Quantitatives 问题

Zray,

Thank you for your answer. I believe your understanding of corelation is correct. And there must be something wrong with my understanding. But I can not figure it out. Can you help?

I'd describe my understanding starting from your conclusion as the following:

(1). according to your conclusion, if there are two stocks, whose Corr is less then 1, then portfoilio consisting of the two stocks should have a risk (standard deviation) less the both of the risk of the two single stock. (because each stock will diversify away some of the other's unsystematic risk) 

is my opinion correct?

(2). if (1) is correct, it may lead to a contradiction.  

let's just use the given data in the question as an example, and ignore the additional third stock. The first two stocks have a standard deviations of 8.5% and 25% respectively, and their correlation coeffienct is 0.001/(0.085*0.25) = 0.047, which is less than 1. So from (1), we will have that a portfolio of the two stocks should have a standard deviation less than min(8.5%, 25%), that is < 8.5%. However, from the given data, we know that the portfolio's standard deviation is 15.5%, which is between the standard deviations of the  two single stock.

Intuitively, it means first we have a portfolio consisting of only one 8.5% standard deviation stock. then we add another stock into the portfolio whose Corr with the former stock is 0.047 and whose standard deviation is 25%. But the newly added stock does not diversify away the unsystematic risk from the original single-stock portfpolio, instead, it raises the risk from 8.5% to 15.5%. This situation is contradictory to the conslusion offered by you as well as how the answer goes.

Could you kindly help looking for the incorrect places in the statement above. Thanks a lot.