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Lecture+16+Nov+9+2011

# Lecture+16+Nov+9+2011 - FINA3104 Lecture16 DarwinChoi...

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FINA 3104: Investment Analysis and Portfolio Management Lecture 16 – The Term Structure of Interest Rates Darwin Choi November 9, 2011 Recap from Last Lecture Bonds & Bond Pricing PV(Coupons) + PV(Face Value) Bond Pricing between Coupons Bond Prices & Interest Rates Inversely & Convexly Related Yield to Maturity Internal Rate of Return Discount Rate 2

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Outline of Today’s Lecture The Term Structure under Certainty Forward Rates and Expected Short Rates Theories of the Term Structure Interpreting the Term Structure 3 Now, let’s look at the yield to maturity for zero coupon bonds (or zeros): 1 year: Bond Value of 1 year Zero = Face Value/(1+ y 1 ) 2 year: Bond Value of 2 year Zero = Face Value/(1+ y 2 ) 2 How do we price a two year coupon bond (coupons are paid annually) if we know y 1 and y 2 ? Yield to Maturity of Zeros 4 Bond Value = T t r ( t ) Coupon 1 ) t 1 ( + r Value Face ( T )) T 1 ( Bond Value = T t y Coupon 1 ) t 1 ( + T y Face ) 1 (
Think of the two year bond as a combination of 2 zero coupon bonds: 1. \$Coupon in 1 year zero 2. \$(Coupon + Face Value) in 2 year zero What should we use as the discount rates r (1) and r (2)? r (1) = y 1 , r (2) = y 2 So, yields to maturity of zero coupon bonds are the discount rates for different time periods Yields and Discount Rates 5 Bond Value = 2 t r ( t ) Coupon 1 ) t 1 ( + r Value Face (2)) 2 1 ( What Is the Term Structure (Yield Curve)? Yield as a Function of Maturity Yield-to- Maturity Time-to- Maturity Descending Yield Curve Ascending Yield Curve Flat Yield Curve Graph all y t = Yield to maturity of t period zero coupon bonds 6

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\$1,000.00 \$841.75 \$909.09 8.000% 10.000% Term Structure under Certainty Time Path of Zero coupon Bond Prices The 2 year bond is currently worth: \$909.09 /1.08= \$841.75 In 1 year, the 2 year bond will be worth: \$1,000.00 /1.10= \$909.09 The 2 year bond’s Yield to Maturity at time 0 is: y 2 = (\$1,000.00 ÷ \$841.75) 1/2 –1 = 8.995% Maturity 1 year 2 years 3 years 4 years Price at time 0 Short Rates 1 year 2 years 3 years
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Lecture+16+Nov+9+2011 - FINA3104 Lecture16 DarwinChoi...

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