The table below shows the possible returns of two assets, x and y together with their probabilities:

Probability $0\mathrm{.}20\mathrm{.}20\mathrm{.}20\mathrm{.}20\mathrm{.}2$

Return of x $(\%)119257-2$

Return of y $(\%)-3152206$

Required:

i$)$ Compute the expected return of each Asset

ii$)$ Compute the variance and standard deviation of each asset iii$)$ Determine the expected return and standard deviation of a portfolio composed of $60\%$ investment in x and $40\%$ investment in y$.$ Compute the coefficient of correlation between the returns of x and y$,$ interpret the results.

iv$)$ a$)$ Compute the expected return and standard deviation of a portfolio formed between x and y if the following investment proportions were used:

Proportion of x $(\%)1007550250$

Proportion of y $(\%)0255075100$

b$)$ Plot a graph of expected portfolio return against portfolio standard deviation.