solution

you know that as the number of stocks in an equally weighted portfolio is increased with each additional stock chosen at random the uniqueness of the portfolio decreases you also know that a typical stock has a beta of 1 assume that the markets return have a standard deviation of 20% and that a typical stock returns have a standard deviation of 40% and a correlation coefficient with market returns of +0.5 .all else being the same what must be the true for the returns for such a portfolio as the number of stocks in it increase.
a. its standard deviation decreasing and its correlation with the market decreases
b.its standard deviation increases and its correlation with the market decreases
c.its standard deviation stays is the same as its correlation with the market increases
d.its standard deviation decreases and its correlation with the market increases