Difference between RAROC and ARAROC

[ydl33060]

Dear David,

I am confuse with the following concept and would appreciate if you could clarify.

Shall RAROC or ARAROC be used to determine the viability of a project?
The study note seems to suggest that ARAROC shall be used but the practice question 1.5 as set out below seem to tell otherwise.

Question 1.5 in the practice question under RAROC:
Why is The answer of I which state that "If a prject's RAROC is greater than the firm's cost of equity capital, then the project should be accepted" is consider true? Shouldn't ARAROC be used instead?

Thank you.

 

[ShaktiRathore]

cost of equity is given by: Rf+B*(Rm-Rf) =re
RAROC>re => RAROC>Rf+B*(Rm-Rf) =>RAROC-Rf>B*(Rm-Rf)
=>[(RAROC-Rf)/B]>(Rm-Rf)
Now [(RAROC-Rf)/B] is nothing but the ARAROC is the RAROC adjusted for risk of the project which is beta B. So therefore it follows,
=> ARAROC>(Rm-Rf) which is the decision rule under ARAROC where the project is accepted when the ARAROC is greater than the market risk premium Rm-Rf. So we finally arrived at the ARAROC decision rule so that it can be stated in the other sense that project is accepted when prject's RAROC is greater than the firm's cost of equity capital. You can work backwards and arrive at this decision rule that is start from the ARAROC formula and arrive at this rule. So stating the project accepting decision rule either this way or the other way around is a matter of choice and is the same thing.

hope it helps and u understood why its this way,
thanks

 

[ydl33060]

Hi Mr. ShaktiRathore,

Thank you for your clarificaiton. I have a better picture now.

Thank you.

 

[Delo]

What is the correct formula for Adj. RAROC?
I noted down Adj. RAROC = RAROC - Rf
...................................................... Beta

But Crouhy mentions following :-

 

[David Harper CFA FRM]

Hi @Delo

Either is correct (both are Crouhy, after all!). The difference is superficial: yours is compared to the expected excess return on the market, E(M) - Rf, while in Box 15-5, the comparison is simply the riskfree rate, Rf. The will both come to the same accept/reject conclusion. For example, let's assume Rf = 3.0% and E(M) is 7.0% such that market excess return, E(M) - Rf = 4.0%. A project with beta of 1.5 has an effective hurdle return of E(R) = 3.0% Rf + 1.5*(7.0% - 3.0%) = 9.0%. So let's say the project returns RAROC of 10.0% which puts it above the hurdle:

• In yours, ARAROC = (10.0% - 3.0%)/1.5 = 4.67% and this is compared to the market excess return of 4.0%, such that the decision is to accept
• In Box 15-5, ARAROC = 10% - 1.5*4.0% = 4.0% and this is compared to the risk-free rate of 3.0%, with same decision outcome. They will always agree, given they are both akin to testing for positive (Jensen's) alpha. I hope that helps. Great observation!

 

[Delo]

Thanks @David Harper CFA FRM . Makes sense.
If exam asks to calc, which one to use ?

 

[Maged]

When I checked old GARP exams, they were used old formula
But in 2016, new formula is there

Adj RAROC = RAROC - Beta (Rm-Rf)

Really strange!
Question is still there: Which formula we have to use ?

BTW, I agree with @David Harper CFA FRM about whether we should agree or reject the project.
Actual Q is what we should do when we asked just to calculate ARAROC

1) Previous: ARAROC = ( RAROC - Rf ) / Beta => to be compared with Rm-Rf
2) Current: ARAROC = RAROC - Beta (Rm - Rf ) => to be compared with Rf

 

[David Harper CFA FRM]

Thanks @Maged ! @Delo You should be able to use either. Consider the practice question 2016 P2.30:

30. A chemical company is considering a project that has an estimated risk-adjusted return on capital (RAROC) of 17%. Suppose that the risk-free rate is 4% per year, the expected market rate of return is 12% per year, and the company's equity beta is 1.5. Using the criterion of adjusted risk-adjusted return on capital (ARAROC), the company should:
a. Reject the project because the ARAROC is higher than the market expected excess return.
b. Accept the project because the ARAROC is higher than the market expected excess return.
c. Reject the project because the ARAROC is lower than the market expected excess return.
d. Accept the project because the ARAROC is lower than the market expected excess return.

GARPs answer uses the previous method, but you can still use the "newer" method: ARAROC (#2) = 17% - 1.5 beta * 8% EMR = 5.0%, which is higher than the risk-free rate. So we Accept, which must be choice (B) given choice (D) is nonsense. I'd be tempted to just use CAPM E[return] = 4% + 1.5*8% = 16%; so the project has positive "alpha" of +1% because it's return is 17%, so accept. I hope that helps!

 

[Member 41305]

Hi David,

Me again. This is one of those questions that I would have got right in the exam .... but never have known it. The reason for my lack of confidence is that although it's clearly an accept decision neither D or B make sense to me!

I see that the above calculation is to accept the project.... but - adjusted RAROC is RAROC - beta(rm-rf) = 17%-1.5(12%-4%) = 5% < market excess return......

