# Unexpected Loss

Since I will never see the answers to the actual test, I am plagued by one question and was wondering if anyone can offer advice on how it can be solved. I know the formula for UL. To solve it, you need 5 inputs:

Principal, Probability of Default, Loss Ratio, Loss Ratio Variance, Probability of Default Variance

On the exam, we were given 4 of these inputs, however Probability of Default Variance was NOT given. How could we possibly answer without knowing this input? I just wagered a guess and used the following thought process, however I know it is not correct. I took the given Probability of Default as the mean of this variable, multiplied by 1.65 (1 standard deviation), and then took the square root of the difference.

Any input on how this should have been solved would be greatly appreciated.

If you notice in book 4 the unexpected loss section briefly mentions that you have to use a binomial variance for probability of default, assuming a 2 state model. var pd = pd(1-pd). In that example it was (.055)*(1-.055)=.051975. However, I did not get an answer that was one of the choices.

Good catch. I didn’t even consider binomial variance. Thanks for the answer.