You are presented with the following information relating to the possible returns on the stock of company $J.$

$\backslash$table$[[$Possible return,Kes $100,$Kes $120,$Kes $130,$Kes $150,$Kes $180,$Kes $220],[$Probability$,0\mathrm{.}05,0\mathrm{.}14,0\mathrm{.}2,0\mathrm{.}36,0\mathrm{.}2,0\mathrm{.}05]]$

Required:

i$)$ Determine the expected return, the standard deviation of returns and coefficient of variation for the above stock.

ii$)$ Suppose you have decided to invest in the above stock, based on the values computed in part $($i$).$

However, you have read in the financial press about the risk$-$reduction benefits of diversification and decided to combine stock J with other securities$.$ Your Financial Analyst has provided you with the following information relating to two stocks of companies $K$ and $L,$ and an outstanding bond issued by company M$.$ Further, the correlation coefficients between the returns on pair$-$wise combinations of the four securities are provided:

$\backslash$table$[[$Security$,$Expected Return $($Kes$),$Standard Deviation $($Kes$),$Correlation with$],[,,,$J$,$K$,$L$],[K,250,50,0\mathrm{.}5,,],[$L$.,80,10,0\mathrm{.}1,(0\mathrm{.}2),],[M,100,20,0\mathrm{.}15,0\mathrm{.}1,0\mathrm{.}3]]$

Your maximum acceptable standard deviation on the resulting porttolio is Kshs$.30$ and you have a total of Kshs $1,500,000$ to invest in all of the above securities$.$ Your financial analyst has suggested that $K$ shs$.300,000$ and $K$ shs $500,000$ should be invested in stock I and bond $M,$ respectively. How much money must you invest in each of the remaining securities to attain your desired risk target?

iii$)$ Compute the coefficient of variation of the resulting portfolio.