Question

All things equal, diversification of total risk is most effective when the ROPC associated with each security in the portfolio are __________ correlated with ________.

A: Negatively correlated with the market.

B: positively correlated with the market.

C: Uncorrelated with the market.

D: negatively correlated with each other securities included in the portfolio.

E: positively correlated with each other securities included in the portfolio.

F: Uncorrelated with each other securities included in the portfolio.

Answer 1

All things equal, diversification of total risk is most effective when the ROPC associated with each security in the portfolio are negatively correlated with each other securities included in the portfolio because when there is a negative correlation between the returns of securities there is a maximum reduction in the risk of the portfolio. There is also a mathematical proof for that.

Risk of a portfolio is measured by it standard deviation which the square root of the variance and we know that variance of a portfolio consisting of three securities is calculated using the below formula:

σ_p² = w₁²*σ₁² +w₂²*σ₂² + w₃²*σ₃² + 2w₁*w₂*ρ_1,2*σ₁* σ₂ + 2w₂*w₃*ρ_2,3*σ₂* σ₃ + 2w₁*w₃*ρ_1,3*σ₁* σ₃

here w_i'sare the weights and σ_i's are the standard deviations of security i whereas ρ_i,j is the correlation between security i and security j

We can hence say that when the securities are negatively correlated with each other i.e. when the correlation between them is negative the variance of the portfolio is reduced and hence its standard deviation ( which is the square root of variance). Therefore, when there exists a negative correlation between pairs of securities in a portfolio, the risk (measured by the standard deviation of the portfolio) is reduced.

So, Option D is correct