Sep 24

Unexpected loss (UL) for a portfolio of credit assets – 9 min briefing

by David Harper, CFA, FRM, CIPM

FRM |

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Previously I reviewed the unexpected loss (UL) for a single credit asset. Following Ong (who is assigned for 2008 FRM), here I review the UL calculation of a two-credit-asset portfolio. Tips for FRM candidates:

  • The additional key parameter is the pairwise default correlation (rho). My example here (from Ong Table 6.2) only requires a single default correlation; but a portfolio of N credit assets contains [N(N+1)]/2 pairwise correlations. Actually, since the diagonals in a correlation matrix are 1.0s, the number of pairwise correlations = COMBIN(N,2) where COMBIN(N,2) = [N(N+1)]/2 - N .
  • Pairwise correlation has no impact (does not enter) portfolio expected loss. Pairwise correlation impacts only portfolio unexpected loss.
  • Given imperfect pairwise correlation (correlation < 1.0 or 100%), the portfolio unexpected loss must be less than (<) the sum of individual unexpected losses. This makes unexpected loss (under these conditions) sub-additive (a coherence criteria).

Screencast:

Comments

  1. sridhar 26 Sep 2008

    David: This seems so similar to computing the Portfolio VaR. But in the case of Portfolio VaR for a portfolio of two assets—we include the relative weights in the computation. That is:

    VaR(p) = sqrt(w1^2*VaR1 + w2*VaR-2 + 2w1w2*rho*VaR-1*VaR_2)

    1. In computing the cumulative UL, why are we not accounting for relative weights of the two assets in the credit portfolio?

    2. Are the relative weights “subsumed” somewhere else?

    --sridhar

    PS: I might sound like a broken record—but I can’t say enough positive things about these mini-screencasts. Great pedagogical technique.

  2. Andy 08 Oct 2008

    Dear Sridhar,
    Please notice that we have already taken care of weights or portfolio values while calculation respective Unexpected losses and thats why you see only ULs in the final formula.

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