Uncertainty of capital productivity and declining discount rates

ABSTRACT

This paper considers the problem of instantaneous certainty-equivalent (ICE) discountrate when future return on capital is uncertain. We show that the ICE discount rate equals the expected return under atransformed risk-adjusted probability measure. Our approach allows us to analyze theICE discount rate regardless of the distribution of future return on capital. We provethat the ICE discount rate decreases as the delay time or the coefficient of relative riskaversion increases in a general setting. Our results lend further supports to adopting thedeclining discount rate (DDR) schedule for long-range projects with uncertain futurereturns on capital.

KEYWORDS:

• Instantaneous certainty-equivalent discount rate
• risk-adjusted PDF
• DDR schedule

JEL CLASSIFICATION:

• D61
• E43
• G12

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ The Gamma distribution of future interest rates is surveyed in Weitzman (2001). It can be interpreted as the actual distribution in this sense.

² On the topic of risk-neutral measures and its various applications in asset pricing, readers are referred to, for example, Harrison and Kreps (1979) and Shreve (2004).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [71501065, 71221001, 71790593, 71572055, 71573077, 71850012]