Alternatively, ARAROC = RAROC-Rf / Beta = 17%-4% / 1.5 = 8.6% > market excess return!

Hence I've managed to prove both B&D which is either true genius at work or materially flawed - I suspect the latter!

On the hypothesis that genuis has deserted me this morning could you point out my disconnect please

Thanks

Rob

 

[David Harper CFA FRM]

Hi @RobKing I think the disconnect is that your first test should be "but - adjusted RAROC is RAROC - beta(rm-rf) = 17%-1.5(12%-4%) = 5% > risk-free rate." So you would accept. As discussed above and where this first caused confusion is that GARP (Crouhy) proposed two ARAROC tests, neither of which is terribly intuitive to me both correctly itemized by @Maged above. Using the 2016 practice exam question P2.30 assumptions of RAROC = 17.0%, Rf = 4.0%, β=1.50, and R(m) = 12%:

1. Previous: ARAROC = ( RAROC - Rf ) / Beta => to be compared with Rm-Rf. In this case, (17.0% - 4.0%)/1.50 = 8.67% which is greater than 8.0% = R(m) - Rf = 12.0% - 4.0%
2. Current: ARAROC = RAROC - Beta (Rm - Rf ) => to be compared with Rf. In this case, 17.0% - 1.5*(12.0% - 4.0%) = 5.00% which is greater than the riskfree rate of 4.0%.

It remains easiest, for me, to simply calculate the (Jensen's) alpha of the RAROC. In this case, Jensen's alpha = 17.0% - 4.0% - 1.50* (12.0%-4.0%) = +1.0%; i.e., above the SML, so to speak, and therefore "accept." I hope that clarifies!

 

[Member 41305]

Thanks David: Jensen's alpha approach works best with me.....

 

[dbansal]

Hello,

I am confused as to what the correct formula for ARAROC? In the formula sheet ARAROC is given as (RAROC - RF) / Beta where as in the example questions / answers I see ARAROC = RAROC - B(Rm-Rf)

Thanks!

 

[David Harper CFA FRM]

@dbansal the exam is in less than a week, so it would be so really helpful if you could search first. (Because Nicole and I really will try to help everybody as much as we can in the final week, but it's harder when there are too many wholesale repeats). In this case, an "ARAROC" search is very effective as this has been discussed many times; e.g., https://forum.bionicturtle.com/threads/difference-between-raroc-and-araroc.6669/

 

[sohinichowdhury]

David, is it correct to say that while RAROC adjusts returns for only non-systemic/firm-specific risk (by deducting the expected loss), ARAROC adjusts for both systemic and non-systemic risk (by also deducting the equity beta)? Thank you!

 

[David Harper CFA FRM]

Hi @sohinichowdhury I like your question, but I didn't quite "agree" because I have a slightly different interpretation(s), and I acknowledge there seem to be two different, valid interpretations of ARAROC, depending on whether we refer to the simpler Crouhy or the more difficult Grinold interpretation.

Start with RAROC. How is RAROC risk-adjusted? To me, the "risk adjusted" in RAROC is via the deduction of EL in the numerator that is matched with the UL (equal to EC) in the denominator which excludes EL; i.e., the denominator is UL not UL+EL. This is why RAROC is risk-adjusted. So the weakness of this, in a simpler interpretation, is that one project with a RAROC of 9.0% might have high correlation to the firm's existing portfolio; but another project with a RAROC of 9.0% might have low correlation to the firm's existing portfolio/business. The latter is better for the firm. ARAROC incorporates the project's beta to give credit, or penalize, the project's return for it's contribution to the businesses risk. This seems to me theoretically elegant, and it's based on Grinold's interpretation, but this is the more difficult approach and I don't think it's gotten traction in the FRM.

Rather, the simpler approach is: the beta is the firm's beta, and ARAROC is simply making the firm's hurdle rate explict via the firm's beta. Per Crouhy (emphasis mine),

"The risk adjustment, β(RM – rf), is the excess return above the risk-free rate required to compensate the shareholders of the firm for the nondiversifiable systematic risk they bear when investing in the activity, assuming that the shareholders hold a well-diversified portfolio. When the returns are thus adjusted for risk, the hurdle rate becomes the risk-free rate." -- Crouhy, Michel; Galai, Dan; Mark, Robert. The Essentials of Risk Management, Second Edition . McGraw-Hill Education. Kindle Edition.

This ARAROC is simply accounting for the systematic risk of the project and adjusting the hurdle likewise. Project risk is here a function of the project's systematic risk.

In this way, I would rephrase your distinction, I would say something like:

"while RAROC adjusts returns by deducting the expected loss [<-- I agree with this part!], RAROC ignores the direct influence of the project's volatility (aka, standard deviation, total risk) and its correlation/beta to either the firm or the market, which means that it can be artificially increased by high-beta projects, while ARAROC adjusts for systemic risk and non-systemic risk (by also deducting the equity beta) by "deducting" either the firm's equity beta (in the simple approach) or the project's beta (with respect to the firm, in the advanced approach)."

I hope that's helpful! Thanks,