在投资组合构建中拥抱碳不确定性（英）

Embracing carbon uncertainty inportfolio construction by Fan Dora Xia and Omar Zulaica Monetary and Economic Department June 2026 JEL classification: G11, G28, Q54, Q56 Keywords: carbon footprints, sovereign debt, portfoliooptimization, risk parity BISWorking Papers are written by members of the Monetary and EconomicDepartment of the Bank for International Settlements, and from time to time by othereconomists, and are published by the Bank. The papers are on subjects of topicalinterest and are technical in character. The views expressed in this publication arethose of the authors and do not necessarily reflect the views of the BIS or its membercentral banks. This publication is available on the BIS website (www.bis.org). Embracing Carbon Uncertainty in Portfolio Construction Fan Dora Xia*Omar Zulaica*,1 *Bank for International Settlements Abstract We propose a framework for constructing fixed-income portfolios of sovereignbonds that integrates financial and environmental considerations.Central to ourapproach is the introduction ofcarbon returns, a concept analogous to financialreturns, modeled as random variables to capture the inherent uncertainty of futurecarbon emissions. Based on the financial and carbon return profiles of individualcountries’ sovereign bonds, we employ an algorithm inspired by Hierarchical RiskParity (HRP) to construct portfolios that balance each country’s contribution to theportfolio’s tail risk, as measured by expected shortfall, of financial and carbon re-turns. Focusing on developed market sovereign bonds, our results demonstrate thatit is possible to design portfolios that effectively align decarbonization objectiveswith financial performance, both in-sample and out-of-sample, while accommodat-ing diverse investor preferences. JEL Classification: G11, G28, Q54, Q56Keywords: carbon footprints, sovereign debt, portfolio optimization, risk parity 1Introduction Institutional investors, such as reserve managers, are increasingly recognizing the im-portance of integrating climate risk considerations into their portfolios.This reflects abroader move for institutional investors to embed sustainability—spanning environmen-tal, social, and governance (ESG) goals—into portfolio construction.In 2020, (Fenderet al. (2020)) showed that sustainability was a relevant objective for at least one thirdof central banks.2 Fender et al. (2022), in turn, highlight ways in which such consid-erations can be put into practice in public investors’ portfolios.Within this broaderESG agenda, climate-related risks have emerged as both the most measurable and policysalient dimension for fixed income investors, which motivates our focus in what follows. Presumably, the integration of climate considerations into investment decision-makingis driven by two key factors. The first are the risk implications of climate change, whichnecessitate action. These may arise from physical risks, such as the increasing frequencyand severity of extreme weather events, or from transition risks linked to regulatorypolicies, technological advancements, and shifts in consumer preferences towards a low-carbon economy. The second factor is the potential for institutional investors to influenceclimate outcomes through their investment strategies, such as by raising the fundingcosts of environmentally damaging activities (Scatigna et al. (2021); Xia and Zulaica(2022)).3To illustrate this, Swinkels et al. (2025) argue that government bond investorscan help close the financing gap for the sustainable development goals (SDGs) by directingcapital toward governments with strong yet underfunded sustainability policies, and givepractical examples of how investors can integrate SDG scores in portfolios of developedand emerging markets. In practice, for investors with longer horizons, such objectives are often justified purelyfrom a risk management perspective. For others, where mandates allow, actively influ-encing climate outcomes may also align with their broader goals (Carstens (2024)). Re-gardless, given the central role of government bonds in institutional investors’ portfolios,reducing their carbon footprints has become a pressing practical concern. Two key ques-tions arise when building decarbonized portfolios for sovereign securities: the first is howto measure the portfolio’s carbon footprint; the second is how to blend the notion of a carbon footprint with considerations of the portfolio’s financial performance. The existing literature frequently employs constrained optimization frameworks todecarbonize sovereign bond portfolios.These frameworks typically prioritize portfoliofinancial returns—such as minimizing tracking error relative to a benchmark or index-while incorporating carbon footprint considerations via carbon budgets. These budgetsconstrain the portfolio’s carbon footprint, typically measured as the weighted sum ofcountries’ carbon emissions, with the weights corresponding to each country’s allocationwith