Marchés de taux d'intérêt UE 104. Chapter 2. Tutorial. Fixed Income Markets (Marchés de taux d intérêt)

Transcription

1 Chapter 2. Tutorial Fixed Income Markets (Marchés de taux d intérêt) 1 Exercise 2.1 Consider a BTAN issued in the primary market with the following characteristics: Maturity = 5 years, Nominal value = 1,000,000, Coupon rate = 8%. A SVT (French primary dealer) is interested in purchasing this security for an annual yield of 8.5%. Determine the bidding price of the SVT? 2 1

2 Exercise 2.2 Consider a BTAN in the secondary market with the following characteristics: Maturity = 1 year and 38 days, Nominal value = 1,000,000, Coupon rate = 9%, Yield to maturity (taux actuariel) = 9.25%. Compute the price of the BTAN. 3 Exercise 2.3 * On December 12, 2001, the Karlex company announced an issuance program of bonds with the following features: maturity = 10 years, bullet maturity, issuance date = December 21, 2001, coupon frequency = annually, every December 21 coupon rate = 6%, par value = 2,000, redemption price = at par. Market conditions at issuance Yield required on the issue = 6.15% 4 2

3 Exercise 2.3 cont d 1. Given the yield required by the market for the issue, 1.1. what should be the issue price? 1.2. if the bond was issued at par, what should be the redemption premium? 2. Suppose that on February 29, 2008, the discount rate is equal to 5%. Compute, on that date, 2.1. the present value of the bond, 2.2. the accrued interest, 2.3. the clean price. 5 Exercise 2.4 * The Divan company has issued fixed-income securities for a global nominal amount of $112 million. Features Number of outstanding securities = 2.24 millions Maturity = 10 years Bullet maturity Issuance date = September 18, 2002 Coupon rate = 4.25%, Coupon frequency = semi-annual Coupon dates = September 18 & March 18 Issue price = at par Redemption price = at premium 6 3

4 Exercise 2.4 cont d 1. Compute (in dollar) 1.1. the nominal value of each bond, 1.2. the value of a coupon. 2. Market conditions at issuance: bond-equivalent yield equal to 4.45%. Compute the redemption price (price + premium). 3. Market conditions on the October 25, 2010: bond equivalent yield equal to 7%. Compute (in % of par value) 3.1. the present value of the bond, 3.2. the accrued interest, 3.3. the clean price. 7 Exercise 2.5 Suppose that an investor purchases a 15-year 8% coupon bond at par value ($100). The bond is redeemed at par. Coupon payments are semi-annual. 1. Without any calculation, give the value of the yield to maturity (bond-equivalent yield convention). 2. Compute the annual equivalent yield. 3. What are the conditions under which the yield to maturity is the actual rate of return of the bond. 8 4

5 Exercise 2.5 cont d 4. Assuming these conditions are realized, decompose the bond return by calculating 4.1. the total future value of the bond, 4.2. the total income in dollar, 4.3. the coupon payments, 4.4. the interest on interest, 4.5. the capital gain, 4.6. the dollar income without reinvestment, 4.7. the percentage of reinvestment income in the total dollar income, needed to produce a yield of 8%. 9 Exercise 2.6 * Suppose that an investor purchases a 10-year 8% coupon bond issued at par value ( 1,000). The bond is held until maturity and is redeemed at par. The yield to maturity is 8% and the reinvestment rate is 6%. 1. Compute the total return of the bond and the total euro income generated by the investment. 2. Explain why the total return is less than the yield to maturity. 3. What condition makes the total return equal to the yield to maturity? What condition makes it greater than the yield to maturity? 10 5

6 Exercise 2.6 cont d 4. Decompose the total return by calculating 4.1. the coupon payments, 4.2. the interest on interest, 4.3. the capital gain, 4.4. the percentage of reinvestment income in the total euro income. 11 Exercise 2.7 * An investor is considering the purchase of a 5-year floating-rate note that pays interest semi-annually. The coupon formula is equal to 6-month LIBOR plus 30 basis points. The current value for 6-month LIBOR is 5%. The price of this note is What is the value of the discount margin: 40 bp, 45 bp, 50 bp, or 55 bp? 12 6

7 Exercise 2.8 * Suppose that a 10% 15-year bond has the following characteristics: par value = 100, annual coupons, redemption at par, not callable for the next years, callable at 105 in 5 years, callable at par in 10 years. The price of the bond is Determine 1. the yield to maturity (taux de rendement actuariel à l échéance), 2. the yield to first call (TRA à l exercice du 1 er call), 3. the yield to first par call (TRA à l exercice du 1 er call au pair), 4. the yield to worst (TRA minimum). 13 Exercise 2.8 cont d 5. Assuming a reinvestment rate of 5% and a investment horizon of 6 years, compute the total return of the bond if it is called at the first call date. 14 7