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Difference between active and residual return/risk

Thread starter #1
W.r.t information ratio, what would be the difference between the active return & residual return and active risk & residual risk? How are these measured?

David Harper CFA FRM

David Harper CFA FRM
Staff member
Hi akgvarun: active return = portfolio return (P) - benchmark (B). Residual return is alpha. For example, if riskfree = 2% and market return = 6%, then excess market return = 4%. Say portfolio is benchmarket against S&P 1500 which is perfectly correlated to market. If a portfolio's beta is 1.5 and the portfolio's return = 9% for , then
  • active return = 9% portfolio - 6% benchmark = 3%; but this active return is a blend of alpha (i.e., luck and/or skill) & beta (common factor exposure)
  • residual return = 9% - [2% + (6% - 2%)*1.5] = 1.0%; i.e., alpha
In the modern FRM, IR can be either active return/active risk or residual return/residual risk as illustrated by GARP's 2012 Practice E1.Q3: "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, but clarification not needed in this case]."
see (paid members only) http://www.bionicturtle.com/forum/threads/information-ratio-definition.5554/#post-15678

note: by convention, "excess return" = active return and "tracking error" generally refers to active risk; i.e., std deviation (active return). I hope that helps,


Well-Known Member
hi there,
first form of information ratio is given by Rp-Rb/vol(Rp-Rb) where Rp-Rb is the active return over a period for the portfolio and vol(Rp-Rb) is the volatility of these active returns over the same period as which is the active risk/tracking error as mentioned by David can be written as active/active.
second form of the Information ration is given by residual return/residual risk that is how much residual return which is based on managers skills in identifying idiosyncratic risk and thus generates alpha and the volatility of the alphas generated by the manager over a period is the residual risk.

Thread starter #4
So, in case of active return/active risk we are comparing manager's portfolio return/risk vis-a-vis the benchmark return/risk. And in case of residual return, we are comparing manager's portfolio return with the return as per CAPM. However, what will be the residual risk?

David Harper CFA FRM

David Harper CFA FRM
Staff member
Hi akgvarun, Just as Shakti said, residual risk is the standard deviation of the series of residual returns; in both cases, the denominator of IR is the standard deviation of the numerator, as in IR = (return metric)/(standard deviation of the same return metric).

Re "And in case of residual return, we are comparing manager's portfolio return with the return as per CAPM"
Yes, correct for Jensen's alpha, which is a special case. The general idea is: residual return is the manager's portfolio return compared with a paper portfolio exposed to the same betas (in this way, the residual return is only the component remaining which has not been attributed to beta exposure, which is called alpha, and can be luck or skill). Thanks ,


Well-Known Member
Yeah, Qualitatively
As the definition of information ratio suggests that how much information manager know besides the benchmark that he could use to generate those extra returns relative to the benchmark and with what risk he can generate those extra returns that is the volatility of those extra returns. So the information ratio measures this efficiency of manager w.r.t the index as active/active. Manager forecasts of macro and company specific measure comes to test here if they are better better the information ratio.
Similarly how much manager knows about company specific details which is the idiosyncratic risk and thus what is the volatility with which he can generate these idiosyncratic risk related returns assuming that the manager matches the index via macroeconomic factors which is reflected in the beta(Capm rewards these macro risk) and whatever extra information has about company gets reflected in the alpha generated, hence better the manager forecasting ability of company future better the forecast of company to come true and hence better the information ratio. The residual return is the extra return manager earns for bearing this company specific idiosyncratic risk and residual risk is the volatility or risk in generating these returns.
Ultimately it boils down to how good the manager is in forecasting the future of macro-economy and the company.

Hi David and Shakti,

I am a CFA level 2 candidate and I came through this page while searching for clarity on above topic through Google and I had to tell you'll that the above questions and explanation provide a greater understanding about IR, active return/risk and residual return/risk. However, I would also like to understand following questions in continuation to above topic:

1. Active risk is bifurcated in to active factor risk (deviations of portfolio sensitivities against benchmark sensitivities to same set of factors) and active specific risk (deviation of portfolio individual asset weightings against benchmark individual asset weightings), IR based on active/active - wouldn't that explain the skills of manager? as the deviations in style of managing portfolio against its benchmark would be nothing but the function of his skills of forecasting macro-economy and the company.

I did not clearly understand the difference between the purpose of IRs calculated using Active return/risk and the one using residual return/risk. What does each method signify or highlight?

I mean, based on above, it is understood that IR calculated using residuals not only reflects the excess return between portfolio and its benchmark, but also clarifies if it is a function of the beta (common factor) or the skills/luck, then why the need to consider IR based on active return/risk, when residual one provides a better clarity and insight on manager's performance?

2. Similar to active risk bifurcated in to active factor risk and active specific risk, is there a theory or way to bifurcate residual risk in to factor and specific?

3. Simultaneously, while I do acknowledge that CAPM is a special case of Arbitrage Pricing Theory (APT), however, APT gives the opportunity to consider more than 1 factors affecting the return (in this case, more than 1 common factor affecting portfolio and benchmark return). Accordingly, for the purpose of calculating Alpha, can we use APT model for calculating alpha against the CAPM one?
It is understood that APT assumes the unsystematic risk can and is diversified away and hence not priced. Therefore, alpha calculated using APT parameters, would still reflect the skills of the manager in forecasting the future of the macro-economy and the company.

Thank you in anticipation


Well-Known Member
Active/active compares managers e.g we need to compare value managers we should do so by comparing their performance relative to the value index i.e how much they deviate by weights or composition based on information they have on economy thus metric active/active comes handy here to compare value mgrs and appraise them.
Residual/residual compares managers on systematic risk as benchmark that is how much extra mgr is earning relative to systematic risk taken. Here the benchmark becomes systematic risk or CAPM,we compare mgrs after adjusting their performance to benchmark.
Yes you can bifurcate the residual risk into factor and specific risk,there is no sound theory incorporating this i think but yes you can do same.
Yes you can use APT to measure alpha or skill.