The Pricing of Premium Bonds: Comment

John Caks

Journal of Financial and Quantitative Analysis, 1981, vol. 16, issue 3, 397-401

Abstract: In “The Pricing of Premium Bonds,” Livingston [4] presents an erroneous analysis of the coupon effect on yield to maturity (YTM). This comment will present a correct analysis and briefly indicate Livingston's error. Following [4], we will assume no transaction costs, etc., and confine our analysis to N-period bonds (N = 2). The prices of premium bonds (P+) and discount bonds (P−) can be represented as:whereTP = tax rate on income of marginal investors,TG = capital gains tax rate of marginal investors,A = market price of an untaxed N-period $1- annuity,D = market price of an untaxed N-period $1 discounted note,C = coupon,F = “face” or principal amount of bond,and PS, PA, PDS, and PD are the prices of the annuities and discounted notes implicitly in taxable bonds. Expressions (1) and (2) show equilibrium prices as functions of A, D, TP, and TG; cf. McCulloch [6], Caks [2], and Livingston [3, 4, 5].

Date: 1981
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