YTM as a Measure of Return for Bonds

# YTM as a Measure of Return for Bonds - UGBA 103 Summer 2008...

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UGBA 103 Summer 2008 Avinash Verma Yield to Maturity as a Measure of Return for Bonds Y IELD TO M ATURITY AS A M EASURE OF R ETURN FOR B ONDS A Coupon Bond makes a fixed payment, known as Coupon (denoted C ), every period (usually 6 months in the US) during the course of its life (denoted as n periods), and a balloon payment at the end of its life. The balloon payment is called the Face Value or the Maturity Value of the Bond, and is denoted M . The quantity C / M is known as the coupon rate of the bond. Applying our Fundamental Valuation Equation (Price equals sum of PV of future expected cash flows) to these cash flows, and assuming that the cash flows are free of default risk (true when the Bond is issued by the US Treasury), the price of the bond, P , will be: ( 29 ( 29 ( 29 n n n n r M r C r C r C P + + + + + + + + = 1 1 ... 1 1 2 2 1 If we buy an asset for P 0 dollars, hold it for n periods (usually years), and then sell it for P n dollars, our per period return, R n , is unambiguously defined to be: 1 1 0 - n n n P P R In the example above, cash flows occurred only at two points in time, the beginning and the end of the holding period. In the presence of intermediate cash flows (such as coupons), it is not unambiguously clear how the return should be measured. One possible measure of return is the yield to maturity (YTM), denoted y . YTM is defined to be the rate discounted at which the future cash flows of the asset (here a coupon bond) equal its price. In symbols: ( 29 ( 29 ( 29 ( 29 ( 29 n n n n y M y y C y M y C y C y C P + + + - = + + + + + + + + = 1 1 1 1 1 1 ... 1 1 2 The equation above cannot be solved analytically for y . It has to be solved by trial and error. Now, among other things, we are interested in how the percentage coupon rate of the bond, C / M , compares with its YTM for bonds that sell at a premium ( P > M ), at par ( P = M ), and at a discount ( P < M ). Algebraically, for premium bonds, we are interested in: © Avinash Verma 1

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UGBA 103 Summer 2008 Avinash Verma Yield to Maturity as a Measure of Return for Bonds ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 y M C M y C y M y y C y M M y y C M y M y y C M P n n n n n n + - + -
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## This note was uploaded on 02/12/2012 for the course UGBA 101A taught by Professor Mccullough during the Spring '08 term at Berkeley.

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YTM as a Measure of Return for Bonds - UGBA 103 Summer 2008...

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