Question

1. Calculate the coefficient of variation of the following distributions and identify which distribution has the greatest risk. ( You may do the calculation in the Excel but show your work here for partial credits.) (3 points)

Distribution 1                          Distribution 2                        Distribution 3        

Outcome Prob                  Outcome Prob Outcome   Prob

       $100      0.10                     $100            0.20                   $0             0.30

       $400      0.20                     $500            0.30                   $200          0.10

       $800      0.70                     $600      0.50                         $1000         0.60

2. Assume that a loss history is normally distributed with a mean of $5,000 and a standard deviation of $1,500.
3. 1. What’s the probability that the next loss will be greater than $5,750? (1.5 points)

2. If the risk manager is willing to tolerate 2% chance that costs will be greater than the maximum probable loss, what is the maximum probable loss level? (1.5 points)

3. In what range, with 95 % certainty, can we expect the losses to fall this coming year? (2 points)

3. Assume the investment return of a mutual fund during a month follows a normal distribution with a mean of 0.04 and a standard deviation of 0.01. For a fund manager with a risk tolerance level of 1%, what would be the estimated Value at Risk of the fund return? (2 points)

NOTE: You may use the function of morm.dist ( ) and norm.inv ( ) in Excel to figure out the probability of a normal distribution and the z score of a corresponding probability

Answer 1