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# EL/UL ratio

#### coquin22

##### New Member
Schweser:
Smallville Savings Bank (SSB) has a loan portfolio totaling $20,000,000 in commitments. Currently 60% is outstanding. The bank has assessed an average internal credit rating equivalent to 2% default probability over the next year. Drawdown upon default is assumed to be 75%. The bank has additionally estimated a LGD of 60%. The standard deviation of EDF and LGD is 5% and 25%, respectively. The ratio of unexpected loss to expected loss is closest to: The correct answer was B) 4.0. We can calculate the expected loss as follows: EL = AE × EDF × LGD​ Adjusted exposure = OS + (COM − OS) × UGD =$20,000,000 × (0.6) + ($800,000) × (0.75) =$18,000,000.
EL = ($18,000,000) × (0.02) × (0.60) =$216,000.

UL=EA(edf*variance(ldg) + ldg^2*variance(edf))^0.5
UL = $18,000,000 × [(0.02 × 0.252 + 0.62 × 0.052)]1/2 =$834,626
Ratio = $834,626 /$216,000 = 3.86 (closest to 4.0).

This make so sence to me as when double checking:
variance(edf)=0,0025<>edf(1-edf)=0,0196

they cant just take 0,02 then assume it is edf, they should solve edf(1-edf)=0.0025
with two solutons 0.0025 and 0,9974

anybody pls confirm? thanx

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
I agree, standard deviation of EDF = SQRT[EDF*(1-EDF)], and that's the way that assigned M. Ong solves for it.

Here are those assumptions in our XLS: 