Question

Under what circumstances is it possible to remove risk altogether from a portfolio of two risky assets? Fully explain your answer.

Answer 1

The portfolio standard deviation for a 2-asset portfolio is given by

Here, is the weights of asset 1 and asset 2 respectively

is the standard deviation of asset 1 and asset 2 respectively

is the correlation between the two stocks

Let's consider a portfolio consisting of 2 assets such that = -1 ie. the stocks are perfectly negatively correlated

ie both the stocks have equal weight of 0.5 in the portfolio

, ie the standard deviation or the riskiness of the stocks are equal and both the stocks are risky as standard deviation is greater than zero

Under these circumstances, the standard deviation of the portfolio becomes 0.

The standard deviation is also called as the riskiness of the portfolio and a standard deviation of 0 implies that the risk from the portfolio is removed altogether. The critical point here is that if the stocks are perfectly negatively co-related and have the same standard deviation, a risk-free portfolio can construct by equally weighing both the stocks in the portfolio.