## Working paper

# Asset pricing with uncertain betas: A long-term perspective

### Christian Gollier

TSE Working Paper

n. 12-354, November 2012

## Reference

Christian Gollier, “Asset pricing with uncertain betas: A long-term perspective”, TSE Working Paper, n. 12-354, November 2012.

## Abstract

How should one evaluate investment projects whose CCAPM betas are uncertain? This question is particularly crucial for projects yielding long-lasting impacts on the economy, as is the case for example for many green investment projects. We defined the notion of a certainty equivalent beta. We characterize it as a function of the characteristics of the uncertainties affecting the asset’s beta and the economy as a whole. We show that its term structure is not constant and that, for short maturities, it equals the expected beta. If the expected beta is larger than a threshold (which is negative and large in absolute value in all realistic calibrations), the term structure of the certainty equivalent beta is increasing and tends to its largest plausible value. In the benchmark case in which the asset’s beta is normally distributed, the certainty equivalent beta becomes infinite for finite maturities.

## Keywords

asset prices; term structure; risk premium; certainty equivalent beta

## JEL codes

- E43: Interest Rates: Determination, Term Structure, and Effects
- E44: Financial Markets and the Macroeconomy
- G11: Portfolio Choice • Investment Decisions
- G12: Asset Pricing • Trading Volume • Bond Interest Rates