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V: Bonds 14: Term Structure of Interest Rates Term Structure $1000 $1000 (1 Year CDs) @ 3% (1.03)(1+X) = ?? (2 Year CD) @ 4% (1.04)2 Chapter 14: Term Structure of Interest Rates = $1081.60 © Oltheten & Waspi 2012 Decreasing Rates Let x = 4% 2 (1 Year CDs) < $1000(1.03)(1.04) < < 2 Year CD $1000(1.04)2 $1081.60 Increase in demand increases price and decreases yield on 2.year CDs Chapter 14: Term Structure of Interest Rates © Oltheten & Waspi 2012 Increasing Rates Let x = 6% 2 (1 Year CDs) > $1000(1.03)(1.06) > > 2 Year CD $1000(1.04)2 $1081.60 Decrease in demand decreases price and increases yield on 2.year CDs Chapter 14: Term Structure of Interest Rates © Oltheten & Waspi 2012 Equilibrium The market predicts 2 (1 Year CDs) = $1000 (1.03)(1+X) = X = 2 Year CD $1000 (1.04)2 5.0097% Half the smart money is on lower rates and half the smart money is on higher rates Chapter 14: Term Structure of Interest Rates © Oltheten & Waspi 2012 Term Structure Theoretical Predictions 7% 6.0% 6% Yield Curve 5.0% 5% 4.5% 4.0% 4.7% 4% 4.0% 3.0% 3% 3.0% 4.0% 2% 2.0% 1% 0% 1 1.5 2 Chapter 14: Term Structure of Interest Rates 2.5 3 3.5 4 4.5 5 © Oltheten & Waspi 2012 Yield Curve 1999-2013 Chapter 14: Term Structure of Interest Rates © Oltheten & Waspi 2012 Normal Yield Curves Chapter 14: Term Structure of Interest Rates © Oltheten & Waspi 2012 Flat Yield Curves 8% 7% 1999 6% 2006 5% 2005 4% 3% 2% 1% 0% 0 5 10 Chapter 14: Term Structure of Interest Rates 15 20 25 30 © Oltheten & Waspi 2012 35 Inverted Yield Curve 7% 6% 2000 2006 2007 5% 4% 3% 2% 1% 0% 0 5 10 Chapter 14: Term Structure of Interest Rates 15 20 25 30 © Oltheten & Waspi 2012 35 Yield Curve 2007-2013 Chapter 14: Term Structure of Interest Rates © Oltheten & Waspi 2012 Deriving the Yield Curve Yield is a function of Term to maturity Coupon rate Call provisions Liquidity Risk of Default Tax implications Chapter 14: Term Structure of Interest Rates © Oltheten & Waspi 2012 Treasury Securities Represents debt of the US Department of the Treasury Largest most liquid capital market in the world Trade in terms from 1 day to 30 years Chapter 14: Term Structure of Interest Rates © Oltheten & Waspi 2012 Deriving Term Structure Yield is a function of Term to maturity Coupon rate Call provisions Liquidity Risk of Default Tax implications Chapter 14: Term Structure of Interest Rates Don’t have to worry about these any more © Oltheten & Waspi 2012 Treasury Securities T-Bills < 1 year Discount paper T-Notes 2years to 10 years Semi-annual coupon T-Bonds >10 years Semi-annual coupon Chapter 14: Term Structure of Interest Rates © Oltheten & Waspi 2012 Observation #1: 6 month rate Bloomberg shows 6 month T-Bill trading at a yield of 8%* *hypothetical data Chapter 14: Term Structure of Interest Rates © Oltheten & Waspi 2012 Yield Curve 9.0% 8.5% 8.0% 7.5% 7.0% 0 6 Chapter 14: Term Structure of Interest Rates 12 18 24 © Oltheten & Waspi 2012 Observation 2: 12 month rate Bloomberg shows 12 month T-Bill trading at a yield of 8.3%* *hypothetical data Chapter 14: Term Structure of Interest Rates © Oltheten & Waspi 2012 Yield Curve 9.0% 8.5% 8.0% 7.5% 7.0% 0 6 Chapter 14: Term Structure of Interest Rates 12 18 24 © Oltheten & Waspi 2012 Observation #3: 18 month rate Bloomberg shows 18 month 8.5% T-Note trading at a yield of 8.9%* 18 month 12 month 8.5% 0% Yield: 8.3% Yield: 8.9% Is the 0.6% increase in yield because the bond is 6 months longer or because it has coupon payments? Chapter 14: Term Structure of Interest Rates © Oltheten & Waspi 2012 Yield Curve 8.9% 9.0% ?% 8.5% 8.3% 8.0% 8.0% 7.5% 8.5% 7.0% 0 6 Chapter 14: Term Structure of Interest Rates 12 18 24 © Oltheten & Waspi 2012 Buy the Note … Department of the Treasury Principal Sum of $10,000 due April 15, 2015 with interest calculated at 8.5% $425 $425 $425 April 15, 2014 October 15, 2014 April 15, 2015 Chapter 14: Term Structure of Interest Rates © Oltheten & Waspi 2012 1. ... for a total of $9,944.97 $10,425 .089 1 2 $425 .089 1 2 $406.89 Chapter 14: Term Structure of Interest Rates 3 $9,148.52 $425 .089 1 2 $389.56 2 © Oltheten & Waspi 2012 2. Remove the coupons Department of the Treasury Principal Sum of $10,000 due April 15, 2015 with interest calculated at 8.5% $425 April 15, 2014 $425 $425 April 15, 2015 October 15, 2014 Chapter 14: Term Structure of Interest Rates © Oltheten & Waspi 2012 3. Sell the coupons separately $425 April 15, 2014 $425 October 15, 2014 Chapter 14: Term Structure of Interest Rates $425 $408.65 .080 1 2 $425 .083 1 2 2 $391.81 © Oltheten & Waspi 2012 4. Sell the final coupon and principal … Department of the Treasury Principal Sum of $10,000 April 15, 2015 with interest calculated at 8.5% $425 April 15, 2015 Chapter 14: Term Structure of Interest Rates © Oltheten & Waspi 2012 … for $9,144.51 Price of the 18 month note Proceeds from 6 month coupon Proceeds from 12 month coupon Required proceeds from the 18 month coupon and principal Chapter 14: Term Structure of Interest Rates © Oltheten & Waspi 2012 5. Which determines the zero coupon yield $10,425 April 15, 2015 $10,425 Yd 1 2 3 $9,144.51 $10,425 1 Yd 2 3 $9,144.51 Yd 0.0893 Chapter 14: Term Structure of Interest Rates © Oltheten & Waspi 2012 Yield Curve 8.9% 9.0% 8.93% 8.5% 8.3% 8.0% 8.0% 7.5% 7.0% 0 6 Chapter 14: Term Structure of Interest Rates 12 18 24 © Oltheten & Waspi 2012 Yield Curve 9.0% 8.93% 8.5% 8.3% 8.0% 8.0% 7.5% 7.0% 0 6 Chapter 14: Term Structure of Interest Rates 12 18 24 © Oltheten & Waspi 2012 Observation #4: 24 month rate Bloomberg shows 24 month 9% T-Note trading at a yield of 8.92% Calculate the 24 month zero-coupon yield *hypothetical data Chapter 14: Term Structure of Interest Rates © Oltheten & Waspi 2012 Yield Curve 9.5% 8.93% 9.0% 8.5% 8.3% 8.0% 8.0% 7.5% 7.0% 0 6 Chapter 14: Term Structure of Interest Rates 12 18 24 30 © Oltheten & Waspi 2012 Bonds III