Explanation:
Expected loss (EL) is an additive measure calculated as the sum of the expected losses of individual assets (EL = PD × LGD × EAD). Therefore, expected loss is completely independent of default correlation. Default correlation impacts the variance of the portfolio losses (Unexpected Loss) and the tail risk (Credit VaR), but it has absolutely no impact on the expected loss itself. Thus, statement B is false.
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309.3. Assume a portfolio with a total principal value of $1.0 billion divided into n = 20 positions where each position has a default probability of 1.0% and the positions are uncorrelated, as follows:
$1,000,000,000$50.0 millionWe are interested in the 95.0% credit value at risk (CVaR) of the portfolio, where 95.0% CVaR = 95% unexpected loss (UL) net of (excluding) the expected loss. We can vary the granularity of the portfolio by increasing (n), or we can increase the default correlation, but in either case, we maintain the other assumptions, i.e., ceteris paribus. Each of the following is true EXCEPT for which is not?
A
Default correlation is hard to measure or estimate using historical default data
B
Default correlation exhibits too much sway on ("has a tremendous impact on") the credit portfolio's expected loss
C
Default correlations are small in magnitude such that an "optically" small correlation can have a rather large impact
D
The problem created by a portfolio with (n) credits, which require n*(n-1)/2 pairwise correlations, is often solved by assuming all pairwise correlations equal to a single parameter, but that parameter must be non-negative
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