基于正则化的投资组合分析

发布时间：2018-01-15 16:42

本文关键词：基于正则化的投资组合分析　出处：《浙江工商大学》2014年硕士论文　论文类型：学位论文

更多相关文章： 范数正则化 微权重 大权重 稀疏性

【摘要】：投资组合优化作为现代金融理论的核心问题之一,其主要解决的问题是：投资者如何将有限的资金合理分配以达到既定收益下风险最小化或者既定风险水平下收益最大化。传统投资组合优化模型得到的最优解存在微权重过多和大权重过大的问题。微权重指投资者分配到某一资产的资金占全部资金的比例很小。微权重将导致投资者不能在证券市场上买入相应数量的股票(证券市场规定最小交易单位为1手,1手为100股)；同时微权重过多将导致投资组合中存在过多的非零权重；而非零权重的个数越多交易头寸构建时花费的交易成本也就越大。大权重指投资者分配到某一资产的资金占全部资金的比例很大。个别股票的大权重意味着非系统性风险得不到有效的分散化,违背了风险分散化的投资原理。本文主要通过引入l1+l2范数正则化解决经典Mean-CVaR模型的解中微权重过多和大权重过大的问题。l1范数正则化通过给予微权重较大的惩罚从而减少投资组合中微权重的个数(投资组合中的微权重压缩至零权重),减少非零权重的个数,使解具有稀疏性。l2范数正则化通过添加权重二次项和平方根的惩罚项来减小最优投资组合中大权重的数值。本文选取上证300只股票分别对l1、l2和l1+l2范数正则化Mean-CVaR模型进行实证检验并对其实证结果进行了对比分析。(1)相对于Mean-CVaR模型,l1范数正则化能够有效减少最优投资组合中非零权重的个数,通过增大可调系数加大对微权重的惩罚力度使其压缩至零权重,从而使解具有稀疏性；但两者均存在个别绝对值较大的权重对投资组合整体风险产生不可忽视的影响。(2)l2范数正则化相对于Mean-CVaR模型能够减小最优投资组合中的大权重,能有效实现投资的分散化。但l2范数正则化不能有效地减少微权重的个数。(3)l1+l2范数正则化能有效吸收前两者的优点,并利用这些优点弥补单个范数正则化的不足,解决了Mean-CVaR模型所求的解中微权重过多和大权重过大的问题,更适合投资者运用于现实投资决策中。
[Abstract]:Portfolio optimization is one of the core problems in modern financial theory. The main issues addressed are:. How to allocate the limited funds reasonably to minimize the risk under the fixed return or maximize the return at the fixed risk level. The optimal solution obtained by the traditional portfolio optimization model has too many microweights and a large weight. A small proportion of the funds that an investor allocates to an asset. The microweighting will prevent an investor from buying a corresponding amount of stock in the securities market. The minimum trading unit in the securities market is 1 hand. 1 hand is 100 strands; At the same time, too much micro-weight will lead to too many non-zero weights in the portfolio; The larger the number of non-zero weights, the greater the transaction cost to build a trading position. Large weight means that the investor allocates a large proportion of the total funds to a certain asset. The large weight of an individual stock means that it is non-related. Systemic risk can not be effectively decentralized. It runs counter to the principle of risk diversification. In this paper, the introduction of L1. L _ 2-norm regularization solves the problem of excessive differential weight and excessive large weight in the solution of classical Mean-CVaR model. L1-norm regularization reduces differential weight in portfolio by punishing microweights. The number of heavy (. The microweights in the portfolio are compressed to zero weights. By reducing the number of non-zero weights and making the solution sparse. L2 norm regularization reduces the value of the large weight in the optimal portfolio by adding the quadratic term of the weight and the penalty term of the square root. In this paper, 300 stocks of Shanghai Stock Exchange are selected for L1. L _ 2 and L _ 1L _ 2 norm regularized Mean-CVaR model are tested and compared with Mean-CVaR model. The regularization of L 1 norm can effectively reduce the number of non-zero weights in optimal portfolio, and reduce it to zero weight by increasing the adjustable coefficient and increasing the penalty force to make the solution sparse. However, both of them have a significant influence on the overall risk of the portfolio. L2-norm regularization can reduce the large weight in the optimal portfolio compared with the Mean-CVaR model. However, the regularization of L 2 norm can not effectively reduce the number of microweights. The regularization of L 2 norm can effectively absorb the advantages of the former two methods. These advantages are used to make up for the deficiency of single norm regularization, and the problem of too much micro-weight and too large weight in the solution of Mean-CVaR model is solved. More suitable for investors to use in real investment decisions.
【学位授予单位】：浙江工商大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F830.91;F224

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