99th percentile of the unrecovered credit loss为什么要再乘以LGD？

问题如下：

A credit analyst at an investment firm is estimating the 99% credit VaR of a 1-year zero-coupon bond, the only debt issued by the firm. The analyst obtains relevant data presented below:

• Face value of the firm’s 1-year zero-coupon bond: CNY 630 million

• The bond’s expected 1-year probability of default (PD): 6%

• The bond’s 1-year recovery rate: 90%

Assuming the variation of the future value of the bond is solely due to the possibility of default, and the analyst’s estimate of the value of the bond in 1 year at the 99% confidence level is CNY 567 million, what is the bond’s implied 1-year 99% credit VaR?

选项：

A.

CNY 2.52 million

B.

CNY 3.40 million

C.

CNY 3.78 million

D.

CNY 6.30 million

解释：

A is correct.

The 99% CVaR = 99th percentile of the unrecovered credit loss – Expected Loss where,

99th percentile of the unrecovered credit loss = (630 – 567)*(1 – 0.9) million = CNY 6.3 million

Expected Loss = PD x LGD x EAD = 0.06* (1 – 0.9) * 630 = CNY 3.78 million

Therefore,

CVaR at 99% confidence level = 6.30 – 3.78 = CNY 2.52 million.

B is incorrect. CNY 3.402 million is the result of subtracting CNY 3.78*0.1 million from (CNY 630m*0.06*0.1).

C is incorrect. CNY 3.78 million is the EL.

D is incorrect. CNY 6.3 million is the incorrect result of ignoring the EL.