Consider a situation with $4$ assets making up the entire economy and the following ANNUAL expected rates of return and variance$-$covariance matrix:

$0\mathrm{.}120\mathrm{.}250\mathrm{.}0340\mathrm{.}0160\mathrm{.}019$

m$=0\mathrm{.}16$ V$=0\mathrm{.}0340\mathrm{.}880\mathrm{.}0320\mathrm{.}046$

$0\mathrm{.}130\mathrm{.}0160\mathrm{.}0320\mathrm{.}150\mathrm{.}027$

$0\mathrm{.}10\mathrm{.}0190\mathrm{.}0460\mathrm{.}0270\mathrm{.}102$

Find the expected return and standard deviation of the efficient Market portfolio, assuming that CAPM holds and that the riskless rate Rf$=8\%($Annual$).$

Solution: Mean$-$RF Z Weights

$0\mathrm{.}04000\mathrm{.}12670\mathrm{.}23$

$0\mathrm{.}08000\mathrm{.}07210\mathrm{.}13$

$0\mathrm{.}05000\mathrm{.}29320\mathrm{.}53$

$0\mathrm{.}02000\mathrm{.}06240\mathrm{.}11$

$0\mathrm{.}554$

ER $0\mathrm{.}128241816$

Variance $0\mathrm{.}087023979$

Stdev $0\mathrm{.}29499827$