Pricing of Bonds



Chapter 2 - Pricing of BondsAnswer the below questions. Bonus Questions: For parts (a) and (b) compute the Wealth Index, HPR, Annual HPR, Geometric Mean Return and for part (b) the EAR.The portfolio manager of a tax-exempt fund is considering investing $500,000 in a debt instrument that pays an annual interest rate of 5.7% for four years. At the end of four years, the portfolio manager plans to reinvest the proceeds for three more years and expects that for the three-year period, an annual interest rate of 7.2% can be earned. What is the future value of this investment?PT = P0(1+r1)n1 (1+r2)n1P7 = $500,000(1.057)4 (1.072)3 = $768,872.47.Suppose that the portfolio manager in Question 3, part (a), has the opportunity to invest the $500,000 for seven years in a debt obligation that promises to pay an annual interest rate of 6.1% compounded semiannually. Is this investment alternative more attractive than the one in Question 3, part a?PT = P0(1+r/2)n* 2P7 = $500,000(1 + 0.061/2) 7 * 2 = $761,450.98.Part (a) is better. Obviously the initial amount is irrelevant.(1.057)4 (1.072)3 = 1.5377(1 + 0.061/2) (7 * 2) = (1.0305)14 = 1.5229Note for part (a):1.5377 is the wealth index.53.77% is the total holding period return.(1.5377)(1/7) – 1 = 6.34% is the annualized holding period return.6.34% is also the geometric mean return.Note for part (b):1.5229 is the Wealth Index.52.29% is the total Holding Period Return.(1.5299)(1/7) – 1 = 6.19% is the Annualized Holding Period Return.6.19% is also the Geometric Mean Return. 6.19% = (1 + 0.0610/2)2 – 1 = is the Effective Annual Rate for 6.10% APR Semi-Annual Calculate for each of the following bonds the price per $1,000 of par value assuming semiannual coupon payments.BondCoupon Rate (%)Years to MaturityRequired Yield (%)A897B9209C61510D0148Compute the price per for $1 of par value and then multiply by par value (of $1,000 in this case).You should be able to do this in Excel.BondPMTNPERRATEPVPriceA0.04183.5%1.06595$1,065.95 B0.045404.5%1.00000$1,000.00 C0.03305%0.69255$692.55 D0284%0.33348$333.48 Suppose that you are reviewing a price sheet for bonds and see the following prices (per $100 par value) reported. You observe what seem to be several errors. Without calculating the price of each bond, indicate which bonds seem to be reported incorrectly, and explain why.BondPriceCoupon Rate (%)Required Yield (%)U9069V9698W11086X10505Y10779Z10066If the required yield is the same as the coupon rate then the price of the bond should sell at par value. This is the case of bond Z.If the required yield decreases below the coupon rate then the price of a bond should increase. This is the case for bond W. This is not the case for bond V so this bond is not reported correctly. If the required yield increases above the coupon rate then the price of a bond should decrease. This is the case for bond U. This is not the case for bonds X and Y so these bonds are not reported correctly. What is the “dirty” price of a bond?The “dirty” (or “full” or “Invoice”) price is the amount that the buyer agrees to pay the seller. It is the agreed-upon (quoted) price plus accrued interest. The price of a bond without accrued interest is called the clean price. The exceptions are bonds that are in default. Such bonds are said to be quoted flat, that is, without accrued interest.Explain why you agree or disagree with the following statement: “The price of a floater will always trade at its par value.”Disagree. The price will be different from par if the bond’s credit has changed or the reference rate has changed so much that a cap or floor is in effect. The coupon rate of a floating-rate security (or floater) is equal to a reference rate plus some fixed spread. For example, the coupon rate of a floater might be equal to 6-month LIBOR (the reference rate) plus 50 basis points (the spread).The price of a floater depends on two factors: (1) The spread over the reference rate and (2)?Restrictions on the resetting of the coupon rate. For example, a floater may have a maximum coupon rate called a cap or a minimum coupon rate called a floor. The price of a floater will trade close to its par value as long as (1) the spread above the reference rate that the market requires is unchanged and (2) neither the cap nor the floor is reached.However, if the credit on the bond changes and the market requires a larger (or smaller) spread than the bond pays, the price of a floater will trade below (or above) par. If the coupon rate is capped, the floater will trade below par. If the coupon rate is floored, the bond will trade above par. ................
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