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550_446_2010 TA 03

# 550_446_2010 TA 03 - 550.446 Risk Management Analysis and...

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550.446 Risk Management Analysis and Hedging, Spring 2010 TA Section 03 Peter C.L. Lin [email protected] 1 Homework Review 7.19 The delta with respect to the fist factor is 0 . 21 × 5 + 0 . 26 × ( - 3) + 0 . 32 × ( - 1) + 0 . 35 × 2 + 0 . 36 × 5 + 0 . 36 × 7 + 0 . 36 × 8 = 7 . 85 . Similarly, the deltas with respect to the second and third factors are 1 . 18 and - 1 . 24, respectively. The relative importance of the factors can be seen by multiplying the factor exposure by the factor standard deviation. The second factor is about 1 . 18 × 6 . 05 7 . 85 × 17 . 49 = 5 . 2% as important as the first factor. The third factor is about 1 . 24 × 3 . 10 1 . 18 × 6 . 05 = 53 . 8% as important as the second factor. 8.12 (a) A loss of \$1 million extends from the 94 percentile point of the loss distribution to the 96 percentile point. The 95% VaR is therefore \$1 million. (b) The expected shortfall for one of the investments is the expected loss conditional that the loss is in the 5 percent tail. Given that we are in the tail there is a 20% chance than the loss is \$1 million and an 80% chance that the loss is \$10 million. The

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