$($iii$)$ Consider the following applications of the CAPM.

$[10]$

i$.$ Suppose that the stock of the new perfume manufacturer, Eau de Bourse Inc., has been forecast to have a return with standard deviation of $30\%$ and a correlation with the market portfolio of $90\%.$ If the standard deviation of the yield on the market portfolio is $20\%,$ determine the relative holdings of the market portfolio and Eau de Bourse Inc. stock to form a portfolio with a beta of $1\mathrm{.}8.$