Shanshan2023-05-05 11:03:11
ShanshanWhich of the following three statements does NOT justify your belief that the portfolio is a closet index?1. The Sharpe ratio of the portfolio is close to the Sharpe ratio of the benchmark.2. The information ratio of the portfolio is relatively small.3. The active risk of the portfolio is very low. 原版书课后题为什么要选第二个statement？原版书上说While there may be little active risk, the information ratio of a closet index fund will likely be close to zero or slightly negative if value added cannot overcome the management fees. 那说明IR确实是relatively small呀？那就可以justify呀？
回答（1）
Simon2023-05-05 17:53:09
Simon同学，下午好。
1. 原版书中确实有这句话 While there may be little active risk, the information ratio of a closet index fund will likely be close to zero or slightly negative if value added cannot overcome the management fees. 这句话的逻辑是，主动风险小，同时增值无法抵消管理费，那么IR会接近0或者略微为负。从逻辑推理来看，‘主动风险小’+‘增值无法抵消管理费’，这两个条件，可以推断出‘IR会接近0或者略微为负’。但是从结论出发‘IR会接近0或者略微为负’是无法推测出条件‘主动风险小’的。
2. 回到Statement 2，IR很小无法推出closet index。举个例子，比如index是沪深300指数，收益率是10%，然后portfolio里就买了一只股票，收益率也是10%，此时IR=0，但确是主动投资。
努力的你请加油哟~。祝同学顺利通过考试~。
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