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KAKEN_24730193seika.pdf
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高次元データに関するポートフォリオ最適化問題
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コウジゲン データ ニ カンスル ポートフォリオ サイテキカ モンダイ
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Kojigen deta ni kansuru potoforio saitekika mondai
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Portfolio optimization problem for high dimensional data
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白石, 博
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シライシ, ヒロシ
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Shiraishi, Hiroshi
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慶應義塾大学・理工学部・准教授
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Research team head
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科研費研究者番号 : 90454024
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2017
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科学研究費補助金研究成果報告書
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2016
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本研究では, 投資資産が膨大となるような高次元設定の下で (1) 『分散共分散行列の逆行列に対する漸近不偏な推定量を用いた最適ポートフォリオ推定量』および (2) 『ポートフォリオ比率に対する縮小推定量を用いた最適ポートフォリオ推定量』の2つの推定量を提案した。まず, これらの推定量の理論的, 数値的正当性を確認すると同時に, 日本の株価データ(200銘柄)を用いて既存のポートフォリオとのパフォーマンスを(シャープ比や効用関数を用いた指標により)比較し, 提案手法の優位性があることを確認した。
In this research, we propose two types of optimal portfolio estimators when an investor aims to invest a huge number of assets. Suppose that high dimensional data with respect to the past asset return is available. Then we propose (1) Optimal portfolio estimator by using an unbiased estimator for the inverse of the covariance matrix, (2) Shrinkage type estimator for the plug-in portfolio weights estimator. First, we derive the theoretical properties and confirm numerical validity of these estimators. Then, we compare the performance (in terms of the sharp ration and the utility function) with existing portfolios based on the Japanese stock price data (200 issues) and realized the superiority of the proposed method.
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研究種目 : 若手研究(B)
研究期間 : 2012～2016
課題番号 : 24730193
研究分野 : 統計科学
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