Simultaneous pursuit of out-of-sample performance and sparsity in index tracking portfolios
Simultaneous pursuit of out-of-sample performance and sparsity in index tracking portfolios
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DOI：
10.1007/s10287-012-0158-y
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发表时间：
2012-11
影响因子：
0.9
通讯作者：
A. Takeda;M. Niranjan;Jun-ya Gotoh;Y. Kawahara
中科院分区：
文献类型：
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作者：
A. Takeda;M. Niranjan;Jun-ya Gotoh;Y. Kawahara
指数跟踪是一种被动投资策略，其中基金（例如，ETF（交易所交易基金）经理购买一组资产以模仿市场指数。跟踪误差，即，指数和投资组合的表现之间的差异可以通过购买指数中包含的所有资产来最小化。然而，这种策略导致了相当大的交易成本，从而降低了所构建的投资组合的收益。另一方面，具有小基数的投资组合可能导致差的样本外性能。因此，有趣的是，构建一个具有良好样本外表现的投资组合，同时保持投资的资产数量较小（即，稀疏）。在本文中，我们开发了一个跟踪投资组合模型，通过使用L0和L2范数的组合来解决上述相互冲突的要求。L2-范数正则化超定系统以施加平滑性（因此具有更好的样本外性能），并且它将解缩小到相等权重的稠密投资组合。另一方面，L0范数施加了一个基数约束，以实现稀疏性（从而降低交易成本）。本文提出了一种组合权重估计的启发式方法，该方法将贪婪搜索与分析公式相结合，通过对日经225指数及其成分股公司的周收益率和月收益率的历史数据的跟踪和泛化，证明了稀疏组合具有良好的跟踪和泛化性能。
Index tracking is a passive investment strategy in which a fund (e.g., an ETF: exchange traded fund) manager purchases a set of assets to mimic a market index. The tracking error, i.e., the difference between the performances of the index and the portfolio, may be minimized by buying all the assets contained in the index. However, this strategy results in a considerable transaction cost and, accordingly, decreases the return of the constructed portfolio. On the other hand, a portfolio with a small cardinality may result in poor out-of-sample performance. Of interest is, thus, constructing a portfolio with good out-of-sample performance, while keeping the number of assets invested in small (i.e., sparse). In this paper, we develop a tracking portfolio model that addresses the above conflicting requirements by using a combination of L0- and L2-norms. The L2-norm regularizes the overdetermined system to impose smoothness (and hence has better out-of-sample performance), and it shrinks the solution to an equally-weighted dense portfolio. On the other hand, the L0-norm imposes a cardinality constraint that achieves sparsity (and hence a lower transaction cost). We propose a heuristic method for estimating portfolio weights, which combines a greedy search with an analytical formula embedded in it. We demonstrate that the resulting sparse portfolio has good tracking and generalization performance on historic data of weekly and monthly returns on the Nikkei 225 index and its constituent companies.