A second problem is that even with lots of historical data, it is hard to estimate the likelihood of rare events. (By definition, there will be few or no historical examples.)
还有一个问题是,即使我们掌握了大量历史数据,也依然难以预估小概率事件发生的可能性(根据定义,小概率事件的历史案例数量极少甚至从未发生过)。
Portfolio theorists have produced a variety of sophisticated methods to try to update Markowitz's ideas for an uncertain world. But in research published in 2009 in the Journal of Financial Studies, Victor DeMiguel, Lorenzo Garlappi and Raman Uppal showed that the naive 1/N approach outperforms far more complex calculations until a vast amount of historical data are available with which to calibrate them. How much data? For a 50-asset portfolio, about 500 years. Perhaps "don't put all your eggs in one basket" is financial wisdom enough.
研究投资组合理论的专家们发明了多种复杂方法,试图改良马科维茨的理论,使之适应充满不确定性的真实世界。但维克多•迪米基尔(Victor DeMiguel)、洛伦佐•盖勒普(Lorenzo Garlappi)和拉曼•尤博尔(Raman Uppal)2009发表于《财务金融学刊》(Journal of Financial Studies)的一篇论文指出,简单的"1/N"投资策略收益率高于更为复杂的投资策略,除非能有海量历史数据为复杂策略校准。那么需要多少历史数据呢?对于有50种资产的投资组合来说,大约需要500年的历史数据。从这个角度来看,也许"不要将所有的鸡蛋放在一个篮子里"已经足以成为金融领域的至理名言了。
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