Effective annual rate (EAR)- interest accrued at the end of a year as a percentage of the principal amountoP x (1 + i)^number of periods, t = periodic interest rateo(Periodic interest rate – P)/ P = EARAPR doesn’t tell you how much you can expect to earn on each CD and therefore is not a good comparison, instead use the EARo(1 + periodic rate) ^number of periods per year = 1 + EARPricing Securities Promising Multiple PaymentsT- bill = treasury bondStripping- breaking up a security that promises multiples payments into constituent partsMarket price of a coupon in m years: where C is equal annual coupon payments. im= market yield on m-year billsoC / (1 + im) ^mPresent value, the market price, of a t-year bond with a face value of A and acoupon C is just the sum of the present values of the various payments,oP = (C + A) / (1 +it) ^tBonds with a Coupon Period of Less than a YearAmortized LoansAmortized loan- security that promises a series of equal payments. Mostly home mortgages and automobile loansP = C / (1 + i) ^t.same equation as above A is just set to zeroAnnuity- amortized loan with annual paymentsoAnnuity factor = C [ (1/i) x (1 – (1 / (1+ i^t))]Perpetuity- annuity that is payable forever, a bond that pays coupons forever, with payment of the face value deferred indefinitelyoP = C/i this is because, the annuity factor includes the term 1 / (1 + i) ^t and as t gets large the value of this term approaches
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zero so the value of the expression in the square brackets approaches 1 / iMarket Yield on a Security Promising Multiple PaymentsYield to Maturity (YTM)- single interest rate at which the present value of a bond’s coupon and principal payments equals its market priceoP = (C + A) / (1 + i) ^tsolve for the value of i that satisfies thisoThe market yield on a bond is defined as the yield to maturity calculated from its market priceoApproximate yield to maturity (AYTM) formula on page 77Selling at a:oDiscount= the market price of a bond is below its face valueoPremium= the market price of a bond is above its face valueoPar= bond is selling at exactly its face valueApplication: Understanding Treasury ListingsBonds: coupon security, have a maturity of over 10 yearsNotes: coupon security, a maturity of 2 to 10 years Bid price: price that dealers will pay for a securityAsked price: Price at which dealers will sell a security
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