Robust Risk Parity and Covered Call Optimization

拟议的研究将集中在金融投资设计的数学模型和算法的发展。我们考虑基于风险平价优化、指数跟踪和备兑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，而不是使用均值-方差优化。然而，很少有人注意到确定风险平价模型的稳健性。我们已经发现，朴素的风险平价优化方法可以表现出相当大的敏感性参数估计。发展一个强大的制定风险平价优化是我们的研究的一个主要目标。我们将结合预期收益和卖空，形成一般的风险收益风险平价模型。其好处是，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。 投资组合指数化是一种被动投资策略，旨在复制广泛市场指数的风险和回报状况，例如需要Sstimations，我们将通过考虑稳健优化来减轻估计误差。 期权覆盖，如备兑看涨期权的写作已经成为一种有效的方法，提高投资组合的回报。这是投资者将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，备兑看涨期权覆盖还假设投资组合在出售看涨期权之前是已知的。我们寻求开发优化模型，以捕捉一个广义的覆盖呼叫问题，投资分配决策和覆盖呼叫销售同时在资产价格的不确定性。作为一种特殊情况，将开发同时风险平价和备兑看涨期权优化。 从拟议的研究结果将扩大金融优化领域，并在金融投资行业，这是加拿大经济的一个重要部门有显着的实际效益。HQP在研究计划中的培训将使他们做好准备，作为定量金融专业人士参与行业，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.