Session 1- Pricing of Bonds.pdf

1 calculate the reinvested coupons until the end of

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1. Calculate the reinvested coupons until the end of 1st , 2nd, 3rd, and 4th or maturity. 2. Calculate the total value =bond price + reinvested coupons. 3. Find the IRR, given the cost of the bond at actual time. 18/10/17 Fixed Income Securities 28 Year 1 2 3 4 5 Bond Price 100 100 100 100 100 Reinvested Coupon 8 16.64 25.97 36.04 46.93 Total value 108 116.64 125.97 136.04 146.93 IRR 8% 8% 8% 8% 8%

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How to find the sum of reinvested coupons? Set C=8%, y=8%, N=5, year PV=0, FV reinv_coupons=? Reinvested coupons at 8% yield for 5 years = \$46.93 The total future cash inflow? Is the sum of reinvested coupons plus the selling price of the bond. P+ FV reinv_coupons =100+46.93=\$146.93 IRR? Set the C=0 in the calculator. Solve for the yield given the PV=100. The answer: The IRR=? Challenge: What is the IRR if you hold the bond for only 2 years and yield drops to 7% just before you would sell the bond? 18/10/17 Fixed Income Securities 29 Conventional Yield Measures: IRR
Conventional Yield Measures: YTM 2- The Yield to Maturity (YTM) is the yield of the investment that makes the present value of the future cash inflows equal to the actual bond price. ,where y is YTM. o The YTM is the expected return on the investment given the actual price. o The YTM is a forward looking concept. 18/10/17 Fixed Income Securities 30 ( ) = + = N t t t y CF P 1 1

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Conventional Yield Measures: YTM An alternative interpretation: The YTM is the implied reinvestment rate of bond coupons. The investor is indifferent between investing, the amount that equals the actual bond price, at y yield rate for N years or reinvesting the cash ﬂows at YTM for the remaining numbers of years. Note that y=YTM 18/10/17 Fixed Income Securities 31 ( ) ( ) ( ) N N N N CF y CF y CF y P + + + + + = + ... 1 1 1 2 2 1 1
Conventional Yield Measures: YTM We know that a 20year maturity bond is trading at 80. The coupon for the bond is 5% and paid annually. What is the YTM? Given the bond pricing formula, solution not easy. Use guess and trial method. Check first whether the price is lower/higher than par. Input different yields and price the bond. Solution somewhere around 6.85%. Straightforward if using financial calculator. What is YTM if the bond is trading at 120? 18/10/17 Fixed Income Securities 32 Yield Price 5.5% 94 5.7% 91 6.5% 83.4 6.8% 80.6 6.9% 79.7

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Complications 18/10/17 Fixed Income Securities 33
Conclusion The price of the bond depends on time to maturity, yield as well as coupon rate. The price of the bond at maturity is always 100. Price relationship to yield is negatively convex. Yield to maturity is the yield of the investment that makes the present value of the future cash inflows equal to the actual bond price. Internal rate if return is the rate that makes the present value of the future cash inflows equal to the cost of investment. 18/10/17 Fixed Income Securities 34

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APPENDIX REVIEW 18/10/17 Fixed Income Securities 35
Reviewing Time Value Future Value: The future value (FV n ) of any sum of money invested today is: P n = P 0 (1+r) n o n = number of periods o P n = future value n periods from now (in dollars) o P 0 =original principal (in dollars) o r = interest rate per period (in decimal form) o (1+r) n represents the future value of \$1 invested today for n periods at a compounding rate of r 18/10/17 Fixed Income Securities 36

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Reviewing Time Value When the same amount of money is invested periodically, it is referred to as an annuity.
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