Question

the standard deviation of the portfolio's return is lower than those of the two securities, A and B. What is the intuition behind this? Is it always the case? Examine how the returns on these two securities behave. Do they move together or in opposite directions?

Answer 1

The standard deviation of the portfolio's return made up off by two risky securities will always be lower than individual security's standard deviation. This happens as the risk is getting diversified between two stock and their correlation is not same and hence often they lowers each others effect resulting diminishing volatility of return.

This is true for risky securities but for risk free stock (e.g. T-bill) this is not true as there would always be some positive standard deviation of return for risky stocks but for risk free stock this is zero.

The return of these two stock will be dependent on the correlation between them. If the stock A has positive beta and stock B has negative beta, they will minimize each other's effect and will increase if they have same types of correlation.

Hence, if they have same kind of correlation then they will move together and will go opposite direction if their correlation is negative.