YCM 2001 - Yield Curve Theories

# YCM 2001 - Yield Curve Theories - Theories of the Yield...

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1 Theories of the Yield Curve Copyright © 1996-2006 Investment Analytics

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Copyright © 1996-2006 Investment Analytics Yield Curve Theories Slide: 2 The Yield Curve What is the yield curve? How is the curve constructed? Why is the yield curve shaped the way it is? Why does its shape change? How can a trader profit from this?
Copyright © 1996-2006 Investment Analytics Yield Curve Theories Slide: 3 Zero-Coupon Bonds, Face Value \$1,000: Term Price Discount YTM 1 925.93 1/(1+y 1 ) 8.000% 2 841.75 1/(1+y 2 ) 2 8.995% 3 758.33 1/(1+y 3 ) 3 9.660% 4 683.18 1/(1+y 4 ) 4 9.993% Spot Yield (Zero Coupon Yield) y 1 is called the one year spot rate y 2 is called the two year spot rate The Yield Curve

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Copyright © 1996-2006 Investment Analytics Yield Curve Theories Slide: 4 Years to Maturity 8% Spot Rate 1 4 Yield Curve Example
Copyright © 1996-2006 Investment Analytics Yield Curve Theories Slide: 5 In practice we have coupon bonds, not just zeros Term Price Discount YTM 1 925.93 Z 1/(1+y 1 ) 8.000% 2 841.75 Z 1/(1+y 2 ) 2 8.995% 3 952.40 C Bond in year 3 is a coupon bond Pays 8% coupon (\$80 per year) How do we proceed? Building a Yield Curve

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Copyright © 1996-2006 Investment Analytics Yield Curve Theories Slide: 6 Method: split into coupon and principal payments and treat each as a zero Then solve equation: 952.40 = \$80/(1+y 1 ) + \$80/(1+y 2 ) 2 + \$1080/(1+y 3 ) 3 y 1 & y 2 are known y 3 = 10.020% 1 2 3 \$80 \$80 \$1,080 Bootstrapping