Equation with too many variables

[shanlane]

Hello,

I was looking at one of the equations in Jorion and it looks there is some circular referencing and I was hoping you could clear it up for me.

Equation 17.7 seems is supposed to help determin how much capital to give to different managers. However, at least one of the variables is a function of the allocations. We can set a limit for Tracking error for the port, but then we still need the information ratio for the portfolio. We can only get this if we have the total excess return for the portfolio which would depend on the allocations to each manager.

In the example problem (Table 17.4) he seems to just pull some number out of thin air but I am not sure which he starts with.

Am I missing something?

Thanks!

Shannon

 

[David Harper CFA FRM]

Hi Shannon, Briefly, I think you are basically correct. Here is a spreadsheet (that i used to include in the course, but I've lately excluded as it just seems to get no love from the exam) of my mimic of Table 17-4: https://www.dropbox.com/s/d7ouoqk21uhyq5s/jorian 17-4b.xlsx

It's definitely circular, although not (IMO) in a problematic way (it's an optimization to find the highest portfolio IR conditional on a TEV constraint). After I tried to reproduce him entirely in an internally dynamic replication, I think i decided that Jorion's "shortcut" is to assume (out of thin air) a portfolio TEV of 4.0%, which i think renders the circularity trivial. (ie, trivial enough to reproduce in the simple XLS). In this sense, i think you are on to him . I don't think that implicates 17.7, which strikes me as necessarily circular but not unholy. I'm rusty on the particulars, no time or i'd look deeper now, thanks,

 

[David Harper CFA FRM]

... actually, in HASTE i misspoke, as i open the XLS, the TEV is not a problem, it is merely the specified constraint on the portfolio. By design, it can be whatever. Then a goal seek on E18 performs the optimization. Yes, it's circular, but it's not a problem (i.e., it is not a case of too many variables, but rather an optimization problem in the circularity). The XLS, I think demonstrates Jorion: enter desired TEV constraint into cell D16, then minimize red cell E18, which implements Jorion's 17.7.

 

[shanlane]

That makes perfect sense. Jorion's explanation sounded like he used optimization to come up with the formula instead of using optimization within the formula.

Thanks!

Shannon

 

[afterworkguinness]

If you still have the spreadsheet, I'd love a copy.
The notation in this section is quite confusing. When Jorion defines Information Ratio he uses omega for TEV, but further down the page he defines omega_i as tracking error. Then a possible typo (I can't find errata for the text to verify)

mu_p = sum(x_i*mu_i) = sum(x_i*(IR_i * omega_i))

But IR_i * mu_i (as opposed to IR_i * omega_i) would equal mu_i