I apply the law of one price arbitrage to price long

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I Apply the Law of One Price (arbitrage) to price long-term bonds. Robert J. McKeown (U of T) ECO358 Week Seven
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Term Structure of Interest Rates The Yield Curve Sometimes referred to as the “Term Structure of Interest rates”. Bonds of di erent maturities typically have di erent yields to maturity. I That is: you may expect, e.g., 1% return per year when holding a 1-year bond, yet 2% per year when holding a 2-year bond. Yield curve = YTM as a function of a bond’s maturity. Robert J. McKeown (U of T) ECO358 Week Seven
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Term Structure of Interest Rates The Yield Curve Let’s focus on the YTM of zero-coupon government bonds. Note: zero-coupon bonds of maturities greater than one year are “synthetic” (i.e., the gov’t does not issue such bonds): a third party has provided the service for a small fee). I e.g., a zero-coupon bond with a 2-year maturity means you receive only the face value in 2 years. Robert J. McKeown (U of T) ECO358 Week Seven
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Term Structure of Interest Rates Yield Curves for Government of Canada Zero-Coupon Bonds y-axis represents yields, x-axis represents months. Robert J. McKeown (U of T) ECO358 Week Seven
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Term Structure of Interest Rates The Yield Curve Why do short-term and long-term yields di er? What can yield curves tell us about the present and future economic environment? Robert J. McKeown (U of T) ECO358 Week Seven
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Term Structure of Interest Rates Arbitrage and the Yield Curve I All YTMs are relevant. Consider annual coupons so the bond equivalent yield is the e ective annual rate. Suppose that YTM rates for zero-coupon bonds with maturities for any given year k is y k . These are the appropriate discount rates to find the present value of the bond’s coupon payments. Why is this the right rate? By the Law of One Price! Robert J. McKeown (U of T) ECO358 Week Seven
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Term Structure of Interest Rates Arbitrage and the Yield Curve II The return you receive on a coupon-paying bond can be replicated using a series of zero-coupon bonds. You can get the same coupon (and risk) by investing an appropriate amount into the k-year zero-coupon bond! Robert J. McKeown (U of T) ECO358 Week Seven
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Term Structure of Interest Rates Arbitrage and the Yield Curve III Example: a 2-year gov’t bond with $10,000 face value and 10% coupon. The price and discounted cashflows are: P = 0.1 ( 10, 000 ) ( 1 + y 2 ) 1 + 0.1 ( 10, 000 ) ( 1 + y 2 ) 2 + 10, 000 ( 1 + y 2 ) 2 P = 1, 000 ( 1 + y 2 ) 1 + 11, 000 ( 1 + y 2 ) 2 Where y 2 is the YTM. Robert J. McKeown (U of T) ECO358 Week Seven
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Term Structure of Interest Rates Arbitrage and the Yield Curve IV To prevent arbitrage, its price must equal that of a portfolio of zero-coupon bonds with a total face value of $1,000 maturing in one year, and $11,000 maturing in two years. Denote the YTM on a t-year zero-coupon bonds as yk t and calculate the total price of all zero-coupon bonds in the portfolio: P k = 1, 000 ( 1 + yk 1 ) 1 + 11, 000 ( 1 + yk 2 ) 2 Robert J. McKeown (U of T) ECO358 Week Seven
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Term Structure of Interest Rates Arbitrage and the Yield Curve V To prevent arbitrage, it must be the case that: P k = P 1, 000 ( 1 + yk 1 ) 1 11, 000 ( 1 + yk 2 ) 2 = 1, 000 ( 1 + y 2 ) 1 + 11, 000 ( 1 + y 2 ) 2
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  • Summer '14
  • ATAMAZAHERI
  • Zero-coupon bond, Robert J. McKeown

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