Effect of cash on IR?

I don’t understand why adding cash would cause a shrink in the information ratio of a portfolio of risky assests?

IR = active return / active risk The way I remember it, adding cash reduces active return (uninvested cash has no return). Another way to look at it is: IR = TC X IC X BR0.5 If you hold cash, you reduce the number of uncorrelated bets (breadth). IC and TC are constant. So IR declines.

This helps a lot, thank you!