# z-score of an active return with a no-volatility benchmark

I don't know how to approach the problem I am having. Basically, the statement I am trying to make is: the fund's return is X standard distribution away from the mean.

Normally, for a single fund, you should just take its

(return - 0)/volatility*sqrt(t)


if the return was 37% and the volatility was 40%, it would be (0.37 - 0)/.40 = 0.925 standard deviations away from the mean. The probability of this or lower happening is ~17.88%.

For an active return, you would do the same thing, but do active return/tracking error

(return_fund - return_bench)/tracking_error*sqrt(t)


Now here is where I am stuck. What if the benchmark is cash. This has a return, but no risk, so would we still approach this the same way? Meaning the tracking_error used is just the fund's volatility?