# Examination II. Fixed income valuation and analysis. Economics

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1 Examination II Fixed income valuation and analysis Economics Questions Foundation examination March 2008

2 FIRST PART: Multiple Choice Questions (48 points) Hereafter you must answer all 12 multiple choice questions. Please check the correct answers in the boxes. Only one answer is correct per question and you should check only one box. For each question you have first the number of points given for a correct answer and then the points subtracted for a wrong answer. If you do not answer a question it will count as zero points. If you change your mind, surround the marked answer. The answer surrounded with a circle will not count. 1. Economics (4 points / point) The following data represents country A: Nominal GDP for 2005 Real GDP for 2006 GDP Deflator for 2006 = USD 175 billion = USD 185 billion = 1.375% more than the GDP Deflator of the reference year. The Nominal GDP of the country for the year 2006 is USD billion. USD billion. USD billion. USD billion. 2. Economics (4 points / point) For a country having a closed economy, the relation between its GDP and GNP can be described as, Its GDP is equal to its GNP. Its GDP is more than its GNP. Its GDP is less than its GNP. Insufficient data to know the relation. 3. Economics (4 points / point) In an open economy, the balance of payments of any country; Is always zero. Is strictly positive only if net exports are positive. Is strictly positive only if net exports are negative. Insufficient data to answer. Page 1 / 8

3 4. Economics (4 points / point) Which of the following statements is wrong regarding the IS-LM model? The demand for goods and services depends on the interest rate of the economy. The demand for liquidity (money) for the transaction motive does not depend on the interest rate of the economy. The government expenditure depends on the level of the output of the economy. The money (liquidity) supply does not depend on the level of interest rates in the economy. 5. Economics (4 points / point) Sometimes one says that exchange rates follow an ARCH process, i.e. an Autoregressive Conditionally Heteroskedastic process. What can you say about ARCH features? Returns are serially independent, i.e. the return and the volatility have no particular temporal structure. The returns volatility is serially correlated (i.e. correlated through time). There is no volatility clustering. No financial data presents this feature. 6. Fixed income (4 points / point) The 1 year spot rate is 3.95%, while the 2 year spot rate is 4.05%. Suppose you buy a two-year zero coupon bond; after 1 year, the yield curve has remained unchanged. What is the total return of your investment after one year? Less than 4.00%. 4.00%. 4.05%. Greater than 4.05%. Page 2 / 8

4 7. Fixed income (4 points / -2 points) Suppose that the interest rate curve has a parallel shift downward: which of the following bonds will have the larger price appreciation? A 5-year fixed rate bond with a duration of 4 years. A floating rate note linked to short term rates. A 10-year zero coupon bond. 8. Fixed income (4 points / point) The 3-year spot rate is 4%; the 5 year spot rate is 5%; calculate the 2-year forward rate 3 years from now (i.e. the forward rate from end of year 3 to the end of year 5). 2.00%. 3.52%. 4.52%. 6.52%. 9. Fixed income (4 points / point) Which of the following statements is wrong? Investors should buy low coupon securities and sell high coupon securities if they expect the market yield to decrease. Investors should buy high coupon securities and sell low coupon securities if they expect the market yield to increase. For a given maturity and a given initial market yield, the volatility of a bond s price decreases as the coupon rate increases. For bonds having different coupon rates but identical maturity dates and yields to maturity, the percentage change in the value of such bonds is larger, the larger the coupon rate for any given change in the yield to maturity. Page 3 / 8

5 10. Fixed income (4 points / -2 points) The Macauley duration of a bond is Always smaller than the bond s time to maturity. Always bigger than the bond s time to maturity. Smaller than or equal to the bond s time to maturity. 11. Fixed income (4 points / point) The price of a bond in local currency is dependent On the yield curve, the quality of the issuer, the maturity and the coupon of the bond. Only on the quality of the issuer. Only on the coupon and the maturity of the bond. None of the above answers is correct. 12. Fixed income (4 points / -2 points) In which economic situation can an inverted yield curve be observed? When the market expects a solid economic growth in an inflationary environment. When the market expects a strong deceleration of the economy in a non-inflationary environment. An inverted yield curve can never be observed. Page 4 / 8

