 # sortino ratio

Seems that there are two ratios in cfai notes. One that uses risk free rate and another that uses minimum acceptable rate. Which is it? Or is it a case of just using the information you’re given?

it is mar but if no mar given you can assume it to equal risk free rate.

Pg 91 of the cfai book gives a detailed template of all of these calcs.

Good to know the difference between Sortino ratio and Roy’s safety first ratio.

[Wrong]

Both have (Rp-MAR) as numerator. But denominator is different. In Sortino it’s maximum drawdown while it is portfolio std in Roy’s safety first ratio.

[Corrected]

Both have (Rp-MAR) as numerator. But denominator is different. In Sortino it’s downside deviation while it is portfolio std in Roy’s safety first ratio.

^

sortino ratio denominator is not max drawdown. it is downside deviation

page 88 of bk 5 says sortino uses risk free rate by downside dev

page 268 of same book says Sortino is return less MAR by downside dev

I don’t know which one to use if both are given

I suppose you can check if it is a hedge fund / alt investment q or a risk management q

lol

In the book it states that the sortino ratio is similar to Sharpe if you use the Rfr as the MAR, the only difference is the use of downside deviation.

This is true, and the answers would be exactly the same if the return distribution is normal. However, for hedge funds this is hardly ever the case since they usually produce meaningful skewness and kurtosis.

Roy’s is actually a closer relation to Sharpe since it actually uses the entire return distribution in its denominator - the same as Sharpe, and the only difference is the use of the MAR. If MAR = Rfr then these two equations will always be equivalent.

good point

does everyone agree with the following:

standard deviation (variance) = standard deviation (variance) above and below mean

semi deivation (semivariance) = standard deviation (variance) below mean

downside deviation (target semivariance) = standard deviation (variance) below a MAR (i.e. rfr or 0%)

for semi-variance (and semi-deviation) which mean is used ? population mean or mean of semi-deviations?

population mean right? then you take the mean of those below the mean of the population and calculate your st dev of the new set of data points (below the population mean only)

population mean. the whole point is not to punish the manager for volatility about the population mean

yes, yes, yes

Thanks all for pointing out it. I edited the post, just not to mislead others who refer this forum future. Thanks again.