# Proper way to calculate the realized indiviual stock sharpe ratio

From the textbook, sharpe ratio is (return-riskfree rate)/risk

However I wonder if I can use (return-index return)/risk, where the index acts as the benchmark, to calculate the sharpe ratio?

I am quite confused about the difference between these two.. Thanks

Sure you could use this formula so-called Ex-post Sharpe ratio in which you consider in the numeratorof the formula the differential between the realized asset return and its benchmark. Using this approach always disclose for transparency purposes the benchmark under consideration, in particular if you're doing some comparison analyses. You'll consequently avoid some biases than resorting to the problematic selection of an adequate risk-free rate ( flat yields on T-bills or adhoc rates on money market instruments). Hope it helps.