Question to Investment A Screen cast

[arnemartin]

Hi David,

I have two questions to the Investment A Screen cast. There were two things that were not clear to me:


- On slide 83 you calculate the return on surplus to 5%. Then you get the change in surplus to be $50. Are you taking 5% of the Assets? Why would you not take 5% of the Surplus and get $5?

- On slide 89 you define the tracking error as the difference between the active return and the return of the benchmark. Is not active return the difference between the return of the portfolio and the return of the benchmark? Would the Tracking Error not be the active return?


Thanks for clarifying these two points.


Regards,
Arne

 

[David Harper CFA FRM]

Hi Arne,

Great points. Short answer, I agree with you, but I am following Jorion's (assigned) Chapter 17 here. In both instances you cite, I (personally) think Jorion's definitions are confusing.

Slide 83 (if you'd like to review the dynamic XLS it is here. I mirrored Jorion's example), Jorion defines return on surplus as growth in surplus divided by assets; i.e., change in surplus / assets = return on assets - return on liabilities (liabilities/assets).

So okay, the numerator is change in surplus. That makes sense! Then he writes (page 432), the change [in surplus] is delta surplus = change in assets - change in liabilities. Normalizing by the initial value of the assets, we have ROS = change in surplus / assets" Ultimately, i think his definition of ROS is confusing, it looks more like ROA. But it has some logic as it = ROA - leveraged ROL. I'd be interested in your view given this background?...

Slide 89. I think i mentioned in the audio that Jorion is odd here. What you say, being consistent with Grinold is totally correct: "Is not active return the difference between the return of the portfolio and the return of the benchmark? Would the Tracking Error not be the active return?" Yes, correct, agreed! Jorion has employed unusual definitions/terminology here:

* Jorion's tracking error = Grinold's active return
* Jorion's tracking error volatility = Grinold's (and everybody elses!) tracking error.

So, tracking error in Jorion is an "exception." Clearly everywhere else, "tracking error" is volatility of the active return. Thanks for surfacing these points...

David

 

[arnemartin]

Hi David,

Thanks for clarifying the two points. It does make sense now, though it is still a bit confusion.

I had a look at the original texts and can see the differences on the tracking error. I guess I just have to make sure I remember the differences and don't confuse myself with them. Though it should be easier now that I've spent some extra time thinking about this.

Thanks a lot. Your help is much appreciated.


Regards,
Arne

 

[David Harper CFA FRM]

Arne, sure thing.

I prefer to "ignore" Jorion's definition of TE especially because elsewhere we study the information ratio and both Amenc and Grinold for example, have IR = active return/tracking error. David