STATIC FUND SEPARATION OF LONG‐TERM INVESTMENTS
STATIC FUND SEPARATION OF LONG‐TERM INVESTMENTS
复制标题
长期投资的静态资金分离
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Scott Robertson
中科院分区：
文献类型：
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作者：
P. Guasoni;Scott Robertson
本文证明了一类静态资金分离定理，该定理适用于具有长期投资期限和固定相对风险厌恶度的投资者，以及具有随机投资机会的投资者。最优投资组合分解为几个无偏好基金的恒定组合，这些基金对所有投资者都是共同的。每个基金的权重是一个常数，可能取决于投资者的风险厌恶程度，但不取决于状态变量，状态变量会随着时间的推移而变化。反之亦然，每个基金的组成可能取决于国家，但不取决于风险厌恶，因为一个基金出现在不同投资者的投资组合中。我们证明了这些结果的两类模型与一个单一的状态变量，和几个资产的状态与常数相关性。在线性类中，状态是一个Ornstein-Uhlenbeck过程，风险溢价是仿射的，而波动率和利率是常数。在平方根类中，状态服从平方根扩散，期望收益率和利率在状态下是仿射的，而波动率在状态的平方根上是线性的。
This paper proves a class of static fund separation theorems, valid for investors with a long horizon and constant relative risk aversion, and with stochastic investment opportunities. An optimal portfolio decomposes as a constant mix of a few preference‐free funds, which are common to all investors. The weight in each fund is a constant that may depend on an investor's risk aversion, but not on the state variable, which changes over time. Vice versa, the composition of each fund may depend on the state, but not on the risk aversion, since a fund appears in the portfolios of different investors. We prove these results for two classes of models with a single state variable, and several assets with constant correlations with the state. In the linear class, the state is an Ornstein–Uhlenbeck process, risk premia are affine in the state, while volatilities and the interest rate are constant. In the square root class, the state follows a square root diffusion, expected returns and the interest rate are affine in the state, while volatilities are linear in the square root of the state.