Explanation:

The risk contribution (RC) or unexpected loss contribution (ULC) of each asset in a two-asset portfolio is given by: $RC_1 = \frac{UL_1^2 + \rho_{1,2} \times UL_1 \times UL_2}{UL_P}$ $RC_2 = \frac{UL_2^2 + \rho_{1,2} \times UL_1 \times UL_2}{UL_P}$

Given:

$UL_1 = \`$ 16.0`$
$UL_2 = \`$ 9.40`$
$\rho_{1,2} = 0.180$
$UL_P = \`$ 20.0`$

Calculating the respective contributions: $RC_1 = \frac{16.0^2 + 0.180 \times 16.0 \times 9.40}{20.0} = \frac{256 + 27.072}{20.0} = \frac{283.072}{20.0} \approx 14.15$ million

$RC_2 = \frac{9.40^2 + 0.180 \times 16.0 \times 9.40}{20.0} = \frac{88.36 + 27.072}{20.0} = \frac{115.432}{20.0} \approx 5.77$ million

The nearest values are ` $14.2` million and \`$ 5.8` million, respectively.

921.3. Consider a credit portfolio that contains the following two positions:

`$300.0` million exposure with default probability (PD) of 2.0%, loss given default (LGD) of 20.0% and σ(LGD) of 10.0%

`$100.0` million exposure with default probability (PD) of 6.0%, loss given default (LGD) of 60.0% and σ(LGD) of 30.0%

The default correlation between the positions is 0.180. As the individual exposures' unexpected losses are `$16.0` and `$9.40` million, the portfolio's unexpected loss (UL) is given by sqrt(`$16.0`^2 + `$9.40`^2 + 20.180`$16.0`*`$9.40`) = `$20.0` million. Which are NEAREST to the respective risk contributions (RC) of exposures, which are also known as (aka) each exposure's unexpected loss contribution (ULC)?

$14.2 and $5.8 million

$11.3 and $8.7 million

$9.5 and $10.5 million

$8.1 and $11.9 million

Financial Risk Manager Part 2

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