Remember, the expected returns and standard deviation of X are 10% and

7% respectively, and those of Y are 20% and 10% respectively.

Now asset Z has expected returns of 15% and standard deviation of 12%.

The correlation between X and Y is 0.10, that between Y and

Z is 0.90, and that between X and Z is 0.

You can set up the Excel spreadsheet as you can see.

Cell B5 contains the sum of the weight of the three risky assets

in the MVE portfolio.

The formula for the MVE portfolio's expected return is in cell C7 and

its standard deviation is in cell D7.

The Sharpe ratio for the MVE portfolio is in cell C8.

You want to maximize the Sharpe ratio using

solver subject to the cell B5 being equal to 1.

That is, the weights must add to 1.

Once you run Solver, you will see that the weights of X,

Y, and Z in the MVE portfolio are 0.2274,

1.7793 and negative 1.0067, respectively.

The Sharpe ratio of the MVE portfolio is 1.94.

What does the Sharpe ratio of 1.94 mean?.

For every 1% of risk, the MVE portfolio gives an excess return of 1.94%.

Given X, Y and Z and risk-free rate of return of 5%,

the maximum Sharpe ratio you can achieve is 1.94.

The MVE portfolio is represented by the red dot in the figure that you see.

Its expected return is 22.76%, and

its standard deviation of returns is 9.16%.

If you look at the weights,

you can see that the weight of Z in the MVE portfolio is negative.