Correlation of a Risk Free Asset & Market Portfolio

Im confused on this issue, hopefully someone can help. I know that a risk free asset has a standard deviation, variance and covariance = 0. However I have read two different quotes that appear to contradict each other to me: 1) “A risk-free asset has zero correlation with risky assets” 2) “Given that the assets are perfectly negatively correlated, the return is certain, and it is considered risk free” I just dont know, if it is risk free, is r=0 or r=-1? Also, the S&P (Market Portfolio) has a SD of 1, variance of 1 and has no unsystematic risk. What is R?

They are talking about risk free assets and zero variance portfolio. For individual risk free asset, variance = covariance = correlation with any other risky asset = 0 If you combine 2 risky assets with r = -1, your portfolio will have 0 variance and assured return.

Oh that makes sense Sumit With regards to the S&P 500 or the fully diversified market portfolio. What is r, or would that have to be given. Variance = SD = Covariance 1. Correlation = ?

Different assets will have different covariance and correlation with S&P. For any risky asset: Cov(i,M) = Beta of i * Variance of M. Corr(i,M) = Cov(i,M)/Std dev of i and std dev of M.