Single Factor Duration Models in a Discrete General Equilibrium Framework/Discussion

Single factor duration models (SFDMs) for valuing debt securities have come into widespread use by bond practitioners lately, but reception by academic economists has not been as strong. The lack of academic acceptance of SFDMs may be due to the unrigorous development of theoretical bases for these models in some cases. This paper analyzes these weaknesses, constructs explicit theoretical underpinnings for the SFDM, and develops conditions under which the model satisfies general equilibrium conditions. The major economic assumptions on which the SFDM is founded are: 1. Investors maximize expected returns over a known planning period. 2. Only default and option-free debt securities are considered. 3. The true stochastic process is known. 4. Changes in all interest rates on the term structure are perfectly correlated. 5. The return function for an immunized portfolio is non-convex. The SFDM seems to perform better than either 2-factor models or naive maturity matching models. Fisher applauds the direct approach to price change relationship with fixed-income securities. He suggests the future use of these assumptions under more general conditions.