Dynamic portfolio decisions with climate risk and model uncertainty

ABSTRACT

We study the effect of investment horizon on the optimal stock–bond–cash portfolio in a dynamic model with uncertainty about climate change. The stock risk premium is assumed to be an affine function of the average global temperature and an unobserved factor which is estimated via Bayesian learning. We assume that the probability distribution of future temperature is uncertain. The optimal investment strategy, robust to the uncertainty about climate change, is derived in closed form and analyzed for returns on the S&P500 index and the S&P500 ESG index. We find that stock market investment is quite sensitive to climate uncertainty with allocation to the S&P500 index being the most sensitive. We also show that, even for relatively short time horizons, welfare losses from climate uncertainty could be large for investments in either the S&P500 index or the S&P500 ESG index.

KEYWORDS:

• Portfolio choice
• climate change
• model uncertainty
• Bayesian learning

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Shell Faces Climate Change Lawsuit in Dutch Court, Insurance Journal, December 1, 2020.

2 Our assumption that the global temperature affects the stock risk premium is in line with a recent empirical study of Bansal and Ochoa (2017).

3 The assumption that the volatility does not depend on the unobserved factor ${\text{β}}_t$ is necessary to apply the filtering techniques of Liptser and Shiryaev (2001) to obtain an estimate ${\widehat{\text{β}}}_t$ of the unobserved predictor.

4 Our approach to uncertainty modeling is also known in the literature as ‘ambiguity aversion modeling’. See, for example, Xinfeng (2021).

5 The S&P500 data are from Robert Shiller's website http://www.econ.yale.edu/shiller/data.html

6 The data for the S&P500 ESG index are from Bloomberg. For the description of the index see https://www.spglobal.com/spdji/en/indices/esg/sp-500-esg-index/#overview

7 See https://fred.stlouisfed.org/

8 http://berkeleyearth.org/data/

9 This pattern does not hold for ${ϵ}_{25}\left(1\right)=0.3597$ and ${ϵ}_{16}\left(1\right)=0.3563$ for S&P500 index. However, this outcome is due to error of numerical integration used to evaluate DEPs.

10 See Table S2 in Supplementary Information for Daniel, Litterman, and Wagner (2019) for a distribution of different temperature change scenarios.