There are N stocks in the market, each of which has a standard deviation of returns of 10%. Besides, each pair of stocks has a correlation coefficient () of returns of 0.10. Suppose a stock portfolio (P) consists of 10 stocks is created so that the weight of each stock is equal in the portfolio.

a) What is the standard deviation of the P?

b) If the number of stock increases to 30 and the weight of each stock in the portfolio P is equal. What is the standard deviation of P?

c) If the number of stock increases to 50 and the weight of each stock in the portfolio P is equal. What is the standard deviation of P?

d) What can you conclude from (a) to (c)? How can you relate your conclusion with the principle of diversification?