ECO358_L7S2.pdf

# I apply the law of one price arbitrage to price long

• Notes
• 55

This preview shows page 34 - 43 out of 55 pages.

I Apply the Law of One Price (arbitrage) to price long-term bonds. Robert J. McKeown (U of T) ECO358 Week Seven

Subscribe to view the full document.

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
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

Subscribe to view the full document.

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
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

Subscribe to view the full document.

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
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

Subscribe to view the full document.

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
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

Subscribe to view the full document.

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
You've reached the end of this preview.
• Summer '14
• ATAMAZAHERI
• Zero-coupon bond, Robert J. McKeown

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern