Correlation of a Risk Free Asset & Market Portfolio

[cheros16]

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?

 

[sumit_kansal]

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.

 

[cheros16]

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 = ?

 

[sumit_kansal]

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.