# Sortino vs. Roy's safety first

Are these the formulas? Sortino: [Rp -MAR)]/(std dev of MAR or downside deviation) Roy’s Safety first ratio: [Rp - MAR)]/(std dev of port) And if these are the correct formulas I’m guessing that the only difference is the denominator? Sortino uses downside deviation (risk of only achieving minimal acceptable return) while Roy’s safety first ratio uses the standard deviation of portfolio return like in the sharpe ratio. Thanks in advance for any clarification.

I would say that those MAR are different. Sortino’s MAR would be closer to RFR (positive number). MAR in Roy’s safety first is typically a loss that should be avoided.

That’s the way I understand it. RSF is basically the Sharpe ratio adjusted with the minimum return instead of the Risk Free Rate. Sortino is the Sharpe ratio but with downside deviation in the denominator instead of standard deviation. The downside deviation is the standard deviation of returns below the MAR. Schweser says we just need to know what it is and won’t need to know how to calculate it.

Perfect. So Normally in Roy’s safety first you would be adding two numbers in the numerator? Is the rest of my analysis correct?

maratikus Wrote: ------------------------------------------------------- > I would say that those MAR are different. > Sortino’s MAR would be closer to RFR (positive > number). MAR in Roy’s safety first is typically a > loss that should be avoided. I disagree. I think in both cases we are talking about the Minimum Acceptable Return. The difference is the calculation of standard deviation in the denominator.

Dwight Wrote: ------------------------------------------------------- > > I disagree. I think in both cases we are talking > about the Minimum Acceptable Return. The > difference is the calculation of standard > deviation in the denominator. I think what he means Dwight is that Roy’s safety first is usually used with long only portfolios (individuals) who don’t want to lose more than X. While Sortino may be used with Hedge funds and the MAR may be a positive number near Rf due to the Long/Short nature.

With respect to what Maratikus said, I do vaguely remember in one of the exams that the solution had rp - (-rf) and therefore you were adding two numbers together. I was very confused at that point. I think that was the reason for my original quesiton.

mwvt9, so if the question says a hedge fund pm does not want to lose more than the rf rate we would use the roy’s safety first ratio and plug in a negative number?

russianbull Wrote: ------------------------------------------------------- > mwvt9, so if the question says a hedge fund pm > does not want to lose more than the rf rate we > would use the roy’s safety first ratio and plug in > a negative number? I think so. The result of the equation will tell you how many standard deviations the MAR is from the expected return. The numerator is the difference between expected return and MAR and the denominator is total risk (as measured by SD).

Thank you.

I believe what I said above is correct, but that measure wouldn’t be really good for a hedge fund because it assumes normality in returns (usually a bad assumption with HF or anything for that matter).

mwvt9 Wrote: ------------------------------------------------------- > Dwight Wrote: > -------------------------------------------------- > ----- > > > > I disagree. I think in both cases we are > talking > > about the Minimum Acceptable Return. The > > difference is the calculation of standard > > deviation in the denominator. > > I think what he means Dwight is that Roy’s safety > first is usually used with long only portfolios > (individuals) who don’t want to lose more than X. > > While Sortino may be used with Hedge funds and the > MAR may be a positive number near Rf due to the > Long/Short nature. True, different applications, but I still think of the MAR as the same thing in both cases, even after reading your two explanations above. Good points.