Rachel2019-09-01 23:21:31
Rachel老师，请问在多少范围内effective number of stock是属于集中的？
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Chris Lan2019-09-02 10:55:47
Chris Lan同学你好，这块书上也没给出明确的说法说多少是多。
你可以参考一下原版书333页Equation (2) 下面的这一段。
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Malevergne, Santa-Clara, and Sornette (2009) demonstrate that cap-weighted indexes have a surprisingly low effective number of stocks. Consider the NASDAQ 100, a US-based market-cap-weighted index consisting of 100 stocks. If the index were weighted uniformly, each stock’s weight would be 0.01 (1%). In May 2017, the constituent weights ranged from 0.123 for Apple, Inc., to 0.0016 for Liberty Global plc, a ratio of 77:1. Weights for the top five stocks totaled almost 0.38 (38%), a significant allocation to those securities. Across all stocks in the index, the median weight was 0.0039 (that is, 0.39%).
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The effective number of stocks can be estimated by squaring the weights for the stocks, summing the results, and calculating the reciprocal of that figure. The squared weights for the NASDAQ 100 stocks summed to 0.0404, the reciprocal of which is 1/0.0404 = 24.75, the effective number of stocks. Thus, the 100 stocks in the index had a concentration level that can be thought of as being equivalent to approximately 25 stocks held in equal weights.
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