# AS_440_640_Week2.pdf - AS.440.640 Financial Economics...

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AS.440.640 Financial Economics Lecture 2 Zhou, Nan Zhou, Nan AS.440.640 Financial Economics Lecture 2
Bonds Bonds are a form of debt that are held for a fixed term, expiring at the maturity date Issued by sovereign governments, municipalities, and corporations to finance investment projects As with any debt, there is a risk of default if the borrower is unable to meet repayment obligations The greater the chance of default, the higher the rate of return that prospective investors demand as compensation, or equivalently the lower the market price of the bond Zhou, Nan AS.440.640 Financial Economics Lecture 2
Zero Coupon Bond A zero coupon bond promises a single payment, known as the par or face value, due at maturity Market prices are quoted as a percentage of par value, a three year bond priced at 90 3 / 8 sells for 90 . 375 per 100 par value Assume that face value equals 100 unless otherwise specified The yield to maturity is the discount rate that sets the bond price equal to the present value of the promised payment PV = 100 (1 + y ) 3 = 90 . 375 y = parenleftbigg 100 90 . 375 parenrightbigg 1 3 - 1 0 . 0343 Zero coupon bonds are almost always sold at discount, or below par, otherwise the yield would be negative Zhou, Nan AS.440.640 Financial Economics Lecture 2
Coupon Bond A coupon bond promises periodic coupon payments in addition to repayment of par value at maturity Name derives from literal coupons printed on bond certificates that could be clipped and redeemed for payment Intended to be sold near par value with the coupon mimicking an interest payment However, the coupon rate is set by the terms of the bond and does not necessarily relate to the bond’s actual yield which is determined by market forces Suppose that the same entity as the previous example issues a three year bond with an annual coupon of 5 . 625 Year 1 2 3 Cash Flow 5 . 625 5 . 625 105 . 625 Zhou, Nan AS.440.640 Financial Economics Lecture 2
Pricing a Coupon Bond Suppose that the yield on this coupon bond is identical to the that of the zero coupon bond considered earlier y = 0 . 0343 Can find the price by computing the present value, noting that a coupon bond is simply the sum of an annuity and a zero coupon bond PV = T summationdisplay t =1 C (1 + y ) t + F (1 + y ) T = C y bracketleftbigg 1 - 1 (1 + y ) T bracketrightbigg + F (1 + y ) T = 5 . 625 0 . 0343 bracketleftbigg 1 - 1 1 . 0343 3 bracketrightbigg + 100 1 . 0343 3 106 . 155 Note that this bond sells at a premium, or above par, why? Zhou, Nan AS.440.640 Financial Economics Lecture 2
U.S. Treasury Securities Considered to be an extremely safe investment given practically non-existent default risk Coupons on U.S. Treasury bonds are paid semiannually - every six months For example, suppose that a five year Treasury bond has a yield of y = 0 . 0229 and an annual coupon of 2 . 13, this implies that you are entitled to coupon payments of 1 . 065 twice a year To find the price of this bond, use the compounding formula with n = 2 periods per year PV = C n y n bracketleftBigg 1 - 1 ( 1 + y n ) nT bracketrightBigg + F ( 1 + y n ) nT = 1 . 065 0 . 01145 bracketleftbigg 1 - 1 (1 . 0 . 01145) 10 bracketrightbigg + 100 (1 . 01145) 10 99 . 2482 Zhou, Nan AS.440.640 Financial Economics Lecture 2