ACTY 6291 Investments Semester 2 2015 Question 3: Bond Valuation 20 Marks a) A T

Question

ACTY 6291 Investments Semester 2 2015 Question 3: Bond Valuation 20 Marks a) A Treasury bond, maturing on 15 September 2017, has a face value of $100 and pays an annual coupon interest rate of 6.50% semi-annually on 15 March and 15 September each year. The required yield on bonds of this type is 5.70%. What is the maximum price you would be willing to pay for this bond if the settlement date is 22 June 2015? Show your calculations. 5 marks A bond pays semi-annual coupons of 6.70% pa. and is currently trading at a yield to maturity of 8.00% pa. with a maturity of two years and a face value of $1,000. Calculate the duration of this bond. Show your calculations and interpret your answer. b) 5 marks

Explanation / Answer

Inflow 1 Date Interest PVF@2.85% (5.7/2) Discounted inflows 15-Sep-15 3.25 0.9723 3.160 15-Mar-16 3.25 0.9453 3.072 15-Sep-16 3.25 0.9192 2.987 15-Mar-17 3.25 0.8937 2.904 15-Sep-17 103.25 0.8689 89.716 (includes maturity amount of $100) PV of total inflows of the bond 101.840 Hence, the maximum price that can be paid for the bond on 22nd June 2015 is $101.840 Note: Due to semi annual payment, discount rate applied is 5.7%/2. coupon rate is 6.5%/2=3.25% 2 Maturity = 2 years semi annual coupon rate p.a = 6.7% : semi annual rate is 6.7%/2=3.35% YTM =8% Face value = $1000 Period cash flow Period*cashflow PV @4% (8%/2) PV of the cash flows 1 33.5 33.5 0.9615 32.21 2 33.5 67 0.9246 61.95 3 33.5 100.5 0.8890 89.34 4 1033.5 4134 0.8548 3533.76 Total 3717.26 Duration of the bond = $3717.26/1000= 3.717 Duration is the measure of bond's sensitivity to interest rate changes. The higher the bond's duration, the greater its sensitivity to the change in price, which is volatility. I did not use formula method, which is complicated and not easy to understand. Let us assume in the above example that the market yield increases by 20 basis points, which means 0.2% Then, the approximate change in bond's price is; (-3.717*0.2%) = 0.007434 or -0.7434% Note: It is -ve as, when bond yield increases, the price decreases & vice versa.

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