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The Pricing of Premium Bonds: Comment

Published online by Cambridge University Press:  06 April 2009

John Caks
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Extract

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:

where

TP = 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].

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 16 , Issue 3 , September 1981 , pp. 397 - 401
Copyright
Copyright © School of Business Administration, University of Washington 1981

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References

[1]Caks, J. “The Coupon Effect on Yield to Maturity.” Journal of Finance (03 1977), pp. 103–115.CrossRefGoogle Scholar
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[5]Livingston, M. “Bond Taxation and the Shape of the Yield-to-Maturity Curve.” Journal of Finance (03 1979), pp. 189–196.Google Scholar
[6]McCulloch, J. “The Tax-Adjusted Yield Curve.” Journal of Finance (06 1975), pp. 811–830.Google Scholar
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[8]Schaefer, S. “The Problem with Redemption Yields.” Financial Analysts Journal (07–08 1977), pp. 59–67.CrossRefGoogle Scholar