March 2025
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19 Reads
We build a state-of-the-art dynamic model of private asset allocation that considers five key features of private asset markets: (1) the illiquid nature of private assets, (2) timing lags between capital commitments, capital calls, and eventual distributions, (3) time-varying business cycle conditions, (4) serial correlation in observed private asset returns, and (5) regulatory constraints on certain institutional investors' portfolio choices. We use cutting-edge machine learning methods to quantify the optimal investment policies over the life cycle of a fund. Moreover, our model offers regulators a tool for precisely quantifying the trade-offs when setting risk-based capital charges.
![Confidence regions of (p,ξ)$(p, \xi)$ for the baseline model and equity premium isoquants. This figure shows the 95% and 99% confidence regions of (p,ξ)$(p, \xi)$ for the baseline model and the equity premium isoquants implied by the asset pricing moment restriction (41) for γ=3,10,24$\gamma = 3, 10, 24$. The parameter p$p$ represents the disaster probability, and ξ$\xi$ characterizes the inverse of the average disaster size. The efficient GMM estimates are (p̂,ξ̂)=(0.012,78.79)$(\widehat{p}, \widehat{\xi }) = (0.012, 78.79)$, indicated by the red dot inside the confidence region. Four additional points mark the intersections of the equity premium isoquants for γ=3$\gamma = 3$ and γ=24$\gamma = 24$ and the boundary of the 95% confidence region. Only p$p$ and ξ$\xi$ are treated as unknown to the econometrician; all other parameters are treated as auxiliary parameters with fixed known values, as a part of the functional‐form specification. [Color figure can be viewed at wileyonlinelibrary.com]](https://www.researchgate.net/profile/Winston-Dou-2/publication/379033076/figure/fig1/AS:11431281452950174@1747925367118/Confidence-regions-of-p-xp-xi-for-the-baseline-model-and-equity-premium_Q320.jpg)
![Asymptotic confidence regions for parameters (p,ξ)$(p, \xi)$ and the identified worst‐case direction. This figure depicts the dark‐matter measure through the 95% confidence regions for the asymptotic distribution of the efficient GMM estimators for four “acceptable” calibrations. In Panels A through D, the dark‐matter measure is equal to ϱ(θ)=1.78×104$\varrho (\theta) = 1.78\times 10^4$, 5.60×102$5.60\times 10^2$, 74.03, and 1.49, respectively, which are obtained in the direction marked by the vector vmax$v_{\max }$. Parameter p$p$ is the disaster probability, and ξ$\xi$ characterizes the inverse of average disaster size. Only p$p$ and ξ$\xi$ are treated as unknown to the econometrician; all other parameters are auxiliary parameters with fixed known values as a part of the functional‐form specification. Therefore, the dark‐matter measure is defined based only on θ=(p,ξ)T$\theta = (p, \xi)^T$. [Color figure can be viewed at wileyonlinelibrary.com]](https://www.researchgate.net/profile/Winston-Dou-2/publication/379033076/figure/fig2/AS:11431281452869975@1747925367430/Asymptotic-confidence-regions-for-parameters-p-xp-xi-and-the-identified_Q320.jpg)
![Monte Carlo experiments for disaster risk models. In Panel A, we simulate 1,000 independent yearly time series with length n=2,200$n = 2,200$ to capture a pooled sample of 100 years for 22 countries, similar to Wachter (2013). In Panels B and C, we set δr=0.4$\delta _r = 0.4$ and simulate 400 independent yearly time series with length n=100$n = 100$ (i.e., 100 years) and break point π=1/2$\pi = 1/2$. Only the uncertainties about p$p$ and ξ$\xi$ are accounted for; all other parameters are auxiliary parameters as a part of the functional‐form specification. [Color figure can be viewed at wileyonlinelibrary.com]](https://www.researchgate.net/profile/Winston-Dou-2/publication/379033076/figure/fig3/AS:11431281452989346@1747925367729/Monte-Carlo-experiments-for-disaster-risk-models-In-Panel-A-we-simulate-1-000_Q320.jpg)
![Monte Carlo experiments for time‐varying disaster risk models. In this simulation experiment where all of the parameters except ρ$\rho$ are treated as auxiliary parameters, the dark‐matter measure is equal to ϱ(θ)=1.5×105$\varrho (\theta) = 1.5 \times 10^5$ and ϱ(θ)=4.3×102$\varrho (\theta) = 4.3 \times 10^2$ for model M1 and M2, respectively. In Panel A, we simulate 1,000 independent yearly time series with length n=2,200$n = 2,200$ to capture a pooled sample of 100 years for 22 countries similar to Wachter (2013). In Panels B and C, we set δr=0.05$\delta _r = 0.05$ and simulate 400 independent yearly time series with length n=100$n = 100$ (i.e., 100 years) and break point π=1/2$\pi = 1/2$. Only the uncertainty about ρ$\rho$ is accounted for; all other parameters are treated as auxiliary parameters as part of the functional‐form specification. [Color figure can be viewed at wileyonlinelibrary.com]](https://www.researchgate.net/profile/Winston-Dou-2/publication/379033076/figure/fig4/AS:11431281452950177@1747925367898/Monte-Carlo-experiments-for-time-varying-disaster-risk-models-In-this-simulation_Q320.jpg)
![Monte Carlo experiments for long‐run risk models. In this simulation experiment where all the parameters except ν$\nu$ are treated as auxiliary parameters, the dark‐matter measure is equal to ϱ(θ)=1.03×105$\varrho (\theta) = 1.03 \times 10^5$ and ϱ(θ)=22.34$\varrho (\theta) = 22.34$ for model M1 and M2, respectively. In Panel A, we simulate 1,000 independent monthly time series with length n=1200$n = 1200$ (i.e., 100 years). In Panels B and C, we simulate 400 independent monthly time series with length n=1,200$n = 1,200$ (i.e., 100 years) and break point π=1/2$\pi = 1/2$. We set δr=0.02$\delta _r = 0.02$ for Panels B and C. In the simulation experiment, we assume that all of the parameters except ν$\nu$ are treated as auxiliary parameters, fixed at known constant values and subsumed into the functional form of the moment function (i.e., model specifications). [Color figure can be viewed at wileyonlinelibrary.com]](https://www.researchgate.net/profile/Winston-Dou-2/publication/379033076/figure/fig5/AS:11431281453225554@1747925368065/Monte-Carlo-experiments-for-long-run-risk-models-In-this-simulation-experiment-where-all_Q320.jpg)
