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Risk Management in
Islamic Financial Instruments
APPENDIX B: CREDIT RISK MEASUREMENT
Sundarajan (2005) states that the measurement of three components, which allow us to
calculate loss, (1) the probability of default, (2) potential credit exposures at default, and (3)
loss given default, are key requirements of the New Basel Capital Accord.
Aurn Sundarajan (2005) offers specific equations for calculating risk in investment deposit
returns, which can be calculated based on the variance of R
I
.
VAR (R
I
) = (A/DI)
2
[VAR (R
A
– S
p
) + VAR (R
P
) – 2Cov(R
A
-S
p
, R
P
)]
+ (AK/DI)
2
VAR (R
E
) (5)
Similarly, the risk in return to capital can be found by calculating the variance of R
K
and its
components based on an equation.
Mudaraba Profit(RM) can be written as (ignoring Investment Risk Reserves for simplicity)
RM = A(R
A
-P
A
) – AR
P
– K R
K
Where R
A
= return on assets, R
p
= Profit Equalization Reserves (as a % assets)
S
p
= Provisions as a % of assets,
R
K
= Return on Capital assigned for the purpose of computing distributable Mudaraba
income.
Rate of Return for Investment Account holders (R
I
) can then be calculated by applying the
agreed share on Mudaraba income.
R
I
= αRM/DI = α [A (R
A
-S
p
-R
P
-K R
K
)] / DI
The total return on capital can be calculated to ensure that total income accruing to
banks’ own funds - equal to assigned return on capital plus income earned as a Mudarib –
provides as required return on equity of R
E
.
R
E
= (1-α) RM/K + R
K
Combing (1) & (2)
R
I
= A (R
A
-S
p
-R
P
) - KR
E
DI
R
K
= 1 R
E
─ (1- α) A (R
A
-S
p
-R
P
)
α α K
The equations above were extracted from Sundararajan (2005).