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I need to find the weights of the market portfolio with three risky securities given the following information:

$\mu_1=0.08$
$\sigma_{1}^{2}=0.0255$
$c_{12}=0.00225$
$\mu_2=0.1$
$\sigma_{2}^{2}=0.0025$
$c_{13}=-0.0036$
$\mu_3=0.06$
$\sigma_{3}^{2}=0.0144$
$c_{23}=0 \\$

My textbook tells me to use the following formula to find the weights of market portfolio $$w_m=\frac{(m-Ru)C^{-1}}{(m-Ru)C^{-1}u^T}$$ where $m$ is the expected return matrix, $R$ is the risk-free return rate, $5\%$ in this example, $u$ is just the matrix $[1 \quad 1 \quad 1]$ and $C^{-1}$ is the inverse of the covariance matrix that is created using the variance and covariances of the securities.
I have tried to do this twice, once on excel and I keep getting the weights $w=[-0.04477 \quad 1.02203 \quad 0.02274]$ but the answer key says the weights are $w=[0.438 \quad 0.012 \quad 0.55]$
does anyone know if this is the correct formula or if I am doing something wrong? All those numbers are correct and I know how to multiply matrices.

idknuttin
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    Without doing the computation, something seems off about the "answer key" solution. Asset $2$ has the highest expected return and the lowest volatility...surely one would want their portfolio to emphasize that asset. Yet the answer key advises disregarding it. Are you sure the raw parameters are accurate? – lulu Feb 28 '16 at 23:54
  • are you saying the weights I got are a better representation based on the expected returns of the securities? – idknuttin Feb 28 '16 at 23:58
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    Oh, absolutely. Well, expected returns adjusted for volatility. The volatility of asset $2$ is so very low (a tenth that of asset $1$) that my immediate thought would be that the weights ought to be ${0,1,0}$ . Which, of course, is basically your answer. – lulu Feb 29 '16 at 00:00
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    Is $c_{ij}$ the covariance between assets $i,j$? – Hypergeometricx Mar 01 '16 at 16:56
  • @hypergeometric yes – idknuttin Mar 01 '16 at 16:59
  • I compared my answers with a few of my classmates and we all got the same answers, I am concluding that the answer key is wrong, wouldn't be the first time – idknuttin Mar 01 '16 at 17:00
  • Can you show the intermediate results i.e. $C^{-1}$, and the denominator and numerator of $w_m$? Post an image, if that's faster. – Hypergeometricx Mar 01 '16 at 17:02
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    On Excel, using both the matrix formulas, and also Solver optimization, the optimal weights are [-0.02701, 0.99989, 0.02712]. – Hypergeometricx Mar 02 '16 at 16:45

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