The Value of a Cure: An Asset Pricing Perspective [report]

Viral Acharya, Timothy Johnson, Suresh Sundaresan, Steven Zheng
2020 unpublished
We provide an estimate of the value of a cure using the joint behavior of stock prices and a vaccine progress indicator during the ongoing COVID-19 pandemic. Our indicator is based on the chronology of stage-by-stage progress of individual vaccines and related news. We construct a general equilibrium regime-switching model of repeated pandemics and stages of vaccine progress wherein the representative agent withdraws labor and alters consumption endogenously to mitigate health risk. The value
more » ... h risk. The value of a cure in the resulting asset-pricing framework is intimately linked to the relative labor supply across states. The observed stock market response to vaccine progress serves to identify this quantity, allowing us to use the model to estimate the economywide welfare gain that would be attributable to a cure. In our estimation, and with standard preference parameters, the value of the ability to end the pandemic is worth 5-15% of total wealth. This value rises substantially when there is uncertainty about the frequency and duration of pandemics. Agents place almost as much value on the ability to resolve the uncertainty as they do on the value of the cure itself. This effect is stronger -not weaker -when agents have a preference for later resolution of uncertainty. The policy implication is that understanding the fundamental biological and social determinants of future pandemics may be as important as resolving the immediate crisis. Proof. From the evolution of capital stock for the representative agent (16), we obtain the Hamilton-Jacobi-Bellman (HJB) equation as follows for each state s ∈ {1, . . . , S − 1} 0 = max Using the conjecture for the objective function (17) for J J J(s), calculating the derivatives with respect to q, J J J q (s) = H(s)q −γ and J J J qq (s) = −γH(s)q −γ−1 , and differentiating with respect to labor l, we A.6 obtain the first-order condition as J J J q (q)αl α−1 µq + 1 2 J J J qq (q)αl α−1 σ 2 q 2 − J J J q (q(1 − χ∆)) ξε∆q = 0 (A.9) the pandemic state 1 as "On" state. C.3 Proof of Proposition 4 Proof. The value of a cure (vaccine) V(s) satisfies: J J J(0)(q) = J J J(0) [(1 − V(s)) q] (A.17) where J J J(0) is evaluated at (1 − V(s)) q. Substituting for J J J(s) from (17) , we obtain
doi:10.3386/w28127 fatcat:e4ihkc6aobh2nehbngcqdkc7xa