EXAMINATION II: Fixed Income Analysis and Valuation Derivatives Analysis and Valuation Portfolio Management Questions Final Examination March 2010
Question 1: Fixed Income Analysis and Valuation (56 points) You are working in the Treasury department of an international bank. The bank is well-known and it can issue the government guaranteed bond if necessary. Your Management Board has asked for your advice related to the ongoing turbulences and dislocations in the financial markets. The current yield curve based on Mid-Swap rates is as follows (daycount convention: 30/360; 1 basis point = 0.01%). Year 1 2 3 4 Mid-Swap rate 3.50% 3.00% 2.70% 2.50% Implied spot (or zero) rate??? 2.48% Discount factor??? 0.90653 Table 1 a) Initially you are requested to provide some basic answers and calculations. a1) How would you define the above yield curve? (2 points) a2) Calculate the implied spot (or zero) rates and discount factors for the years 1 to 3 in the above table. (9 points) a3) Based on the pure expectation hypothesis, what are the projected yields for zero bonds in one year with times to maturity of 1, 2 and 3 years? a4) Please provide a graph which describes the way in which the price of a 4-year par bond develops from today (100%) until maturity at unchanged yields (no calculation of the bond prices is required, only an assessment of above/below/at 100% levels). Price 100% 0% 4 0 Years to redemption Page 1 / 9
b) You have identified a funding need for the bank in the 3 year time bucket. As a consequence, you are suggesting a 3 year bond issuance at an amount of EUR 3 billion. The related yield for non-government guaranteed paper of your bank stands at Mid-Swap +195 basis points (bps). Alternatively, you could suggest to your Management Board the issuance of a government guaranteed bond with a spread of +30bps over the Mid-Swap rate. In order to get such government guarantee, the bank would need to pay to the guarantor (the government) both i) 50bps p.a. as an arrangement fee and ii) 100bps p.a. to cover the protection cost. b1) What is the funding advantage (or disadvantage) in basis points when accessing the government guarantee? (5 points) b2) Calculate the present value of the funding advantage (or disadvantage) under b1) based on the planned issuance volume of 3bn Euro. Use the discount factors you calculated under a2); in case you did not calculate them then just take the yields from Table 1 as proxies for the spot rates and thus derive the discount factors; in case you did not solve b1) assume a 10bps funding advantage. (5 points) b3) Briefly describe the pros and cons of accessing the government guarantee under the given circumstances from the perspective of your bank. (4 points) c) As an additional precautionary crisis measure you are intending to establish a EUR 25bn liquidity portfolio of highly liquid government bonds. Assume that the average maturity of this portfolio is 3 years and the average yield of the related government bonds stands at Mid-Swap -70 bps. Calculate (in EUR) the annual cost of carrying such a liquidity portfolio by applying a refinancing cost of Mid-Swap +195bps. (4 points) d) Your Management Board also asks you to come up with an idea as to how to best capitalize on dislocations in the financial markets. Against this background you are contemplating the investment in a 1-year Asset Backed Security (ABS) with a fixed annual coupon of 4.5% at a current yield of Mid-Swap +295bps. d1) Calculate the total return of such an investment after one year assuming the security gets repaid at 100% ( holding period rate of return ). Use the swap rates for 1 year given in Table 1 as the yield basis before spread for today s ABS price. (3 points) d2) Outline the 3 most important risk factors associated with such an investment in the current turbulent market environment. (3 points) e) Finally, your Management Board is interested in a convertible bond issue from ABC Co. The company raises funds by equity and convertible bonds and has no other debt. It has a total of 1 million outstanding shares and its share price is 100 dollars. The convertible bond has a face value of 100 million dollars, maturity of 1 year, coupon of zero (i.e. a discount bond), conversion price of 100 dollars. Assume that the convertible bond will be converted to equity, redeemed as a bond or defaulted on depending solely on corporate value (the total value of equity and the convertible bond) at maturity. The Board asks you the following questions: Page 2 / 9
e1) If the convertible bond is converted to equity, what will be the increase in the number of ABC Co.'s shares? (3 points) e2) If the convertible bond is converted to equity at the end of 1 year, what will that imply about corporate value? (3 points) e3) If the convertible bond goes into default at the end of 1 year, what will that imply about corporate value? (3 points) Page 3 / 9
Question 2: Derivatives Valuation and Analysis (13 points) Drescotts Inc is a quoted company that does not pay any dividends. Its share price is currently USD 50. A securities company offers a European call option on this stock with a maturity of 1 year and a strike price of USD 40. Its offering price is USD 10. Assume that the continuously compounded interest rate is 10% per annum. Make the following calculations rounding to the second decimal point. The share price at maturity is denoted as S(1). a) You think there is an arbitrage opportunity by combining the stock of Drescotts Inc with the European call option the securities company offers. What kind of positions do you need to take at the current point in time in order to take advantage of this arbitrage opportunity? In your answer, consider the stock position to be 1 unit. (4 points) b) What is this investment s payoff at maturity? Draw a graph and mark the corresponding values on the axes, providing supporting calculations. (5 points) Payoff 0 S(1) c) Explain why the investment in a) is called an arbitrage opportunity. If the option price does not move after many investors take advantage of this arbitrage opportunity, will the share price rise or decline? Explain briefly. (4 points) Page 4 / 9
