How to use RAROC?

[ajsa]

Hi David,

Adjusted RAROC compares with equity risk premium to decides if a project should be approved. I wonder what should be compared with RAROC for a project? cost of equity? what exactly is cost of equity? is it required return of equity (RFR + beta * (market return - RFR))? If so RAROC's approach is same as ARAROC's, right? but i read ARAROC is an improvement on RAROC..

Thanks.

 

[David Harper CFA FRM]

Hi ajsa,

It's a *great* observation (we've grappled with Crouhy's ARAROC each year on this point...). IMO, the Crouhy presentation (the assigment) is flawed, but what he seems to say is straightforward, where as you imply, the ARAROC is not much different than a Treynor ratio. That is, he says the beta is equity firm beta, such that:

proceed with project if ARAROC > market's equity risk premium (i.e., market return - riskless), such that
proceed if ARAROC = (RAROC - Rf)/(firm's equity beta) > Market return - Rf,
if (RAROC - Rf) > Firm Equity Beta * (Market return - Rf)
IF RAROC > Firm Equity Beta * (Market return - Rf) + Rf

in short, proceed if
RAROC > E[r] under CAPM where E[r] is the firm's equity cost of capital

As presented, and agreeing with you, I read Crouhy's distinction between RAROR and ARAROC as superficial:
RAROC: when the hurdle is some fixed cost of equity capital that is invariant to the firm's capital structure
ARAROC: when the hurdle rate is (properly) adjusted for firm leverage (ie.., ceteris peribus, higher leverage implies higher equity beta)

....that's what Crouhy says, or what I think he says after reading it a few dozen times in the last four years
...but in my less-than-certain opinion, in the spirit of Stulz Chapter 4 (where, when adding a project to the firm, the key relationship is the marginal risk added by the project; i.e., the beta of the project with respect to the firm), it should instead be a project beta (but it's a bit of a rabbit hole...)
...so i think one can accept that Crouhy's ARAROC is merely a fancy way of saying "instead of fixed hurdle, the hurdle should reflect the firm's equity cost of capital as reflected by the CAPM...and since CAPM captures the firm's systematic risk via beta (correlation with market), ARAROC reflects a risk-adjusted hurdle"

Hope that helps, probably not?

David

 

[ajsa]

Hi David,

I understand RAROC's formula is pretax return, right?

Thanks.

 

[David Harper CFA FRM]

Hi ajsa - Yes, as per our other thread, while I have seen after-tax versions, the FRM has never studied an after-tax version (e.g., the current relevant RAROC is Crouhy and it's pretax) ... as we noted in the other thread, it introduces the "issue" of how to treat the denominator: after tax return in numerator (okay, that's not hard) but do we after-tax the denominator and, if so, why? and how? (IMO, this is non trivial b/c the denominator in RAROC, unlike say EVA, is not a capital resource with tax shield, it's a risk measure of required capital)...David