The following are the closing prices for two stocks $($UP and DOWN$)$ over a $6-$day period.For this question use the information about Stock UP and DOWN from question $1),$ particularly

the daily returns you calculated in part b$).$

a$)$ Calculate the covariance and correlation between the returns of Stock UP and DOWN using the

geometric average.

b$)$ Let$$s consider $2$ portfolios. One portfolio invests $50\%$ in stock UP and $50\%$ in stock DOWN. The

second portfolio invests $80\%$ in stock UP and $20\%$ in stock DOWN. Calculate the expected return

and standard deviation of each portfolio $($use the geometric average$).$

c$)$ Suppose you have a client, Ursula. Based on surveys you feel Ursula has a risk aversion of A $=2.$

Based on this information, which of the two portfolios from part b$)$ would you recommend for u