本文關(guān)鍵詞：基于正則化的投資組合分析　出處：《浙江工商大學(xué)》2014年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 范數(shù)正則化 微權(quán)重 大權(quán)重 稀疏性

【摘要】：投資組合優(yōu)化作為現(xiàn)代金融理論的核心問題之一,其主要解決的問題是：投資者如何將有限的資金合理分配以達(dá)到既定收益下風(fēng)險(xiǎn)最小化或者既定風(fēng)險(xiǎn)水平下收益最大化。傳統(tǒng)投資組合優(yōu)化模型得到的最優(yōu)解存在微權(quán)重過多和大權(quán)重過大的問題。微權(quán)重指投資者分配到某一資產(chǎn)的資金占全部資金的比例很小。微權(quán)重將導(dǎo)致投資者不能在證券市場上買入相應(yīng)數(shù)量的股票(證券市場規(guī)定最小交易單位為1手,1手為100股)；同時(shí)微權(quán)重過多將導(dǎo)致投資組合中存在過多的非零權(quán)重；而非零權(quán)重的個(gè)數(shù)越多交易頭寸構(gòu)建時(shí)花費(fèi)的交易成本也就越大。大權(quán)重指投資者分配到某一資產(chǎn)的資金占全部資金的比例很大。個(gè)別股票的大權(quán)重意味著非系統(tǒng)性風(fēng)險(xiǎn)得不到有效的分散化,違背了風(fēng)險(xiǎn)分散化的投資原理。 本文主要通過引入l1+l2范數(shù)正則化解決經(jīng)典Mean-CVaR模型的解中微權(quán)重過多和大權(quán)重過大的問題。l1范數(shù)正則化通過給予微權(quán)重較大的懲罰從而減少投資組合中微權(quán)重的個(gè)數(shù)(投資組合中的微權(quán)重壓縮至零權(quán)重),減少非零權(quán)重的個(gè)數(shù),使解具有稀疏性。l2范數(shù)正則化通過添加權(quán)重二次項(xiàng)和平方根的懲罰項(xiàng)來減小最優(yōu)投資組合中大權(quán)重的數(shù)值。 本文選取上證300只股票分別對l1、l2和l1+l2范數(shù)正則化Mean-CVaR模型進(jìn)行實(shí)證檢驗(yàn)并對其實(shí)證結(jié)果進(jìn)行了對比分析。(1)相對于Mean-CVaR模型,l1范數(shù)正則化能夠有效減少最優(yōu)投資組合中非零權(quán)重的個(gè)數(shù),通過增大可調(diào)系數(shù)加大對微權(quán)重的懲罰力度使其壓縮至零權(quán)重,從而使解具有稀疏性；但兩者均存在個(gè)別絕對值較大的權(quán)重對投資組合整體風(fēng)險(xiǎn)產(chǎn)生不可忽視的影響。(2)l2范數(shù)正則化相對于Mean-CVaR模型能夠減小最優(yōu)投資組合中的大權(quán)重,能有效實(shí)現(xiàn)投資的分散化。但l2范數(shù)正則化不能有效地減少微權(quán)重的個(gè)數(shù)。(3)l1+l2范數(shù)正則化能有效吸收前兩者的優(yōu)點(diǎn),并利用這些優(yōu)點(diǎn)彌補(bǔ)單個(gè)范數(shù)正則化的不足,解決了Mean-CVaR模型所求的解中微權(quán)重過多和大權(quán)重過大的問題,更適合投資者運(yùn)用于現(xiàn)實(shí)投資決策中。
[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.
【學(xué)位授予單位】：浙江工商大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：F830.91;F224

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