possibility that cigarettes are an unusual industry with respect to new product introduction.

New Product Inflection Points

New product diffusion is often modeled as an S-curve. The idea being that there is some period where the dare of the product is getting traction very slowly and that, when it hits, the share increases rapidly to some saturation point. The Bass-style diffusion models generally allow for this sort of process.

I'm thinking this is not a particularly good model for sophisticated CPG companies, especially if they are using some brand extension. This is so for two main reasons.

First, companies that rely one an extant sales organization are much better able to establish a wide number of outlets, reducing the search- and word-of-mouth effects.

Second, and more interesting (to me, anyhow), established organizations seem to benefit from a ready understanding by the market of the option value of new product trial.

The intuition is as follows. The market understands that a new product has both risks (overall product liking as well as switching costs, if any exist) as well as benefits (it could be much better). Brand extension serves both to reduce the variance on the prior belief about the liking as well as increase the prior estimate of the expected liking value. Higher expected value plus lower variance equals better deal.

In this case, we would expect the potential for a gain in utility to outweigh the risk for almost everyone who would consider trial of the new product.

It seems to me there are two implications from this thinking. First, such effects must be two-edged: reducing risk for consumers already purchasing something from the line but necessarily increasing risk for outsiders. If so, then trial should be weighted toward cannibalization at a greater than fair share proportion. That's interesting, I think.

Second, this might drastically shorten the length of time that new product promotions should be run: you wouldn't need long promotions if everybody already gets the idea that they should try the product sooner rather than later. In that case, what would matter would be things like watching for inflection points to know when most of the market has already seen the "option" purchasers act.

It would be interesting to look at these sorts of market penetration for line extensions to see when these points happen and how predictive they are of eventual share.

And We're Back

Long delay because of the relocation from Atlanta to Richmond, as well as the attendant school selections, spousal job searches, home search, and assorted adjustment costs.