The following example is taken from [4, Chapter 6]. Consider three assets with expected returns, standard deviations, and correlation matrix given by:

Assume further that the risk-free return is 5\%. Then, we should solve the following system of linear equations.There is an inconsistency, as returns have been multiplied by 100 and covariances by , but this is inconsequential Why?

The system can be simplified to

whose solution is

The sum of the three variables is 18/63. Dividing the pseudoweights by this normalization factor, we get the actual portfolio weights

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0.14 0.06 1.0 0.5 0.2 = 0.08 0.03 R = 0.5 1.0 0.4 0.20 0.15 0.2 0.4 1.0