We can use the Sharpe Ratio to determine if adding an asset creates a better (higher) minimum variance frontier.

The Sharpe ratio is calculated using the following formula:

Sharpe Ratio = (E(Rasset) – RF)/σasset

Calculate the Sharpe ratio for the current portfolio and then calculate the Sharpe ratio after adding the new asset.

If the Sharpe Rationew port > (Sharpe Ratiocurrent port * ρ(new asset, current port)), then the new asset should be added.

ρ(new asset, current port) = correlation coefficient between the current portfolio’s returns and the new asset’s returns