In the mid 1980s at First Interstate, I participated in serious discussions about how the Merton model of risky debt could be used to diversify credit risk. In the early 1990s, I actively marketed default probabilities based on the Merton concept in Japan. I wrote two books advocating the model in the 1990s as well. Now my view of the model has completely changed. This blog explains how and why that came about.

From 1982 to 1987, I served as a senior vice president for strategic planning and later senior vice president for funding at First Interstate Bancorp. My boss Don M. Griffith and I met often with the predecessor of KMV to see if there was a way First Interstate could participate in the diversification loan pool that was proposed using the concepts of Robert C. Merton’s well known model of risky debt. Because of the risks of adverse selection, the pool concept never came to fruition but I was intrigued by the ideas behind it.

After a 3 year “vacation” in the investment banking department at Lehman Brothers in Tokyo, I founded Kamakura Corporation and we began working with Gifford Fong and his partner Oldrich Vasicek on a project basis with Gifford Fong Associates. Later, I called Oldrich after reading about his involvement with another firm called KMV. In short order, Kamakura became the Japan distributor for the Merton model default probabilities that KMV produced. I was a passionate believer that the model must be right, even though I never asked for any statistical proof that the model was indeed an accurate predictor of default. I never thought to ask for such proof, because it was so obvious to me that the model “must” work. I was a true believer.

In 1995, Robert Jarrow joined Kamakura Corporation as managing director for research. He was soon to publish (with Stuart Turnbull, 1995) the first random interest rates model of risky debt using the hazard rate or reduced form approach, where bankruptcy is a continuous time probabilistic risk. I asked Bob why he would spend so much time on this new approach when “fixing” the Merton model seemed like a much easier research path. I’ve written about Bob’s response before and how it humbled me. He told me that making the Merton model better was “too hard” for him to do in a tractable way. He argued that management’s choice of capital structure was dynamic and interactive with the macro economy. If that’s the case, only a huge dynamic programming exercise could properly derive the firm’s default probability via the modeling of the firm’s capital structure. “That won’t be practical in my lifetime,” said Bob, “for someone with thousands of counterparties.

I wasn’t convinced and I remained a huge believer in the Merton approach while Bob pursued the reduced form approach. In 1993, David Shimko, Naohiko Tejima, and I had published a paper called “The Pricing of Risky Debt When Interest Rates are Stochastic” in response to what we thought was a very reasonable demand by major Japanese financial institutions who were potential clients of KMV default probabilities. This paper combined two models of Robert Merton (the original risky debt model and his model of options pricing when interest rates are random) and the term structure model (1977) of Oldrich Vasicek, who reviewed our approach. Bob and I then met with the KMV team and formally requested them to include macro-economic factors like interest rates explicitly in the model to address the concerns of potential clients that these were important. To make a long story short, KMV wasn’t interested in this approach and we parted friends, but with the announcement that Kamakura was going to do it ourselves.

Beginning in 1995, we started working on a multiple models approach even though I continued to believe that the Merton model would work better. My 1996 book with Kenji Imai Financial Risk Analytics didn’t even discuss the reduced form approach. Out of deference to Bob Jarrow, however, reduced form models were going to be included in our product line even if they didn’t work well. Diversification was a virtue both from an analytical and a commercial point of view.

One of the first things we did was to test how well the models worked if one purchased bonds and used both models to hedge the position. We used a very high quality new issue non-call bond spread data series from First Interstate, which I had started collecting in 1984 and which my successors were willing to provide to me after Wells Fargo had purchased First Interstate. No matter how we did the numbers, the hedging performance contest between the two models was unambiguous. The reduced form approach was very effective, and the Merton model to my enormous surprise was not. In fact, “no hedge” except for interest rate risk performed better than the Merton model on the First Interstate series. In trying to understand why that happened, we asked this question, “What percent of the time was it in fact true that the First Interstate common stock price and credit spreads moved in opposite directions?” This movement was that predicted by the Merton model. I was shocked to find that a Merton model-consistent movement happened less than half the time on the First Interstate data series, which was a weekly time series. Bob Jarrow and I published this finding in an article in 1998, and to say it prompted controversy was an understatement. Hate mail was a new experience for me. The more thoughtful commentators suggested that we looked at a much larger data set, and so we did. That paper, published in 1999, confirmed that it was a general phenomenon across a wide range of companies of varying credit quality, even as the time interval lengthened. What was very clear was that the implication of the Merton model (spreads and stock prices moving in opposite directions 100% of the time) was rejected on statistical grounds on every sample.

Still, many traders would go long the bonds and short the stock as a hedge. The Wall Street Journal, in an August 12, 2005 page 1 article, described the hundreds of millions of dollars in losses from this strategy at the time Ford and GM were downgraded to junk in May 2005. In spite of the accumulating evidence that making the Merton model work better was not going to be easy, I kept trying. We became convinced that the key problem was the implicit Merton assumption that the dollar amount of debt outstanding remained constant. Again, we used First Interstate data to project debt issuance forward in such a way that we’d great more realistic default probabilities and hedges than we had gotten so far. Even as a former treasurer of First Interstate, I ultimately concluded that Bob Jarrow had been right all along. The amount of funding that we had done was a function of the environment. When the business cycle looked likely to worsen, we strengthened capital and issued longer term debt in anticipation. When the cycle was turning up, we held off on equity issues and shortened maturities. After I had left First Interstate, the firm in fact was unable to roll over commercial paper but had been conservative enough that it could withdraw totally from the CP market. None of this dynamic behavior is embedded in the highly stylized Merton risky debt model, because that would have required the kind of dynamic programming approach that Bob Jarrow had predicted.

Leading up to the KRIS default probability service launch in 2002, Jorge Sobehart and his colleagues at Moody’s published a string of papers showing that a “hybrid model” that included the Merton default probabilities was much more accurate than a pure Merton approach. With every one of the KRIS default probability versions (four so far), we found that the reduced form approach worked the best, followed closely by a hybrid approach. The pure Merton theory approach trailed far behind. Our most recent performance results were published in 2007 and closely paralleled the results of Bharath and Shumway (first version 2004, published in the Review of Financial Studies in May 2008) and Campbell et al (first version 2004, published in the Journal of Finance, December 2008).

Both our tests and the Campbell paper were based on 1.4 million monthly observations, and it was impossible for me to deny the truth. Bob Jarrow was right. A model which proposes one random factor (the value of risky assets) as the sole explanatory variable for stock and bond prices was simply too stylized to be realistic. In spite of the many Merton extensions, which David Lando’s book summarizes nicely, the gap in accuracy versus the reduced form approach has not been closed.

For me, as a former true believer, the success of the reduced form approach in predicting default is a scientific fact that’s impossible to deny. All the same, like a lost love, I wanted the Merton model to be better than it turned out to be!

Donald R. van Deventer

Kamakura Corporation

Honolulu, July 30, 2009