14: Term Structure of Interest Rates V: Bonds 14: Term Structure of Interest Rates

Term Structure Predict X $1000 $1000 (1 Year CDs) @ 3% (1.04)2 = $1081.60 © Oltheten & Waspi 2012

Increase in demand increases price and decreases yield on 2.year CDs Decreasing Rates Let x = 4% 2 (1 Year CDs) < 2 Year CD $1000(1.03)(1.04) < $1000(1.04)2 $1071.20 < $1081.60 Increase in demand increases price and decreases yield on 2.year CDs

Decrease in demand decreases price and increases yield on 2.year CDs Increasing Rates Let x = 6% 2 (1 Year CDs) > 2 Year CD $1000(1.03)(1.06) > $1000(1.04)2 $1091.80 > $1081.60 Decrease in demand decreases price and increases yield on 2.year CDs

Equilibrium The market predicts 2 (1 Year CDs) = 2 Year CD $1000 (1.03)(1+X) = $1000 (1.04)2 X = 5.0097% Half the smart money is on lower rates and half the smart money is on higher rates

Term Structure Theoretical Predictions Yield Curve © Oltheten & Waspi 2012

Normal Yield Curves © Oltheten & Waspi 2012

Flat Yield Curves © Oltheten & Waspi 2012

Inverted Yield Curve © Oltheten & Waspi 2012

Deriving Term Structure Yield is a function of Term to maturity Coupon rate Call provisions Liquidity Risk of Default Tax implications

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

Deriving the Yield Curve Yield is a function of Term to maturity Coupon rate Call provisions Liquidity Risk of Default Tax implications

Treasury Securities T-Bills T-Notes T-Bonds < 1 year Discount paper 2years to 10 years Semi-annual coupon T-Bonds >10 years

Observation #1: 6 month rate Bloomberg shows 6 month T-Bill trading at a yield of 8%* *hypothetical data

Yield Curve © Oltheten & Waspi 2012

Observation 2: 12 month rate Bloomberg shows 12 month T-Bill trading at a yield of 8.3%* *hypothetical data

Yield Curve © Oltheten & Waspi 2012

Observation #3: 18 month rate Bloomberg shows 18 month 8.5% T-Note trading at a yield of 8.9%* Is the 0.6% increase in yield because the bond is 6 months longer or because it has coupon payments? 18 month 8.5% 12 month 0% Yield: 8.9% Yield: 8.3%

Yield Curve 8.9% ?% Coupon Rate 8.5% © Oltheten & Waspi 2012

Department of the Treasury Principal of $10,000 due . Buy the Note … Department of the Treasury Principal of $10,000 due . with interest calculated at 8.5% $425 August 20, 2019 August 20, 2018 February 20, 2019 August 20, 2019 © Oltheten & Waspi 2012

... for a total of $9,944.97 © Oltheten & Waspi 2012

Department of the Treasury Principal of $10,000 due . 2. Remove the coupons Department of the Treasury Principal of $10,000 due . with interest calculated at 8.5% $425 August 20, 2019 $425 $425 August 20, 2018 August 20, 2019 February 20, 2019 © Oltheten & Waspi 2012

3. Sell the coupons separately $425 August 20, 2018 $425 February 20, 2019 © Oltheten & Waspi 2012

4. Sell the final coupon and principal … Department of the Treasury Principal of $10,000 due . with interest calculated at 8.5% $425 August 20, 2019 August 20, 2019 © Oltheten & Waspi 2012

… for $9,144.51 Price of the 18 month note -$9,944.97 Proceeds from 6 month coupon $408.65 Proceeds from 12 month coupon $ 391.81 Required proceeds from the 18 month coupon and principal $9,144.51 © Oltheten & Waspi 2012

5. Which determines the zero coupon yield $10,425 August 20, 2019 © Oltheten & Waspi 2012

Yield Curve 8.9% Coupon Rate © Oltheten & Waspi 2012

Yield Curve © 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

Bonds III