7SSMM707 Page 1 of 5 SECTION A – Answer only TWO questions Question 1 A fund manager owns a portfolio of 10 stocks. Explain how the manager can reduce the systematic risk of his portfolio by 10% over the next year using futures. Will the expected return on the manager’s portfolio also drop by 10% Is it possible for the manager to perfectly hedge his exposure to equity risk Explain your answers. [15 marks] Question 2 The Swiss National Bank (SNB) introduced a peg to the Euro in 2011. On January 15, 2015, the SNB suddenly announced that it would no longer hold the Swiss Franc at a fixed exchange rate to the Euro. The graph below shows you the performance of the Swiss Franc against the Euro over the five years leading to the peg abandonment: before 2011 there was a period of high exchange rate volatility, followed by a period of stability while the peg was in place (from September 2011 to January 2015), and a dramatic one-day surge upon the peg’s abandonment. See Next Page 7SSMM707 Page 2 of 5 Explain how you would calculate the daily 95% VaR of your exposure in the EUR/CHF currency pair while the peg was in place using the model building approach. [15 marks] Question 3 At the beginning of 1995, General Motor’s pension funds were under- funded by $9.3 billion. Even though the company injected $10.4 billion during the year, at the end of 1995 the pension funds were still underfunded. Knowing that interest rates dropped during 1995, explain what must have happened. Explain how GM could have hedged its risk using (i) an immunization strategy and (ii) interest rate swaps. [15 marks] Question 4 a) What does the option delta refer to For a standard European put option, draw the graph of the delta as a function of the price of the underlying asset. b) You have delta hedged a long call position on a stock. The stock price drops. Explain how you would adjust your hedge. [15 marks] See Next Page 7SSMM707 Page 3 of 5 SECTION B – Answer ALL Questions Question 1 Consider a 5-year bond with a face value of $100 that pays an annual coupon of 6% and is currently rated BBB. The expected recovery rate in case of default is 51.13%. In the table below, you are given the probabilities that in one year (i) the bond issuer maintains its BBB rating, (ii) is upgraded to AAA, AA or A or downgraded to BB, B or CCC and (
iii) defaults. Rating Probability (%) AAA 0.02 AA 0.33 A 5.95 BBB 86.93 BB 5.3 B 1.17 CCC 0.12 Default 0.18 Consider also the one-year forward yield curve for zero-coupon bonds with different maturities and credit ratings (rates are discretely compounded): Years to Maturity Rating 1 year 2 years 3 years 4 years AAA 3.60% 4.17% 4.73% 5.12% AA 3.65% 4.22% 4.78% 5.17% A 3.72% 4.32% 4.93% 5.32% BBB 4.10% 4.67% 5.25% 5.63% BB 5.55% 6.02% 6.78% 7.27% B 6.05% 7.02% 8.03% 8.52% CCC 15.05% 15.02% 14.03% 13.52% See Next Page 7SSMM707 Page 4 of 5 a) Compute the volatility of the above bond in one year. b) Is the volatility a coherent risk measure Explain. c) Compute the 1-year Value-at-Risk and Expected Shortfall of the above bond at a 99% confidence level. [25 marks] Question 2 A farmer is currently growing wheat and plans to sell it in September next year. He needs to plan his budget now, because of upcoming expenses. Suppose that the futures price of wheat for September delivery is ￡100 per ton. There is 50% probability that the spot price of wheat in September will be ￡90 per ton or ￡110 per ton. a) Suppose that the farmer is certain that he will need to sell 2 tons of wheat in September. Explain how the farmer could lock in today his future revenue. b) Suppose now that the farmer is not certain about the quantity of wheat he will produce and therefore will need to sell in September. For each possible price of wheat, there are two equally likely quantities, i.e., there are four equally likely price-quantity pairs, which are shown in the Table below. Price (￡) Production (tons) 90 2.5 90 1.8 110 2 110 1.5 7SSMM707 Page 5 of 5 i. Suppose the farmer takes a futures position on his expected production of wheat in September. Will this strategy help him reduce his risk Explain why. ii. Design a hedging strategy that minimizes the variance of the farmer’s revenue in September. [25 marks] Question 3 You hold a bond portfolio that consists of (i) a 4-year bond with a face value of $100 that pays an annual coupon of 10%, and (ii) a 2-year bond with a face value of $100 that pays an annual coupon of 20%. The yield curve is flat at = 5%. You are worried about fluctuations in the price of your portfolio. Explain how you can hedge your risk using 3-year zero-coupon bonds with a face value of ￡100. [20 marks] End of Paper