Question

If two investments have a correlation of (-1) you can reach a portfolio with a zero risk as measured by standard deviation. Is this true or false? Explain

Answer 1

Answer: The given statement is true.

Explanation:
Portfolio risk of a two asset (investments) portfolio is calculated as:
[(Wa*sa)^2+(Wb*sb)^2 + 2*Wa*Wb*(-1)*sa*sb]^(1/2)

Here, -1 refers to the correlation between the asset returns
Wa,Wb refers to the weight of the assets in the portfolio, and sa and sb refers to the standard deviation of the assets

Simplifying the equation, we get;
=[(Wa*sa-Wb*sb)^2]^(1/2)
=(Wa*sa-Wb*sb)
=0

So, if the above condition is met, we can get a zero risk portfolio.