How do you calculate the correlation of an asset to a portfolio, when for all assets in the portfolio you know there: correlation to each other, volatility and weight in portfolio.
For example: Assets 1,2,3&4 all have volatility of 15%. Assets 1&2 have a correlation of 1 and all other pairs of assets correlation = 0.
With a portfolio of 16.7% in Assets 1 & 2 and 33.3% in 3 & 4, What I am reading states that all assets (1,2,3,4) have a correlation of 0.577 with the portfolio.
How is this calculated? Is there a formula that can be applied to broader examples with more varied asset volatilities and correlations?