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1 MCQ Questions 1) C 2) C 3) B 4) B 5) A 6) D 7) D 8) B 9) C 10) C 11) D 12) C 13) D

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2 PART B: Bonds QUESTION 1 [15 Marks] Students need to determine the 2-year and 2-year forward rates. They are given the YTMs of coupon bonds, so they need to derive spot rates first, which they then use to derive forward rates, the forward rates will determine how much return they will realise from rolling over the bond . 𝐻?? = ? 1 − ? 0 + ? ? 0 Derive the spot rates for 2-year spot rate first. The 2-year coupon bond has a coupon rate of 7%, par value and price of R98.21. 98.22 = 7 1+6% + 𝑅107 (1+𝑦 2 ) 2 𝑦 2 = 8.07% . Derive the spot rates for 3-year spot rate first. The 3-year coupon bond has a coupon rate of 8%, par value and price of R100. ?97.47 = 8 1 + 6% + 8 (1 + 8.08%) 2 + ?108 (1 + 𝑦 3 ) 3 𝑦 3 = 9.38% Determine the forward rates for year 2 and year 3 ? ? = [ (1 + 𝑦 ? ) ? (1 + 𝑦 ?−1 ) ?−1 ] − 1 ? 1 = [ (1+8.07%) 2 (1+6%) 1 ] − 1 = 10.2% ? 2 = [ (1 + 9.38%) 3 (1 + 8.07%) 2 ] − 1 = 12.1% The forward rates are 10.2% and 12.1%. Nothando believes are underestimated. Forward rates as per Nothando’s assumptions ? 1 = 10.2% + 1% = 11.2% ? 2 = 12.1% + 2% = 14.1% If she buys a 1-year zero coupon bond she will pay R94.34 and receive R100 at the end of year 1. Reinvesting that R100 will yield 11.2% for the second year and 14.1% for the third year. ? 0 = 94.34 ? 3 = 100(1 + 11.2%)(1 + 14.1%) = 126.88 𝐻?? = 126.88−94.34 94.34 = 34.50% QUESTION 2 [10 Marks]
3 a) A flat yield curve implies that all spot interest rates are the same. When the spot rate is the same for every maturity, successive applications of the forward rate model will show that all the forward rates will also be the same and equal to the spot rate. b) Reinvestment risk is the risk caused by reinvesting fixed payments at a lower rate due to an environment of declining interest rates. The investor of a callable bond is exposed to this risk because as interest rates fall there is a greater likelihood that the callable bond will be called by the issuer firm and the investor will be forced to reinvest the proceeds at a lower interest rate. c) A puttable bond is typically issued as it is potentially advantageous to the buyer of the bond and therefore sells at a premium when issued, compared to vanilla bond it sells a higher price. Some students will say a puttable bond may be issued at a lower coupon compared to a similar vanilla bond (to compensate the issuer), hence the issuer will benefit from low interest payments. Some students will say a company that is less attractive to investors may issue a puttable bond to attract investors because a puttable bond is more beneficial to investors. d) The Macaulay duration is expressed in years (or time) and it shows the weighted average number of years required to recover the initial costs of the bond, whereas the modified is expressed as percentage and it shows the sensitivity of the bond price to a 1% change in interest rates. Y ou use the Macaulay duration for immunisation Markers: e) One possible answer: I disagree, it’s not perfect measure for the following reasons; its assumptions are unrealistic, its assumes you hold the maturity, hence you actual return will be different from the YTM if you don’t inte nd to hold the bond to maturity, it also

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• Fall '19
• dangote cement

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