7SSMM707 Risk Management

This paper is part of an examination and counts towards the award of a degree. Examinations are governed by the College Regulations under the authority of the Academic Board. Assessment Format: 7SSMM707 Examination 2020/21 Module code and title: 7SSMM707: RISK MANAGEMENT Examination Period: Period 2, June/July 2021 Time allowed: Students should spend no longer than 2-3 hours on this paper. The paper will be available for 24-hours from 10:00 BST on 01/07/2021. Student will need to submit their answers by 10:00 BST 02/07/2021. Word count: The answer to each question should not be more than 300 words (i.e., approximately 2/3 of a typed page single-spaced).

INSTRUCTIONS TO CANDIDATES:

1. There are 2 Sections in this paper:

• Section A – Answer TWO questions out of FOUR

• Section B – Answer ALL questions

1. If you answer more questions than specified, only the first answers (up to the specified number) will be marked.

2. Paste any required diagrams and graphs for your answers directly onto the answer sheet using software or uploaded photos.

3. A template answer sheet has been provided on the KEATS page, you should complete the first page ‘cover sheet’ and then type your answers below. Make sure you clearly indicate the questions you are answering (e.g. Section A, Question 1).

4. If you have a PAA cover sheet, you should include this in addition to the template answer sheet.

5. Save your work regularly, at least every 15 minutes.

ONLINE SUBMISSION INSTRUCTIONS:

1. Your answer sheet should be submitted via the Turnitin submission link on the module KEATS page.

1. Ensure your document is submitted through Turnitin with the title CANDIDATE ID – MODULE CODE- e.g. AB12345-7SSMM707

2. Once submitted please check you are satisfied with the uploaded document via the submission link.

3. If you experience technical difficulties uploading your assessment to KEATS please email a copy to mscbankingfinance@kcl.ac.uk with the subject of the email as CANDIDATE ID- MODULE CODE- PERIOD 2 ASSESSMENT. You should attach supporting evidence of technical issues where possible.

Section A -Answer only TWO questions.

Question 1

Suppose you hold a risky asset that delivers a return 𝑅". You wish to hedge against a decline in the price of this asset using a risk-free asset withreturn𝑟 andamarketindexwithreturn𝑅 .Explainhowyouwould $% allocate money between the risk-free asset and the market index so as to minimize your portfolio variance. [15 marks]

Question 2

A portfolio manager wants to hedge his stock portfolio against changes in stock prices. Construct a strategy using options so that changes in the portfolio value are limited in either direction. What is the cost of this hedge to the manager? [15 marks]

Question 3

For each of the following situations, suggest a way in which the respective risks can be hedged. Explain what instrument you would use, what position you would take (long/short), and how you will be able to meet your objective. a) Bank A has purchased 5-year BBB-rated corporate bonds, and is worried about default risk. b) A firm expects to borrow money in six months from today for a three-month period and is worried about interest rate risk. [15 marks] 2

Question 4

Describe and compare the model-building approach with the historical simulation approach for calculating the VaR. Does the VaR satisfy the subadditivity property? Explain why basing banks’ capital requirements on a risk measure that fails to satisfy subadditivity may create the wrong incentives for the bank. [15 marks]

Section B - Answer ALL Questions

Question 1

An insurance company must make payments to a customer of $10 million in 1 year and $4 million in 5 years. The yield curve is flat at 10%.

1. a) Compute the present value of the firm’s liabilities.

2. b) Compute the modified duration of the firm’s liabilities. What is the approximate percentage change in the value of liabilities predicted using the duration if all interest rates increase by 1 basis point?

3. c) If the company wants to immunize its obligations to this customer with a single zero-coupon bond, what maturity bond must it purchase?

4. d) “To reduce interest rate risk, an insurance company that has a positive surplus (i.e., the value of its assets exceeds the value of its liabilities) should invest in assets that have longer duration than its liabilities.” Explain whether you agree with this statement. [35 marks]

Question 2

A company has an 1-year bond outstanding with a face value of $100 and a coupon of 8% per year payable annually. The yield on the bond (expressed with continuous compounding) is 6.0%. Risk-free rates are 4.5% for all maturities. The recovery rate is 35%. Defaults can take place half way through the year. Estimate the risk-neutral default probability. [20 marks] 4

Question 3

1. a) Portfolio A consists of 500 shares of stock and 500 calls on that stock. Portfolio B consists of 800 shares of stock. The call delta is 0.6. Explain which portfolio has a higher dollar exposure to a change in the stock price.

2. b) You are long a call option on stock ABC. You have delta-hedged your position. You hear on the radio that the CEO of ABC has been arrested for running a massive Ponzi scheme. The stock price of ABC drops. Explain (qualitatively) how you would adjust your hedge. [15 marks]