Duration, Systematic Risk, and Employee Valuation of Default-Free Pension Claims: Reply

Duration, Systematic Risk, and Employee Valuation of Default-Free Pension Claims Introduction The modern economic and financial theory of pensions owes much of its evolution to two distinct but mutually consistent models of the labor market, namely the implicit lifetime contract (LC) model, and the compensating wage differentials (CD) model. (1) Empirical support for both models has been growing in recent years. (2) Under the LC paradigm, a firm's pension promise is a binding obligation which should be valued by the sponsor at the riskless discount rate, so as to reflect the highest degree of certainty that this promise will be honored at muturity. (3) Under the CD model, wages internalize the workers' valuation of pension claims, such that their total compensation equals the value of their lifetime marginal product. (4) Whereas the LC framework clearly identifies the riskless rate as the appropriate discount rate for valuation of the pension obligation by the sponsor, (5) considerable ambiguity appears to surround the appropriate discount rate for employee valuation of the pension claim. Skinner (1980, p. 32), for example, expresses doubt that employees factor risk into this valuation, and dismisses risk as irrelevant for pension accounting. In contrast, the empirical evidence on the CD model cited above appears to confirm that employees factor risk into their valuation of pension claims, as reflected by the corresponding wage differentials. In particular, Smith (1981) provides evidence which suggests that employees demand a risk premium on the pension promise itself, distinctly from any default-risk premium on the plan's under-fundedness. (6) Ippolito (1986, p. 175) also stated that underfunding a pension plan entails payment of a risk premium to the employees, and that this premium constitutes a cost to the sponsor. However, he does not address the notion of a distinct risk premium on the pension promise itself. Furthermore, he explicitly ignores risk premium components in his analysis of the sponsor's pension cost. At the policy level, several studies by Pesando (1982, 1984a, 1984b, and 1985) and by Pesando and Clarke (1983) have invoked the LC-CD framework to analyze recent pension reform initiatives and pension accounting issues, both in Canada and the United States. Invariably, such analyses rest, implicitly or explicitly, on the assumption that the employees share the sponsor's interpretation of the pension contract, and thus value their pension claim by using a riskless discount rate. To the extent that the employees' "true" (but unobservable) discount rate does or should embody a risk premium (as suggested by the evidence on the CD model cited above), the quantitative analyses in these studies may incorporate significant biases, (7) and reconsideration of their policy implications in this light may be warranted. This, however, would remain largely a matter of conjecture, unless the employees' discount rate for pension promises is assessed in a direct manner. The main purpose of this article is to present a method for performing such an assessment. To our knowledge, no such method has yet been developed. In the process, it is shown that even if employees considered theirn pension claims to be entirely free of default risk, (8) their discount rate, properly determined, would incorporate a premium that compensates them for the systematic risk of this claim. The article is organized as follows: In the first section, the relationship between systematic risk and duration for default-free bonds is formulatied, and numerical estimates of this relationship for Government of Canada (GOC) bonds are presented. The same framework is then applied, in the second section, to formulate the systematic risk of dafault- free pension claims (viewed as long-term bonds) (9) as a function of their duration. Application of this function in the framework of the capital asset pricing model (CAPM) shows how the employees' discount rate for pension claims can be assessed. …