# ACTSC445 Study Guide - Quiz Guide: Long-Term Capital Management, Space Shuttle Challenger, Emperor Xuan Of ChenExam

by OC2719308

School

University of WaterlooDepartment

Actuarial ScienceCourse Code

ACTSC445Professor

Jiahua ChenStudy Guide

QuizThis

**preview**shows half of the first page. to view the full**2 pages of the document.**ACTSC 445/845 – Fall 2014

ASSIGNMENT 1 DUE: Friday 3rd October, 12.50pm

Hand in to Chen Xu in TA Oﬃce M3 3108 between 12.00pm and 12.50pm.

1. Investigate one of the following risk management failures. You should write a brief

summary of the case (aim for around 500 words), followed by a list of the most critical

risks, using the classiﬁcation from the course notes. Explain brieﬂy, for each risk, why

you consider it relevant to the case.

Select one from

•The Walkerton Water Tragedy

•The space shuttle ‘Challenger’

•Long Term Capital Management

Notes:

- You may use any resources you ﬁnd, but you should use your judgement as to the

reliability of your sources.

- You should cite your sources.

- You should write your answers in your own words unless you are directly quoting

from a source, in which case you should make it clear that you are quoting from

someone else’s materials, and give proper attribution.

2. (a) Show that the CTE for N(µ, σ2) losses is

CT Eα=µ+σ

1−αφQα−µ

σ

where φ(z) is the standard N(0,1) density function, and Qαis the α-quantile of

the distribution.

(b) Hence, verify that the CTE is sub-additive for correlated normally distributed

losses.

3. A trader has a $0 VaR99% constraint for her 7-trading day losses. That is, her trading

strategy must have a 99% VaR less than or equal to 0 on a 7-day horizon. Assume 256

trading days in a year.

She has constructed a portfolio of derivatives on a stock with initial value S0= 100.

The value at T= 7/256 of ST/S0follows a lognormal distribution with parameters T µ

and T σ2, where µ= 0.05195 and σ= 0.31.

She has decided on the following strategy:

Purchase 1 million seven-day call options with a strike price of 87,

Sell short 1 million seven-day call options with a strike price of 88,

Finance the cost of the call options by selling short Mseven-day put options with

a strike price of 87.

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