One such measure is referred to as risk-
adjusted return on capital, or RaRoC where
capital is defined as economic capital.
50

Fundamentals of Financial Risk Management
Risk-adjusted Performance
This can be defined simply as:
where NI is net income, R represents revenues,
D is debt costs, O is operating expense and EL
is expected loss, EC is economic capital and
HR is the bank’s hurdle rate.
51
RaRoC
NI
EC
HR
NI
R
D
O
EL

Fundamentals of Financial Risk Management
Risk-adjusted Performance
A value for RaRoC that meets or exceeds the
target return HR is a viable project.
An alternative way of expressing risk-
adjusted performance is with the shareholder
value-added (SVA) metric.
It basically modifies RaRoC by adjusting for
the cost of capital using the HR as the unit
measure of capital cost.
It may be formally
defined as:
52
SVA
NI
HR
*
EC
0

Fundamentals of Financial Risk Management
Risk-adjusted Performance
SifiBank Holding Co. has conducted its
assessment of economic capital across
each business unit according to the earlier
discussion in this chapter aggregating
across credit, market and operational risk
with the estimates shown in Table 6-3.
SifiBank Holding Co. has a target rate of
return of 15%.
53

Fundamentals of Financial Risk Management
Risk-adjusted Performance
As useful as this may be it still ignores potential risk diversification effects that may
exist between business units.
Drawing from portfolio theory, the VaR for SifiBank Holding Company can be
defined as the following:
where represents the ith business units weight (percent of portfolio assets) and is the
correlation coefficient between business unit i and j.
The correlation coefficient can
also be used to define the covariance between any two business units as follows:
To be more accurate, the correlations might actually exist among different risk types
across units and the risk analyst would thus need to compute compute a matrix of
correlations for each combination of risk (i.e., credit, market, operational) and
business unit.
While this adds to the complexity of the problem, the above example preserves the
conceptual portfolio VaR problem.
54
VaR
P
w
i
2
VaR
i
i
1
3
2
w
i
w
j
VaR
i
VaR
j
ij
j
1
3
i
1
3
ij
ij
i
j

Fundamentals of Financial Risk Management
Risk-adjusted Performance
Applying this formula to SifiBank Holding
Company’s business units based on the correlation
structure among the divisions results in a portfolio
99% VaR of $238 billion.
This obtained by taking the unit VaR for each
division (defined as the standard deviation of each
division times 2.33), aggregating across the
weighted sums for each division at the bottom of
the table, taking the square root of that result and
multiplying it by the portfolio value of $1 trillion.
55

Fundamentals of Financial Risk Management
Risk-adjusted Performance
56

Fundamentals of Financial Risk Management
Risk-adjusted Performance
The fact that the correlations between
business units are not perfect (i.e., ) suggests
that there is a risk diversification benefit
resulting in lower VaR than in that case.

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- Spring '14
- Apland,Jeffrey
- Normal Distribution