Statistics for Business: Decision Making and Analysis, 3rd Edition

... values of X tend to happen with large values of Y, and small values of X with small values of Y. By increasing the chance that the largest and smallest pair up, positive dependence increases the chance of big deviations from μ_X + μ_Y and inflates the variance.

(p. 242 )

Although it is more variable than we might have guessed, the mixed portfolio has a larger Sharpe ratio than either IBM or Microsoft alone. The Sharpe ratio of the mixed portfolio that combines IBM with Microsoft is

$$S\left(X+Y\right)=\frac{\left({\mu }_X+{\mu }_Y\right)-2r_f}{\sqrt{\text{Var}\left(X+Y\right)}}\approx \frac{0.22-0.03}{\sqrt{14.64}}\approx 0.050$$

Diversifying, spreading the investment over two stocks, improves the Sharpe ratio, but not as much as adding the variances ...