Which one is the formula for Information/Sortino Ratio?

[Steve Jobs]

The formula used for calculating the information/sortino ratio in several practice questions is not consistent. Here are the formula used:

Information Ratio:
Formula 1 =Alpha / Tracking Error
Formula 2 =[Return(portfolio) - Return(Benchmark)] / Tracking Error
Formula 3 =Mean Returns / Tracking Error

Sortino Ratio:
Formula 1=[Return(portfolio) - Return(risk-free)] / [Mean Standard Deviation(min)]^0.5
Formula 2 =[Return(portfolio) - Return(min. acceptable)] / Semi-Standard Deviation
Formula 3 =[Return(portfolio) - Return(risk-free)] / Semi-Standard Deviation
Formula 4 =[Return(portfolio) - Return(min. acceptable)] / [Mean Standard Deviation(min)]^0.5

Which one to use/memorize for the exam?

 

[ShaktiRathore]

hi
as per my understanding formulas are:
Sortino Ratio:[Return(portfolio) - Return(min. acceptable)] / Semi-Standard Deviation
Information Ratio:[Return(portfolio) - Return(Benchmark)] / Tracking Error
visit links:http://forum.bionicturtle.com/threads/information-ratio-definition.5554/
http://forum.bionicturtle.com/threa...iance-mean-squared-deviation.6418/#post-20459
thanks

 

[Steve Jobs]

I read those previous posts regarding the same issue, any way what I'll do is to use whatever data provided in the question.

However, it's an example of inconsistency and discrepancy from what should be defined as standards/principles(if there is/should be). How in practice the risk manager will defend his position if such ratios are not defined clearly?

 

[David Harper CFA FRM]

Thanks Shakti, as usual, for the helpful links.

• With respect to the information ratio (IR), GARP actually (responding to feedback) has clarified it, per the errata link (above) to the the 2012 practice question, where they do at least meet key criteria of ratio consistency. GARP wrote: "The information ratio may be calculated by either a comparison of the residual return to residual risk, or the excess return to tracking error." Note: TE = active return
  
  So, I think GARP has realistically decided that IR = residual return [aka, alpha] / residual risk; or active risk/active return. In fact, both are employed, so arguably it is realistic to depend on the user to specify. In this way, they correctly exclude Steve's #1 above, which is alpha/TE = residual return/active risk, which is not as ratio consistent as the other two (residual/residual or active/active)
  
• With respect to Sortino, our XLS reflects our longtime approach, which i believe is consistent with the longstanding Amenc assignment:
  Numerator = R(P) - MAR, not R(P) - Rf unless explicitly a special case of MAR = RF; Denominator is ratio consistent with downside deviation; i.e., retrieving R(P) where R(P) < MAR ... not a semideviation where R(P) < mean or R(P) unless special case where MAR = RF.
  Although there is a valid technical debate within this definition of Sortino (is the sum of squared downside deviations divided by the exceptions or the entire set of N; we use N following CIPM actually, but some disagree), the use of downside deviation seems to be okay at least.

 

[Steve Jobs]

Thanks, I should review more recent practice questions to get used to the formula.

 

[bball8530]

Hi David,
I'm confused on what is considered residual risk because in the Foundations PDF on Page 43 you refer to the Tracking Error as the Residual Risk but up above you refer to Tracking Error as Active Risk.
So basically I'm wondering how do you calculate residual risk and how do you calculate active risk when dealing with the Tracking Error?
Thank You.

 

[David Harper CFA FRM]

Hi bball,

Right, well, it's actually not me but that I've been asking GARP for 3+ years to let us settle on fixed definitions, given we've had five authors defining IR and TE; e.g., my latest summary request http://forum.bionicturtle.com/threads/information-ratio-definition.5554/

• Re: tracking error (aka, jorion's tracking error volatility): I am ready to declare TE is active risk (not residual risk; I do see what you mean about p 43, I am going to edit the box to eliminate the suggestion that TE = residual risk. Sorry, I agree that is confusing, I don't want to be suggesting TE is residual risk). I think it is fine to let TE = active risk
• With respect to information ratio, see the link above. Despite the fact I would prefer a standard FRM definition, you can see that GARP is at least has acknowledge the variation by writing a recent question with: "The information ratio may be calculated by either a comparison of the residual return to residual risk, or the excess return [dh note: i.e., active return] to tracking error [dh note: assume active risk].
• I think their IR solution is good: IR is either active/active or residual/residual but not (inconsistently) residual/active.

In summary:

• TE = active risk.
• IR = residual return/residual risk or active return/active risk (I don't think this should be troubling, we have ratio variety throughout finance! What is EPS or PE or ROC? each has several flavors)

 

[bball8530]

Ok thanks, so according to GARP Amenc's answer is incorrect on Page 43 of the PDF as IR = Alpha / Tracking Error which is equivalent to IR = Residual Return / Active Risk which I think we can all agree on is a formula that is being thrown out. So if we get a question on the exam that's asking us for Tracking Error and we know what they're asking for is Residual Return (alpha) / Residual Risk, then how do we calculate the denominator Residual Risk?

 

[David Harper CFA FRM]

GARP is well aware of the definitional variations w.r.t. IR, you won't need to arbitrate between them. In the case of either active risk or active return, either way, it's the standard deviation of a series of excess returns of some sort (active risk = std deviation of series of [portfolio, P- benchmark, B]; residual risk = std deviation of series of alphas). They won't make you struggle with this, they'll give you the TE outright or worse case, as in IR, you are looking for the standard deviation of the thing that's in the numerator;
ie..,

IR = alpha/StdDev(series of alphas); but you won't have time to calculate the denominator, so it's going to be given somewhere
IR = (Return - portfolio)/ StdDev([R-P]); same thing re: denominator, no time to calculate, only calc possible is Expected TE given two assets and correlation

as a purely practical matter, i think the important things are:

• what is alpha? how is that different than return above benchmark, P - B?
• TE = active risk = StdDev(active returns) = StdDev([P-B])
• IR uses a denominator which is a standard deviation of the same thing in the numerator. Anything else here, that i can think of, i am 99% confident GARP will spell out, thanks,

 

[bball8530]

Thank you David, definitely have a better understanding. I just know want to make sure I don't get tripped up on a question as simple as calculating an Information Ratio.

 

[dmitrijskass]

Dear David,

Talking about the denominator of the Sortino ratio - do I understand correctly, that the lower partial moment (LPM) with 2 degrees of freedom used in Sortino ratio is exactly the same as the general semi-deviation, just MAR is used in LPM instead of the sample average return?