# Sortino Ratio, Semideviation vs. Standard Deviation

two questions for you. Thank you for helping.

1. Sortino Ratio: The CFA curriculum calculates it in Reading 31, page 88 as follows: (Annualized rate of return - Annualized risk free rate) / Downside deviation. In Reading 34 on page 268 it uses MAR instead of Annualized risk free rate. On thoughts?

2. Semdeviation vs. Standard Deviation: They both appear to use average return as the threshold. What is the difference?

Thank you very much for your help.

1. was the MAR equivalent to the risk free rate in reading 31? Imagine a manager with an absolute return mandate (i.e. beating cash), in this case the MAR can be the risk free rate. in fact MAR can be anything…

Semideviation=downside deviation?

The equation requires a target return which will be used in both the numerator and denominator. The target itself can be anything (risk free rate, absolute return, rate of inflation).

Only semi-deviation uses a threshold in the denominator to exclude any return above the average. Standard deviation does not do this. The semi-deviation has the advantage of not penalizing a manager whose returns are on average above the mean return. For instance, a manager who is consistently 1 std above the mean return looks statistically no different than one who is consistenly 1 std below when we use standard deviation. Semi-deviation will not penalize such a manager.

No. Semi-deviation uses average return as the threshold. Downside deviation uses a target return (e.g. risk free rate, absolute return) as its threshold.

“Semi-deviation uses average return as the threshold.”

Sounds lik Standard Deviation?

For semi-deviation the average return threshold means that only returns that fall below the average are included in the standard deviation calculation. This keeps above average managers from being penalized. Regular standard deviation uses all returns when measuring volatility.

http://www.investopedia.com/terms/s/semideviation.asp#axzz1w50670im

Thanks for the clarification. Got it.

One difference

Sortino ration - denominator is total no of observations similar to Std dev

Semi - deviation - total no of observation below the mean, rt?

1, Denominatr of Sortino Ratio is the downside deviation. 2, Semivariance: A measure of downside risk. The average of squared deviations that fall below the mean." 3, “Target semivariance: The average squared deviation below a target value.” One quick question: Semideviation is NOT used in any ratio in L3. Right?

Yes I have not seen semi deviation being used anywhere

when i said denominator i was trying to point towards the calculation of the denominator (semi variane , downside dev )

Suppose we have 10 observations where 5 are below target return/avg return

Downside dev - Numerator - sum of Sq dev that fall below mean or target whatever is the case but denominator would still have N-1 i.e 10-1 = 9

whereas in semi deviation —same numerator but Denominator will be 5…?

no , semi-variance is mentioned very briefly . 1 problem in EOC only .

1.semi-variance does not show / reveal any skew in the distribution

1. If semi-variance is applied on a returns distribution that is symmetrical about the mean , you do not learn anything more than you would if you used std deviation.

2. People less familiar with using semi-variance than std dev( less well understood as a risk measure)