Hi @Arsalan Amin Do you happen to recall where your read that correlations impact EL, because I think it might be a misunderstanding? Default correlation does impact unexpected loss (UL) but does not impact expected loss (EL). EL is a mean, while UL is the function of variance, so another way to look at this is that default correlation does not impact the mean. Here is a simple example: two six-sided dice. As random variables, their expected value (the mean) is 7.0. This is true whether they are independent--as they generally are--or correlated. Consider a farcical situation where we glued the two dice together, so their correlation is perfect (i.e., possible rolls are 1-1, 2-2, 3-3, 4-4, 5-5, and 6-6). Compare the two scenarios (independent dice versus perfectly correlated dice)

Two independent 6-sided dice: mean = 7.0, variance = 5.83 = 2.92*2 and standard deviation = sqrt(5.83) = 2.42

Two perfectly correlated 6-sided dice: mean = 7.0, variance = 11.67 and standard deviation = sqrt(11.67) = 3.42; i.e., when the correlation goes from zero to 1.0, the variance doubles while the mean is unchanged.

This is similar with credits where default is modeled as a Bernoulli (i.e., either survive = 0 or default = 1). Using Malz' example (P2. Topic 6), imagine we have a $1.0 million portfolio with 100 equally-sized obligors (i.e., 100 obligors * $10,000 per). Further, let's say they all have PD = 2.0%. Finally, assume zero recovery. If they are independent (implies zero default correlation), the portfolio's expected loss = 2% * 100 * $10,000 = $20,000. As we increase default correlation, this expected loss is unaffected. Even with perfect default correlation, the portfolio EL is still $20,000. However, as default correlation increases, unexpected loss does increases.

Finally, formula-wise, EL = PD * EAD * LGD, and portfolio EL is the weighted sum of individual EL. Default correlation does not enter the EL formulas, whereas it does show up in Portfolio UL. I hope that helps!

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