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Difference between RAROC and ARAROC

Thread starter #1
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

Well-Known Member
Subscriber
#2
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
 

Delo

Active Member
Subscriber
#4
What is the correct formula for Adj. RAROC?
I noted down Adj. RAROC = RAROC - Rf
...................................................... Beta

But Crouhy mentions following :-
upload_2016-5-7_20-58-34.png
 

David Harper CFA FRM

David Harper CFA FRM
Staff member
Subscriber
#5
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!
 
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#7
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
 
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David Harper CFA FRM

David Harper CFA FRM
Staff member
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#8
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!
 

RobKing

Active Member
#9
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

David Harper CFA FRM
Staff member
Subscriber
#10
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 :oops: 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!
 
#12
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

David Harper CFA FRM
Staff member
Subscriber
#13
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