We test a regime-conditional functional-form restriction on aggregate risk-exposure dynamics implied by VaR-constrained intermediary models: exposures contract multiplicatively when capital constraints bind and grow additively (level-independent) when slack. The contraction half follows from binding VaR constraints (Brunnermeier and Pedersen 2009; Adrian and Shin 2010; He and Krishnamurthy 2013). The additive-rebuild prediction is derived under constant-rate capital replenishment; we test the joint restriction on FINRA monthly margin debt (1997-2026). Two findings. First, regime-interacted regression of detrended margin growth on lagged level (T=350 months) yields calm slope -0.040 (p=0.082, additive) and stress slope -0.205 (p<0.001, multiplicative); Wald test on regime x level interaction rejects equal dependence (p=0.0016). Second, the restriction implies drawdown-recovery duration ratio increases with crash depth. On 73 S&P 500 episodes (1950-2026), Cox model gives depth coefficient -13.75 (p<10^{-7}): 75% lower recovery hazard per 10pp deeper drawdown. Continuous-depth regression yields beta=1.22 (p=0.047); beta=1.59 (p<0.001) excluding 1980-82 Volcker. Median duration ratio for crashes >30% is 3.1x; replicates across eight other equity indices. Calibrated Heston, Markov-switching, and block bootstrap nulls match price-level duration asymmetry but lack an exposure state variable, so cannot speak to the regime-conditional flip on direct exposures. We do not claim the exposure test identifies the intermediary mechanism: FINRA margin debt is a noisy proxy. We claim only that the regime-conditional functional form is a sharper target than return-level moments alone, and confirming it on margin debt is consistent with -- not proof of -- the constrained-intermediary mechanism. A companion test on CFTC weekly speculative positioning is left for future work (Sections 5.2 and F).

翻译：我们检验了受VaR约束的中介模型所隐含的、依赖于市场状态的风险暴露函数形式约束：当资本约束收紧时，风险暴露呈乘法收缩；当资本约束宽松时，则呈加法增长（与水平无关）。收缩部分源于VaR约束的绑定（Brunnermeier and Pedersen 2009; Adrian and Shin 2010; He and Krishnamurthy 2013）。加法恢复预测是在恒定资本补充率下推导得出的；我们使用FINRA月度保证金债务数据（1997-2026年）检验了这一联合约束。两项发现如下。首先，将去趋势的保证金增长率对滞后水平进行状态交互回归（T=350个月），得到平稳期斜率-0.040（p=0.082，加法模式）和压力期斜率-0.205（p<0.001，乘法模式）；对状态×水平交互项的Wald检验拒绝了相同的依赖关系（p=0.0016）。其次，该约束意味着回撤-恢复的持续时间比随崩盘深度增加而增大。基于1950-2026年73次标普500事件，Cox模型给出的深度系数为-13.75（p<10^{-7}）：每加深10个百分点的回撤，恢复风险降低75%。连续深度回归的beta=1.22（p=0.047）；剔除1980-82年沃尔克时期后beta=1.59（p<0.001）。对于跌幅超过30%的崩盘，中位持续时间比为3.1倍；这一结果在另外八个股票指数中得以复制。校准的Heston模型、马尔可夫切换模型和块自助法零模型能够匹配价格水平的持续期非对称性，但缺乏风险暴露状态变量，因此无法解释直接风险暴露上的状态条件性翻转。我们并不声称风险暴露检验识别出了中介机制：FINRA保证金债务是一个有噪声的代理变量。我们仅声称，状态条件性函数形式是比仅关注收益率矩更精确的检验目标，并且在保证金债务上确认这一形式与受约束中介机制一致——但并非其证明。基于CFTC周度投机性持仓的配套检验留待未来工作完成（第5.2节和附录F）。