Robust Risk Parity and Covered Call Optimization

拟议的研究将侧重于开发金融投资设计的数学模型和算法。我们考虑基于风险平价优化、指数跟踪和覆盖看涨期权覆盖的投资(资产配置)框架。风险平价是一种相对较新的方法，它使用数学优化来创建投资决策，其中各个资产的风险贡献相等，这很容易导致多样化的投资组合，这与使用均值-方差优化不同。然而，几乎没有人关注确定风险平价模型的健壮性。我们发现，用于风险平价优化的朴素方法可以表现出对参数估计的相当敏感。开发一种稳健的风险平价优化公式是我们研究的主要目标。我们将把预期收益和卖空结合起来，形成基于风险收益和风险平价的一般模型。这样做的好处是，投资者将有能力在构建投资策略时更好地权衡回报和风险平价程度。 投资组合指数是一种被动投资策略，旨在复制一个广泛的市场指数的风险和回报概况，如随后需要的Sstimations，我们将通过考虑稳健优化来减少估计误差。 期权覆盖，如备兑看涨期权，已成为提高投资组合回报的有效方法。这是投资者出售其投资组合资产的看涨期权的地方。这种策略的一个局限性是，看涨期权是根据资产的整个头寸出售的。此外，备兑看涨期权还假设在出售看涨期权之前已知投资组合。我们试图开发优化模型来捕捉一个普遍的看涨期权问题，在这个问题中，在资产价格不确定的情况下，投资分配决策和备兑看涨期权出售都是同时进行的。作为特例，将开发同时风险平价和覆盖呼叫优化。 本文的研究成果将拓展金融优化的研究领域，对加拿大经济的重要组成部分--金融投资业具有重要的现实意义。HQP在研究计划中的培训将为他们作为量化金融专业人员从事行业做好准备，为加拿大充满活力的金融业增添力量。

The proposed research will focus on the development of mathematical models and algorithms for financial investment design. We consider investment (asset allocation) frameworks based on risk parity optimization, index tracking, and covered call overlays. Risk parity is a relatively new approach that uses mathematical optimization to create investment decisions where risk contributions from individual assets are equal which readily results in diversified portfolios unlike the use of mean-variance optimization. However, little attention has been given to determine how robust risk parity models are. We have found that nave approaches for risk parity optimization can exhibit considerable sensitivity to parameter estimations. The development of a robust formulation of risk parity optimization is a major goal of our research. We will incorporate expected returns and short selling to form general risk-return risk parity-based models. The benefit is that an investor will have the ability to better trade-off return and degree of risk parity in constructing investment strategies. Portfolio indexing is a passive investing strategy that aims to replicate the risk and return profile of a broad market index such as the Sstimations are then required, which we will mitigate estimation error by considering robust optimization. Option overlays such as covered call writing has emerged ras an effective method of enhancing returns of a portfolio. This is where an investor will sell call options on the assets of her portfolio. One limitation of this strategy is that call options are sold in correspondence to the entire position of an asset. Also, covered call overlays also assume that the investment portfolio is known prior to selling the call options. We seek to develop optimization models to capture a generalized cover call problem where both investment allocation decisions and covered call selling are done simultaneously under uncertainty in asset prices. As a special case, simultaneous risk parity and covered call optimization will be developed. The results from the proposed research will extend the field of financial optimization and have significant practical benefits in the financial investment industry which is an important sector of the Canadian economy. The training of HQP in the research program will prepare them to engage in industry as quantitative financial professionals adding strength to Canada's vibrant financial industry.