Raroc methology
12. May 2009 07:21
Since the 90s, most of the large international banks
have set up heavy credit risk management systems, and in
particular
in order to measure and monitor the risks they hold on each business line. One
of the goals of theses systems is to allocate capital to each business line and
to compute the overall capital of the bank. All these
techniques are known under the generic acronym RAROC
methodology(Risk Adjusted Return On Capital) ;
implicitly, this methodology focuses on economic based estimations of credit risk, taking into account both all the individual risks and the portfolio view of the bank. The aim of the RAROC methodology is twofold:
1. Risk management: in the financial theory, the bank
aims at reaching its optimal capital structure and finding the proportion of
equity to assets that minimizes the cost of funding. The RAROC methodology is
used for determining the overall capital requirement of the bank and the
contribution of each business line to the total risk of the bank. This process
is called capital allocation.
2. Performance measurement: the RAROC device computes
the profitability of each transaction or business line for the shareholder. The
performance measurement is the result of the interplay between revenues on one
hand, and risk components on the other hand.
Let’s consider
the case of a AA rated bank that wants to capitalize its portfolio in a manner
consistent with a AA rating target. This amount of capital is of course driven
by all the stand alone risks included in the portfolio, but also benefits the
internal diversification of this portfolio. In this sense, this equity capital
requirement is called
economic capital.
Whereas the expected loss is the average loss that the
bank anticipates to loose on its portfolio, the economic capital refers to the
unanticipated losses that occur in extreme situations or market conditions. The
economic capital is the cushion required above the expected loss for the
bank to remain solvent in the event of extreme losses on the bank’s portfolio.
There are many available criteria for defining
economic capital, but generally, economic capital is defined as the amount
required to cushion the portfolio up to a given confidence level. The required confidence
level depends on the target rating of the bank. For instance, if the bank’s
portfolio has an average maturity of 2.5 years, the confidence level is around
99.9% for a AA- target rating. From a mathematical
viewpoint, the economic capital is linked to Credit
Value at Risk (CvaR) of the portfolio and to the expected loss
of the portfolio by the relationship:
EC = VaR 99.9% − EL
The portfolio loss distribution is generally obtained
by Monte-Carlo simulations.
Portfolio managers make the distinction between
marginal capital and incremental capital of a transaction. The incremental
capital is the additional amount of equity capital required when the
transaction is added to the portfolio, whereas the marginal capital is equal to
the contribution of the transaction to the total capital once this
transaction is included inside the portfolio.
To make this more precise, we call P the reference
credit portfolio
and Mx a marginal transaction with nominal amount x.
Finally, we call EC(A) the economic capital of portfolio
A. The incremental capital of the transaction M is
equal to:
ECi = EC(P+ Mx )- EC(P)
The main
property of the marginal capital compared to incremental capital is that the
sum of the marginal capital over all the transactions of the portfolio is equal
to the economic capital of the portfolio. This property leads to an easy
capital allocation on condition that we are able to compute accurately marginal
capitals.
Bank needs is to include risk adjustment functions
into the traditional performance
measures. There are many ways of doing that. One of
them is to introduce risk elements into the traditional
Return On Capital (ROC) ratio defined by:
ROC= REVENUES
allocated capital
Allocated capital is the regulatory capital that the
bank has to allocate to the transaction of interest. Both
revenues and allocated
capital don’t take into account any risk sensitivity. There are several
possibilities to
introduce risk
sensitivity in this equation, at the numerator and the denominator. According
to where we include
a risk adjustment, we are led to different ratios such
as RAROC, RORAC and RARORAC (RISK ADJUSTED PERFORMANCE MEASURES –RAPM) . The
most popular performance measure is the Risk Adjusted Return On Risk Adjusted
Capital (RARORAC), obtained by correcting the revenues by the anticipated
losses on the transaction, and by replacing the allocated capital by the
marginal economic capital of the transaction:
-
RORAC= (financial income – financial costs)/ scaled economic
capital allocation
-
RAROC=(financial income – financial costs – expected losses)/
scaled economic capital alocation
The management may also be interested in the value
created by a marginal transaction or a business line. EVA (Economic
Value Added) is the relevant performance measure for value creation. It is
equal to the revenues less the cost of capital.
from Vivien BRUNEL
Email 
11/25/2010 4:02:35 AM
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