RAROC vs ARAROC

[higaurav]

Hi David,

Request for some more clarity on this concept.

To draw out the context, my understanding is that we can use IRR for "capital allocation" decisions, as (IRR > hurdle rate), NPV will be positive and so we will be adding value the shareholders. Here in this case, I am presuming that RAROC is used in place of IRR or in similar way as IRR, also it has the expected loss information included (which is presumably missing when we use IRR).

Now the points that I am not very clear about are that RAROC seems to be more of an accounting ratio and it do not take into account the future cash flows in calculations (like other investment ratios that we use for capital allocation).

Second, we are assuming that difference/increase in beta due to new project considered and therefore we use ARAROC instead of RAROC (please correct in case this understanding is not right). But we use existing beta only in ARAROC calculation (as we do not have info on the changed beta) then how ARAROC is better than comparing hurdle rate with RAROC....(as I see both should be giving the similar results in case of one beta scenario at company level)

Look forward for your help in understanding this concept...

Rgrds,
OM

 

[David Harper CFA FRM]

Hi Om,

On the first, that's really interesting. I agree with you, our RAROC (in Crouhy the FRM assigned) is a single-period accounting metric. RAROC and EVA are near cousins (they lead to the same conclusion) and EVA is clearly a single period accounting metric (though note, both can be adjusted into single period cash flows metrics. EVA into CVA and, theoretically, I see no reason RAROC could not be adjusted into cash RAROC, though I've not encountered it).

So, RAROC is a sub-class of a single period return on captal measure. As such, it is compatible with multi-period measures like IRR. Our single period RAROC could be extended into multi-period RAROCs: i.e.,

value created = (year1 RAROC)*(year1 Economic Capital)*(1+r) + (year2 RAROC)*(year2 Economic Capital)*(1+r)^2 + ...

Here r is the discount rate, or really, the cost of equity capital. If we observe the market value (value created), we can solve for the (r) as an IRR which discounts the future economic returns to the correct present value. So, I didn't detail this out, but hopefully you'll agree that RAROC as a single period metric is compatible with an IRR notion, not in disagreement with it. In a broad sense, I think, it may not be so much different than using DCF to value shares (multiperiod) versus capitalizing a single-period earnings base (P/E multiple * earnings).

On the second, "we are assuming that difference/increase in beta due to new project considered and therefore we use ARAROC instead of RAROC." Hmmm...part of the confusion (IMO) is that RAROC can refer to an instrument, a business unit or the bank overall. Crouhy's ARAROC demonstration occurs at the firm level: he shows that ARAROC works because the firm's equity beta increases with the expected asset return. In that case, RAROC will only give credit to higher expected return and give a higher RAROC; but ARAROC, as the expected return increases, will give an increasing beta in the denominator and so ARAROC will not really be changing...

At the business unit/transaction level, maybe just think of this like the Treynor ratio (which is sort of is!). If the bank thinks about adding an investment project, it will use the BETA of the INDIVIDUAL PROJECT. Now, just like Treynor ratio, if ARAROC is better than ERP, the investment is doing better than CAPM would require.

David