Part 3 (18 marks) Fixed Income Securities The following table shows the current LIBOR continuously compounded rate with different maturities: For example, the 1-mth LIBOR is 5.0% p.a. compounded continuously. You can treat the LIBOR rates presented in the table above as the discount rates/spot rates with different maturities. Use this table to answer the following two questions (Q1 and Q2 only). 1. (6 marks) Consider a fixed income security with 12 months remaining to maturity. Every quarter (including on maturity), the security holder will receive a variable interest equals to the 3 -mth LIBOR rate In addition, 6 months before maturity (and only at 6 months before maturity), the security holder will receive a variable interest equals to the 6-mth LIBOR rate. The holder will also receive the $100 face value on maturity. Required: (a) ( 2 marks) Draw a timeline and label the cash flows (i.e. coupon payments, buying and selling activities) associnted with the FRNs clearly, (b) (4 marks) What is the current price of the security? Show all of your calculations. 2. (4 marks) Consider an invense flonting rate coupon bond with 1 year remaining to maturity. On maturity, bondholders are expected to receive \$100 face value. Coupons are prid quarterly, and the current 3-mth LIBOR obecrved rate is 5.24% p. . The arnual coupon rate is specified as: Annual coupon rate =24%pa.4C where C is the annual 3-mth LIBOR rate. A soune, for nimplicity, that the aumal 3meth LIBOR number). Required: What is the current price of the invensi flosting rate goupon bond? Show all of your calculations. 3. (8 marks) Several months ago, Swaping Inc issued a unique fixed income security, As of today, the security is maturing in 10 months. The security pays seni-anmual interest, which is equal to X% mimus 2 p.a., where X is equal to the sum of the 6-month and 3-month LIBOR, rates. That is, in mery six months, the interest is defined as: [2L6+4L3]22% where 1.6 (quoted on an annual basis, in \%) is the 6-month LIBOR and 13 (also quoted on an annual basis, in % ) is the 3 -month LIBOR. Assume that the 6-month LIBOR is nlways greater than the 3-month LIBOR and the 3-month LIBOR is alwnys greater than 2% pa. At maturity. the company will pay $100 as the face value of the security. Also, assume all other bonits and floating rate notes have a face value of $100, respectively. Table 1 shows the 3-month and 6-month LIBOR rates observed several months agor For example, two months ago, the 3-month. LIBOR rate was ohrerved at 4.086pa. Thble 2 shows the predieted 3 -month and 6 -month LIBOR rates over the ned few montha: For example, four months from today, the 3-month LIBOR rate is prodicted equal to 6.0% p.a. Table 3 shows the current LIBOR rates (asstine continuous compounding) with different mathrities over the next 10 months: For example, the current 3-month LIBOR rate is 5.9% p.a. compounded contiruonaly. Requirod: Calculate the current price of the sccuinty and describe how you conatruct the replicate portfolion uking zero coupon bond(s) and FRN. Show all working
