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“A Regime-Switching Model of Long-Term Stock Returns” by Mary Hardy, April 2001

GORDON E. KLEIN* Dr. Hardy is to be congratulated for writing this very interesting paper. I read it right after teaching two classes covering the material on Exam 4, and I think that it provides a wonderful example of using the methods of that exam (fitting of model parameters using the method of maximum likelihood, likelihood ratio tests, Schwartz Bayesian Criterion, and Akaike Information Criterion). I would recommend it as a supplement to anybody teaching that material. The objective of the paper is summed up by the title—to find a model for long-term stock returns. In particular, Dr. Hardy describes a 10-year European put option with a strike price of 75 or 100% of stock index value at contract inception. The paper actually develops a model for shortterm (one month) stock returns—a model that is preferred to other candidates using criteria of the likelihood ratio test and similar tests. The main question that I want to address is this: Can this model for monthly stock returns lead to a sufficiently good fit in the left tail of the implied distribution of long-term stock returns to lead to a good estimate of the price of a 10-year put option?