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# RAROC

#### nanchary

##### New Member
Why are we subtracting the economic capital from the total loan value in estimating the ineterst charge?

from our example, Are banks not borrowing 1 billion from the depositors and making a loan for higher charge? The capital requirement for this loan is 100m and banks invest in highly liquid assets to support in case of unexpectetd losses. so we are adding interest on it to the numerator. How bank is raising 100m? is it not from the depositors then in that case banks have to pay interest on 1.1 b not on 900m.

Tks.

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Nanchary,

Right, I agree with you. But I am following Saunder's example in the assigned reading; I think he may miss the circularity. In the reading:

* Loan portfolio: $1 billion @ 9% * Economic capital: 7.5% of$1 billion = $75 million, invested @ 6.5% riskless (T-bills) * Therefore,$925 MM should be raised by deposits ($1 BB -$75 MM), earning 6% for depositors

risk-adjusted return [numerator] = 90 [loan revenue] + 4.9 [about 6.5% on the $75 MM] -$55 [cost of funds: 6% on the $925] -$10 op expense = $14.375 But that implies assets =$1 billion + $75 MM. Therefore, shareholder's equity = 1.075 - 925 > 7.5% EC. So, if shareholders fund$75 million, I agree with you: that's $75 MM cash-like in assets and equity, such that bank funds$1 BB in loans with $1 BB in deposits. And tot assets = 1.075 wit EC = 75 MM = 7.5% of the$1 BB loan.

But that's not what Saunders does in the assigned readings...I think the important thing is the numerator includes return on economic capital (ROC).

David

#### liewpw05

##### New Member
Hi David,

I have similar problems with the understanding of the \$925million raised by deposits in the above example. Your reply does help to clarify.
I have another question on this example : why is the numerator of the RAROC called risk adjusted return? Is it because it also include a deduction for expected loss from default?The expected loss being excluded due to the fact that the bank has to set up provisions for bad loans and credit can't be taken for the expected loss which has been "priced in" the loan interest pricing when assessing expected return on the loan portfolio.

Thanks

Regards,
Peggy

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi Peggy,

On the Saunders example, I still believe Nanchary is correct in spotting the error. He observed that the implied balance sheet is not balanced, which i happen to agree with. But also, it is not crucial to the RAROC ratio. In many cases, RAROC is a divisional metric anyhow...

"why is the numerator of the RAROC called risk adjusted return?"
you may be interested here to connect this Saunders to Chapter 6 of de Servigny (p 244) and his RAROC discussion. The general class of risk-performance metrics is simply:

return/risk

So, RAROC is "cousin" to Sharpe and the risk is in the denominator. Specifically, economical capital is risk adjusted (i.e., greater volatility or higher confidence implies more economic capital required. BTW, to relate to our other thread about regulatory/economic capital, regulatory capital per Basel II is also "risk-adjusted capital." My one sentence summary of Basel II would be "risk adjusted captial." Ergo, we could validly plug-in regulatory capital into the denominator of RAROC!).

While I am here, I want to offer another thought. The RAPM measure are risk-adjusted returns. I like to think, conversely, of VaR as return-adjusted risk (!). As "absolute VaR" = - return + (scale confidence)(scale time)(volatility), greater expected return is offseting VaR. So, VaR is return-adjusted risk, while RAPM (RAROC, Sharpe) are risk-adjusted returns. For what it's worth

"Is it because it also include a deduction for expected loss from default?The expected loss being excluded due to the fact that the bank has to set up provisions for bad loans and credit canâ€™t be taken for the expected loss which has been â€œpriced inâ€ the loan interest pricing when assessing expected return on the loan portfolio. "

What you write is true. But I would tend not to cite the treatment of EL as a reason for calling this risk-adjusted. Rather, i think the most important thing i ever learned about ratios was the rule they should be consistent: the return in the numerator should relate (map) directly to its corresponding (balance sheet) claim in the denominator. For example, ROE is net income/common equity, ROE is not EBIT/equity because EBIT is claimed by debt plus equity holders. The same logic is here to RAROC: the numerator is the earnings base that accrues (is earned by) the economic capital. It would be inconsistent to include EL in the numerator. It would be okay to do that, but if you add EL back to numerator, you should add the corresponding reserve (balance sheet) to the denominator. Finally, there is no magic correct ratio; it would not suprise me if some bank did add back. There is more than one correct RAROC (i.e., I'd argue RAROC is EVA for banks, and there are dozens of EVA variants), as long as it is consistent.

David