6 SECOND PART: Open Questions (112 points) Question 1: Economics (36 points) a) Defining aggregate investment as the fixed investment made by the private sector to build capital stock. a1) Describe the relation between aggregate investment and real interest rates (capital costs). Explain the relation in economic terms. (7 points) a2) Describe the investment relation with respect to the production level in economic terms. (5 points) b) In summer 2007 the financial sector was subjected to the Subprime crisis. One of the main consequences of this crisis was the risk of liquidity supply contraction between commercial banks. Assume a closed economy. b1) Using the IS-LM model, explain what the consequences are of a money supply contraction on the macroeconomic equilibrium. Describe in detail firstly the money market and secondly at the macroeconomic level. Answer by using economic terms and graphics. (18 points) b2) What could be the appropriate solution in terms of monetary policy to limit the consequences of the Subprime crisis? Explain in detail (step by step) in economic terms and by using the IS-LM model. (6 points) Page 5 / 8

7 Question 2: Fixed income (34 points) You have the following bonds (A and B) in your portfolio and are planning to invest in Bond C which is a callable convertible bond. All the bonds have a par value of EUR 100 and have an annual coupon payment which has just been paid. Bond Coupon Price YTM Term to maturity Duration (years) (years) Number* A 6.00% P A YTM A B 6.75% P B 6.00% 5 D B 100 C 6.50% % * Number = Number of bonds in the portfolio a) If the one-year spot rate (R 0,1 ) is 5.00% and the one-year forward rate at the end of the first year (F 1,2 ) is 5.50%, calculate the values for P A and YTM A in the table above. (6 points) b) Calculate the price (P B ) and the duration (D B ) for Bond B. (6 points) c) State the various methods that you could use in deciding whether or not to invest in Bond C. Which method would you prefer and why? (6 points) d) Bond C has a conversion ratio of 5 and is callable after 3 years with a call trigger of 115%. If you suppose that the underlying price will move upwards in such a way that the convertible will be called (i.e. its price reaches the call price of 115%), should you invest in Bond C, if a straight bond of a similar rating and maturity yields 6.50%? Clearly state your assumptions. (5 points) e) Assuming that you have invested in Bond C, calculate your portfolio duration. (5 points) f) Explain the significance of duration as a measure of bond risk. What are its implicit assumptions and restrictions? (6 points) Page 6 / 8

8 Question 3: Fixed income (22 points) Your customer wants to invest an amount of CHF 1 million in bonds. He cannot decide whether he should follow a barbell or a bullet strategy. To show him the effects of an interest rate change, you have these three bonds to choose from. Bond Coupon Maturity (years) Price Yield to maturity (YTM) Duration (years) A 2.75% % 1.97 B 3.00% % 6.41 C 4.00% % a) Create a barbell portfolio using bonds A and C which matches the duration of bond B, computing the proportions of the two bonds in the portfolio. (3 points) b) Assume a sudden change of the interest yield curve: 2 years = +50 basis points 7 years = + 5 basis points 20 years = -30 basis points b1) Using the modified duration, calculate the impact of this change in relative and absolute terms on a bullet portfolio consisting of CHF 1 million (market value) invested in bond B. (4 points) b2) Using the modified duration, calculate the impact of this change in relative and absolute terms on the barbell portfolio created under question a). (11 points) b3) Which of the two strategies bullet or barbell would be the better alternative? Explain by using the results found under b1) and b2). (4 points) Page 7 / 8

9 Question 4: Fixed income (20 points) You hold the following zero-coupon bond portfolio: Bond Coupon Maturity Face value CHF A years 200,000 B years 300,000 In exactly 5 years, you have the possibility to buy your parents house for the amount of CHF 500,000. As you do not intend to borrow money the whole bond portfolio is assigned for financing this transaction. The market yield is currently 3.5% for all maturities. a) Calculate on the asset side the present value and the duration of the bond portfolio. (6 points) b) Calculate on the liability side the present value and the duration of the house buying transaction. (3 points) c) Calculate your actual surplus. (3 points) d) To immunize the surplus you could increase or decrease the market values or the durations on the asset or the liability side. Please tick the right boxes for this specific case. (4 points) Market value Duration Asset side increase decrease increase decrease Liability side increase decrease increase decrease e) You decide to change the house buying date to immunize against parallel interest rate shifts. Calculate the new date. (4 points) Page 8 / 8

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