Assume that there are only three investors in the economy $1,2$ and $3,$ with total wealth of $500,$

$1000,1500$ billion pounds, respectively. There are only four assets in this economy, the risk$-$free

security, and risky stocks A$,$ B and C$.$ The holdings of each investor in each asset $($in billion

pounds$)$ are shown below:

Investor Risk$-$free Asset A Asset B Asset C

$1100100200100$

$2200200400200$

$3-300450900450$

$[$Note that a negative amount invested in the risk$-$free asset means borrowing at the risk$-$free rate$]$

Answer the following questions, showing all relevant calculations.

i$.$ Calculate the weights on each asset that constitute the market portfolio in this economy, and

show that investors $1,2$ and $3$ are in fact holding this portfolio.

$[15\%]$

ii$.$ Suppose that the expected return of the market portfolio is $11\%$ with a standard deviation of

$23\%.$ The risk$-$free rate is $1\%.$ Assuming that investors $1,2$ and $3$ have mean$-$variance

preferences, and given their investment profile in the table above, calculate their coefficient

of risk aversion.