Q$2$

The risk free rate is $4\%$ and the following data is given about assets $x$ and $Z$ :

$($a$)$ What are the Sharpe ratios of the two risky assets?

$($b$)$ Show how you can dominate asset $x$ using a portfolio that combines asset $Z$ and the risk free

asset.

$($c$)$ Show how you can dominate a portfolio with equal weights in asset $x$ and the risk$-$free asset

using a portfolio that combines asset $Z$ and the risk$-$free asset.

$($d$)$ Show $($in general$)$ how you can dominate any portfolio combining asset $x$ and the risk$-$free

asset using a portfolio that combines asset $Z$ and the risk$-$free asset.

Hint: by "general", I mean you assume any general fraction $($like $y_x)$ of wealth in asset X$.$ And

then show how to design a portfolio combining asset $Z($with the fraction $y_z$ of wealth in asset Z$)$

and the risk$-$free asset which will dominate the portfolio of asset $x$ and the risk$-$free rate. So

essentially you will need to show the relationship between $y_z$ of the DOMINATING portfolio and

$y_x$ of the DOMINATED portfolio.