The covariance means that investors have the opportunity to seek out different investments based upon their respective risk adversity. If the covariance is negative then this means that the two instruments move opposite one another depending on the economy. This then becomes a way for investors to diversify some of their risks away.
If an investor were to buy two stocks with a negative covariance then in a boom period one would earn more than the other and vice versa for a recession.
If an investor were to care solely about the return and no risk then an investor might choose two stocks that have a positive covariance based solely on their expected returns. This means that this particular investor has the chance to make a big gain, but also a bad loss. This is because the two instruments will move with each other and there is no diversification in the portfolio of two stocks.
Depending on Tim’s risk adversity he will make different decisions. If he is simply looking solely at the returns he will choose stocks A and C because they have the highest potential returns but also the highest potential loss. If he were very risk averse he would choose stocks A and B because the amount of risk has been diversified away. The final option would not be chosen because stocks B and C have no covariance or correlation between each other. The two stocks simply move independently and there is not as much potential to diversify or maximize the risk and return.
Note: The result assumes weights of 50% will be put into each stock for each investment opportunity.