Question 3: Derivatives Valuation and Analysis (46 points) Consider a Credit Default Swap on Rocket Company plc [the Reference Entity] with a term of 3 years. In a simplified model, the Reference Entity can default during a year, subject to the condition that it did not default earlier, with a (conditional) probability of 2%. The assumed recovery rate is 40% and we assume that default can only happen in the middle of the year. For the sake of simplicity, we also assume that the CDS premium payment occurs annually in arrears at an annual rate s. The risk free interest rate is 3% continuously compounded on an annualized basis. In this question, ignore the CDS counterparty risk. a) Explain in general terms what a CDS is and describe its purpose. (5 points) b) Calculate for the Rocket Company the unconditional survival probabilities (i.e. the probabilities to survive until time t = 1, 2, 3 as seen at time zero) and the unconditional default probabilities (i.e. the probabilities of a default at time t = 1, 2, 3 as seen at time zero) for years 1 to 3 in the above case. Time (years) t = 1 t = 2 t = 3 Probability of Default at time t Probability of Survival until time t (4 points) c) Using the survival probabilities, calculate the present value of expected CDS premium payments by completing the following table, assuming a notional value of USD 1 and an annual premium payment of the CDS equal to s. Time (years) Probability of survival until time t Expected payment Discount factor 1 0.98 0.98 s 0.9704 2 3 Total PV of expected payments (10 points) Page 5 / 9
d) Calculate the present value of expected CDS payoffs and the present value of expected accrual payments by completing the following table. Explain the formulas you used to obtain the figures. Time (years) Probability of default at time t Recovery rate Expected payoff Expected accrual payments Discount factor 0.5 0.02 0.4 0.9851 1.5 0.4 2.5 0.4 Total PV of expected payoff (USD) PV of Expected accrual payments (14 points) e) Using the results obtained in c) and d), calculate the theoretical CDS spread. f) Suppose that an investor has bought the above CDS at the spread calculated under e), and shortly thereafter the CDS spread widens to 200 bps. Calculate the profit/loss amount, assuming that the subscribed notional amount is USD 1 million. (7 points) Page 6 / 9
Question 4: Portfolio Management (16 points) You are the financial advisor to your individual clients. You have been asked by one of your client to answer a number of questions relating to the real estate market [Note: the following questions are based on the general real estate market, not on specific situations which may prevail in certain countries]. a) Your client has only financial assets. He now wants to consider real estate investments as well. Explain to him how the return and risk parameters of real estate compare to the same parameters of stocks and bonds. Explain to him also which one of the following investments is usually least risky among them and why: residential property commercial property industrial property infrastructure b) You explain to him referring to an old study that the correlation between securitized real estate returns and stock returns was relatively high in many countries some years ago. Results in the 0.6-0.7 range for the correlation coefficient were not unusual. However, this correlation coefficient has been decreasing as a result of the growing efficiency of the securitized real estate market. Your client would like to make an indirect real estate investment and asks you if in the long term the return on indirect real estate investments tends to be more correlated to the stock market or to the real estate market. Provide an answer for your client. (4 points) c) Your client decides to make an indirect investment in residential property. He asks you if such an investment will improve the risk-return profile of his portfolio which currently only contains stocks and bonds. How would you answer him? Explain your answer. Page 7 / 9
Question 5: Portfolio Management and Derivatives in Portfolio Management (49 points) You are the fund manager of the BAT Euro Stock Fund. Following a meeting with your staff, you suggest protecting, partially or fully, your stock portfolio because you fear a deep corrective trend in the financial markets due to, first, a registered realised speculative bubble in the real estate market in the last period and, secondly, to the progressive increase of the VIX (CBOE Volatility Index). After having explained your point to the Board of Directors, you are asked to proceed. a) Before proceeding with the implementation of the portfolio insurance plan, you analyse the performance of the Fund in the last 6 months. In particular, you focus on the stock composition of the managed portfolio in the past semester, that is 65% in Euro Value Stocks and the remaining 35% in Euro Growth Stocks. a1) The total returns of the Euro Value Stocks and the Euro Growth Stocks over the period are respectively 4.5% and 3.2%. Compute the total return of the BAT Euro Stock Fund for the last semester. (4 points) a2) Would it have been better in terms of return performance to have had the portfolio wealth equally-weighted in the Growth and Value Stocks? Justify analytically. You charge your staff with working out a protective strategy on the BAT Euro Stock Fund for the next semester. The first target is to protect the managed portfolio against a decline in capital of more than 10% over the next 6 months. The stock portfolio, whose value is EUR 120 million, is well-diversified. The beta of the stock portfolio with the DJ EURO STOXX 50 index is equal to 1.12 and the last quotation of the DJ EURO STOXX 50 is 3,050. The index dividend yield is 2% p.a., while the dividend yield on the stock portfolio is equal to 2.5% p.a. (semi-annually compounded). Finally, the risk-free interest rate is 5% p.a. b) Initially, your financial team proposed to use index put options to insure the whole managed portfolio. b1) Assuming that the insurance cost is to be borne externally from the managed funds, which strike price for options maturing in exactly 6 months should you consider? (10 points) b2) How many option contracts should you purchase or sell, given that the option size with respect of the DJ EURO STOXX 50 is EUR 10 per index point? (4 points) c) The above stock portfolio is well-diversified. What if the stock portfolio was not welldiversified? From a risk management standpoint, discuss the problems of hedging a portfolio that is not well-diversified, providing a comparison with the well-diversified case. (7 points) d) The protective put strategy described above is said to be a static strategy: once initiated, no further intervention is needed, whatever the evolution of the financial market. Page 8 / 9
d1) What are the main practical problems when applying static portfolio insurance? List three of the problems and briefly explain them. d2) Briefly, make a comparison between a static insurance strategy and the application of the so called dynamic portfolio insurance. (7 points) e) The use of a synthetic put option to insure a stock portfolio enables the investor to overcome some of the practical problems related to static portfolio insurance. Based on the case at point b), describe how to create a long synthetic put option by trading directly in the underlying assets, when N ( d 1 ) = 0.5942 (where N indicates the cumulative distribution function of the Normal distribution and d 1 the characteristic coefficient in the well-known Black & Scholes Model). (5 points) Page 9 / 9