The Omega Ratio is the probability-weighted gains divided by the probability-weighted losses after a threshold. You need to calculate the first-order lower partial moments of the returns data. This sounds difficult but it's very easy.
A spreadsheet to implement this formula can be found at the related link below
If the cell range "returns" contain the investment returns, and the cell "threshold" contains the threshold return, then the Omega Ratio is
={sum(if(returns > threshold, returns - threshold,"")) / -sum(if(returns < threshold, returns - threshold, ""))}
where the {} represent a matrix formula
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The related link provides an excel template and some notes on how to calculate the sharpe ratio..pretty simple and effective.
The Sortino Ratio is the actual return minus the target return, all divided by the downside risk. The downside risk is either calculated by the semi standard deviation, or the 2nd order lower partial moment. The related link "Calculate the Sortino Ratio with Excel" provideds an Excel spreadsheet to calculate the Sortino Ratio
calculate the effective return (mean return minus the risk free rate) divided by the beta. the excel spreadsheet in the related link has an example.
No. It can be but need not be. For example, you might calculate the ratio of today's temperature in Celsius and in Fahrenheit and calculate the ratio. That is not a rate.
calculate the ratio between proton&electron