A. Caggia, M.Armanini Financial Investments & Pricing

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A. Caggia, M.Armanini Financial Investments & Pricing 2015-2016 Pricing Bonds A. Caggia, M.Armanini Financial Investments & Pricing 2015-2016

Fixed Income Securities Fixed income securities provide a certain Yield to Maturity (YTM), Note that the yield is certain only if the security is kept untill maturity! Short Term Treasury (Treasury bills); Government bonds; Corporate bonds

Different Issuers of Bonds U.S. Treasury Notes and Bonds Corporations Municipalities International Governments and Corporations Innovative Bonds Indexed Bonds Structured (Floaters, Reverse Floaters)

Fixed Income Securities Zero coupon bond: the only cash flow is the repyment in full at maturity; Straight coupon bond:payment of annual or semiannual fixed coupons plus principal repayment at expiration; Step up /step down bond: the coupon may change overtime; …

Zero coupon bond The Bond is priced today price P and repaid at Z after a set period of time. The simple capitalisation convention is used for period of times shorter than 1 year. Over 1 year the yearly capitalisation convention is used. Time convention: Actual/Actual Actual/360 Actual/365 30/360

Straight coupon bond A bond that pays a coupon on a regular basis (eg BTP). Yield to Maturity (YTM) is generally used to calculate the yield of the coupon bond and it is equal to the interest rate that equals the Present value of the coupons and principal to today price. A coupon bond price could be : Corso tel quel (Dirty Price), including the prorata part of the present coupon (used for settlement) Corso secco (Clean Price)

Bond Pricing PB = Price of the bond Ci = interest or coupon payments n = number of periods to maturity r = discount rate per period

Solving for Price: 10-yr, 8% Coupon Bond, Face = $1,000 PB = $1,148.77 Ct = 80 pa (40 SA) P = 1000 T = 20 periods (10Y) r = 3% semiannual

Yield to Maturity Interest rate that makes the present value of the bond’s payments equal to its price Solve the bond formula for r

YIELD TO MATURITY YTM Where: C = six months coupon YTM = YTM for the period

Bond Prices and Yields Prices and Yields (required rates of return) have an inverse relationship When yields get very high the value of the bond will be very low When yields approach zero, the value of the bond approaches the sum of the cash flows

Prices and Coupon Rates Yield

Listing Where: C = Six Months Coupon n = years to maturity r =six months rate days= days between now and the coupon payment date