A portfolio is equally split between $10$ different stocks, each of which has a beta of

$1\mathrm{.}5$ and the same correlation with the market portfolio. The idiosyncratic component

of returns is uncorrelated across stocks. The annualized volatility of the market is

$15\%,$ and of the portfolio$$s volatility is $24\%.$

Required:

i$.$ What is the volatility of each stock?

ii$.$ What is the correlation between each stock and the market?

iii. What is the correlation between one stock and another?