Motivation
Two goals, one economy — do diversification and climate action align?
A global economy initially dominated by carbon-intensive capital faces a dual imperative: mitigate climate damages by phasing out brown capital, and hold a well-diversified portfolio. These two goals are initially complementary — both require cutting the brown capital share. Over time, however, they conflict: full decarbonisation leaves the economy poorly diversified. This paper quantifies the tension, derives the optimal carbon price, and characterises equilibrium asset prices along the transition path.
1
Diversification motive
Since the economy starts heavily brown-dominated, risk-averse planners want to rebalance — initially reinforcing climate action at no extra political cost.
2
Abatement motive
Climate damages and disaster risk create a negative externality from brown capital. The optimal carbon price (SCC) internalises this and drives the transition further than diversification alone.
3
Interaction & conflict
Around the fully diversified level, the two motives start conflicting. Diversification considerations may keep some brown capital alive even when environmental logic says otherwise.
Model framework
A stochastic two-sector AK economy with recursive utility and climate
A representative agent with Epstein–Zin preferences optimises over two capital stocks \(K_1\) (green) and \(K_2\) (brown). Temperature \(T\) rises linearly in cumulative emissions \(E_t\). Climate damages enter via a DICE-style damage function and via a temperature-dependent disaster intensity \(\lambda_c(T)\). The value function reduces to two state variables \((S,T)\), where \(S=K_2/(K_1+K_2)\) is the brown capital share.
Optimal diversification threshold
\[S^* = \frac{\sigma_1^2 - \sigma_1\sigma_2\rho_{12}}{\sigma_1^2 + \sigma_2^2 - 2\sigma_1\sigma_2\rho_{12}}\]
Total capital volatility is minimised at \(S^*\). With symmetric volatilities \(\sigma_1=\sigma_2\), this gives \(S^*=1/2\), independent of the instantaneous correlation \(\rho_{12}\). The optimal brown share under climate policy lies below \(S^*\) — abatement pushes further than diversification alone would.
Key result — decomposition of climate action
Three forces drive the optimal green transition
By comparing four model variants — varying whether damages and cross-sectoral correlation are present — climate action along the optimal path can be cleanly decomposed into three additive components. The figure below reproduces Figure 3 of the paper for the Nordhaus level-damage specification.
Component I
Diversification
Reduction in \(S\) driven purely by the desire to reduce total capital volatility. Active even with no climate damages; vanishes if \(\rho_{12}=1\).
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Component II
Abatement
Reduction in \(S\) driven by climate damages and the SCC alone. Active even with perfectly correlated capital stocks; dominates at high damage levels.
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Component III
Interaction
Initially amplifies the transition as both motives pull in the same direction; turns negative around 2100 once full diversification is reached, slowing subsequent abatement.
Figure 3 (from the paper). Panel (a): median optimal share of brown capital \(S\) under four calibrations. Panels (b)–(d): the diversification motive (light grey area), abatement motive (dark grey area), and their interaction (black area). With Nordhaus level damages, the economy stabilises near \(S\approx0.20\) in the long run — above zero because diversification benefits prevent full decarbonisation under moderate damage assumptions.
Key result — carbon pricing
How diversification modifies the optimal carbon price
The SCC is primarily determined by the abatement motive and grows in line with GDP. Diversification plays a secondary but non-negligible role, particularly for low-damage calibrations where the carbon tax is heavily state-dependent in \(S\).
SCC proportional to GDP
The optimal carbon tax starts at $26/tCO₂ (level damages) or $138/tCO₂ (disaster damages) in 2020 and grows in line with GDP — consistent with efficient carbon pricing along a balanced growth path.
Diversification raises the SCC for low \(S\)
When the economy approaches the fully diversified share \(S^*\), the carbon tax must be higher to keep abatement going against the diversification brake. For level damages, this effect can swing the SCC by up to 30% depending on \(S\).
Disasters roughly double the SCC
Climate disasters (temperature-dependent Poisson shocks) roughly double the optimal carbon tax at 2020 temperatures. The diversification effect is dominated in this scenario — abatement considerations take over entirely.
Learning-by-doing accelerates transition
Falling green energy costs (LBD/Wright's law) add a third incentive to decarbonise. The optimal carbon tax is slightly lower because the LBD externality is partly internalised via a renewable subsidy, yet the qualitative decomposition remains intact.
Key result — asset pricing
Carbon premium, risk-free rate, and risk premia along the transition
Equilibrium risk-free rate — decomposition
\[r^f_t = \underbrace{\delta + \tfrac{1}{\psi}\mu_C}_{\text{impatience + growth}} \;-\; \underbrace{\tfrac{1}{2}\gamma\!\left(1+\tfrac{1}{\psi}\right)\|\sigma_C\|^2}_{\text{diffusion precaution}} \;-\; \underbrace{\sum_{i\in\{e,c\}}\lambda_i(T)\,\mathbb{E}\!\left[1-(1-\ell_i)^{-\gamma}+\tfrac{\psi^{-1}-\gamma}{1-\gamma}(1-(1-\ell_i)^{1-\gamma})\right]}_{\text{disaster precaution}} \;+\; \underbrace{(\cdots)}_{\text{temperature interaction}}\]
The disaster precaution term dominates quantitatively. Because \(\lambda_c(T)\) rises with temperature, delayed climate action permanently lowers the risk-free rate through heightened precautionary savings — a channel absent in one-sector IAMs.
Risk-free rate falls with temperature
Higher temperatures raise climate disaster intensity \(\lambda_c(T)\), amplifying precautionary savings and pushing \(r^f\) down. A less ambitious climate policy thus permanently lowers equilibrium interest rates — a macrofinancially significant side-effect of inaction.
Carbon premium is positive under BAU, can turn negative under optimal policy
Under BAU with a high brown capital share, brown assets earn roughly 0.4% extra per year. As the SCC is internalised and the brown share falls, the premium declines and can become negative — green firms outperform, consistent with Pastor, Stambaugh & Taylor (2021, 2022).
Why it matters
Implications for investors, policymakers, and central banks
Central banks & financial stability
Delayed climate action lowers the risk-free rate through rising precautionary savings — not just through physical damages. Climate stress tests should model the feedback between carbon pricing credibility and equilibrium interest rates, rather than treating the rate path as exogenous.
Institutional investors & ESG
Early in the transition, brown assets provide genuine portfolio diversification benefits worth up to 1.5% of capital. Divestment mandates should account for this hedge value. As the brown share falls below the diversification optimum, the calculus reverses and green overweighting is rationally justified even without ESG preferences.
Carbon pricing strategy
The diversification motive gives policymakers a free early push: reducing the brown capital share initially costs nothing in terms of financial welfare. Only once the economy approaches the diversification optimum must policy actively counter the diversification drag — making front-loading of carbon pricing both efficient and politically easier.
BAU distorts financial markets
Being stuck in business-as-usual does not only hurt the real economy. Compared to the social optimum, equilibrium interest rates fall substantially and risk premia on brown assets are higher and positive — capital is misallocated as long as the carbon externality remains unpriced.