Relative Risk v/s Active Risk (Active management Risk)

[Hardy Noman]

Hi David / Shakti.

Can you please explain the difference between Relative Risk v/s Active Risk.
(Jurion Chapter 7 - AIM 55.5)

Schweser Definitions as under :



-->RELATIVE RISK - is measured by excess return, which is the $ loss relative to the benchmark, the shortfall is measured as the difference between the fund return and that of a benchmark.

-->ACTIVE RISK - risk from the fact that the manager may make decisions which lead to deviation from the designated weights.

From the definition and explanations provided, they seem to be the same thing
are there any differences between the 2 risks
Also, how would VaR help in budgeting these risks?

Thanks a ton!
Hardy.

 

[ShaktiRathore]

Active return of portfolio is the excess portfolio return relative to the benchmark. Active return= portfolio return-Benchmark return,this can be positive or negative. Active Risk is the standard deviation of these active returns. That is how much portfolio returns are deviating from the benchmark that is whats the active risk of the portfolio, greater deviation from the benchmark means greater active risk and lower deviation from the benchmark means lower active risk. Manager takes risk by deviating from the benchmark and when the portfolio returns deviate form benchmark means taking risk relative to the benchmark and in the mean time earns active return while doing these. Active risk is used in information ratio active return/active risk.
While relative Risk i think(not sure on this) relates to relative Var=maximum loss portfolio can suffer =std Deviation of portfolio returns*z*Value, thus the relative risk measures the standard deviation of portfolio returns*value*z i.e. how much loss portfolio can suffer relative to the benchmark. So max loss that can occur relative to the benchmark is the std Deviation of portfolio returns*z*Value less return on benchmark this is how much worse that the portfolio return can get relative to the benchmark this is relative risk. For e.g if expected benchmark return is 1% and portfolio relative Var is -2% than relative risk of portfolio is -2%-1%=-3%. Normally in calculating the relative Var we take the benchmark as 0 so that relative var is the std Deviation of portfolio returns*z*Value-0=the std Deviation of portfolio returns*z*Value which measures the max. loss the portfolio can suffer at a given confidence level and over a period of time, That is how worse the returns of portfolio can get.
thanks

 

[Hardy Noman]

Thank you for your assistance.
the explanation of relative risk seems plausible.

One more thought hitting my head was....
Active risk is a form of Relative Risk....i mean relative risk seems to be a broader (and includes active risk) than Active risk.
Relative risk could be relative to any other portfolio or benchmark or asset (eg. relative to other managers portfolio or bond portfolio etc.)
when the investment portfolio is compared relative to its benchmark it is called active risk (which is a special case of relative risk)

Just a thought...not sure if its correct.
does it look reasonable?

Cheers!
Hardy.

 

[David Harper CFA FRM]

Going back to the original question, I think two things complicate the comparison (I will include this in current feedback to GARP ... I appreciate we have yet another triangulation data point).

1. Jorion's Chapter 17 definitions, as far as I can tell, include the following two sets: Absolute vs. Relative Risk; and Policy-mix versus Active-management Risk; i.e., "Active Risk" is not included here. Active risk is a synonym for tracking error: the standard deviation of R(P) - R(B), or StdDev[Active Return]. When ShaktiRathore writes above "Active Risk is the standard deviation of these active returns," that is correct with FRM precedents. So, in Hardy Noman 's original post, it is important to replace "Active Risk" with "Active-management Risk"
2. Related, the absolute versus relative risk concerns how we measure the overall portfolio return. Absolute/relative can be difference even before we introduce a benchmark; as Shakti may be implying above, we can consider the loss "relative to the expected future value" rather than "absolute to the current position." If we then introduce a benchmark, we are better off to deal in (additionally) the active (i.e., portfolio vs. benchmark) versus residual (i.e., portfolio vs. beta-expected). But these are all still overall portfolio. It is an additional, different step to conduct performance attribution that dis-aggregates the portfolio return into policy-versus-active-management (note Jorion disaggregates an Absolute Risk into Policy and Active-Management; this is analogous to Bodie Kane's attribution into Asset Allocation-versus-Security-Selection, although not exactly as the attribution can operate into at least four levels: strategy/policy, tactical/asset, manager, security).