Buy-and-hold mean-variance portfolios with a random exit strategy
研究了在风险厌恶框架下，买入持有投资者如何利用阈值停止规则作为随机退出策略，将投资期限不确定性转化为盈利机会，并提供了最优权重的解析近似和夏普比率的推广。
We show how buy-and-hold investors can move from horizon uncertainty to profit opportunity. The analysis is conducted under a risk-averse framework rather than the standard Markowitz formulation in the case of i.i.d. asset processes. We make this practical achievement by considering a threshold stopping rule as the strategy to determine when to exit the market. The resulting investment horizon is random and can be correlated with the market. Under this setting, we first provide an analytical approximation to optimal weights, and then identify a class of reference variables associated with the stopping rule that leads to ex-ante improvements in portfolio allocation, vis-a-vis the fixed exit time alternative. The latter conclusion is based on a generalization of the Sharpe ratio, adjusted for horizon uncertainty. The obtained investment suggestion is simple and can be implemented empirically.