v: bonds 14: term structure of interest rates. chapter 14: term structure of interest rates term...

V: Bonds

14: Term Structureof Interest Rates

Chapter 14: Term Structure of Interest Rates © Oltheten & Waspi 2012

Term Structure

$1000 (1 Year CDs) @ 3%

(2 Year CD) @ 4%

$1000 (1.03)(1+X) = ??

(1.04)2 = $1081.60


Decreasing Rates

Let x = 4%2 (1 Year CDs) < 2 Year CD$1000(1.03)(1.04) < $1000(1.04)2

< $1081.60

Increase in demand increases price and decreases 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

> $1081.60

Decrease in demand decreases price and increases yield on

2.year CDs


Equilibrium

The market predicts2 (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

Chapter 14: Term Structure of Interest Rates

1 1.5 2 2.5 3 3.5 4 4.5 50%

1%

2%

3%

4%

5%

6%

7%

3.0%

5.0%

6.0%

4.0%

2.0%

3.0%

4.0%

4.7%4.5%

4.0%

Term Structure

Yield Curve

Theoretical Predictions

© Oltheten & Waspi 2012


Yield Curve 1999-2013


Normal Yield Curves


Flat Yield Curves

0 5 10 15 20 25 30 350%

1%

2%

3%

4%

5%

6%

7%

8%

20062005

1999


Inverted Yield Curve

0 5 10 15 20 25 30 350%

1%

2%

3%

4%

5%

6%

7%

200720062000


Yield Curve 2007-2013


Deriving the Yield Curve

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 Term Structure

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

Don’t have to worry about these any more


Treasury Securities T-Bills

< 1 year Discount paper

T-Notes 2years to 10 years Semi-annual coupon

T-Bonds >10 years Semi-annual coupon


Observation #1: 6 month rate

Bloomberg shows 6 month T-Bill trading at a yield of 8%*

*hypothetical data


Yield Curve


0 6 12 18 247.0%

7.5%

8.0%

8.5%

9.0%


Observation 2: 12 month rate

Bloomberg shows 12 month T-Bill trading at a yield of 8.3%*

*hypothetical data


Yield Curve


0 6 12 18 247.0%

7.5%

8.0%

8.5%

9.0%



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 month8.5%

Yield: 8.9%

12 month0%

Yield: 8.3%


0 6 12 18 247.0%

7.5%

8.0%

8.5%

9.0%

8.0%

8.3%

Coupon Rate

8.9%

?%

8.5%

Yield Curve


Buy the Note …

Department of the Treasury

Principal Sum of $10,000 due April 15, 2015with interest calculated at 8.5%

$425April 15, 2014

$425October 15,

2014

$425April 15, 2015


1. ... for a total of $9,944.97


$9,148.52

2.089

1

$10,4253

$406.89

2.089

1

$425

$389.56

2.089

1

$4252


2. Remove the coupons


Principal Sum of $10,000 due April 15, 2015with interest calculated at 8.5%

$425April 15, 2015

$425April 15, 2014

$425October 15,

2014



3. Sell the coupons separately

$425April 15, 2014

$425 October 15,

2014

$408.65

2.080

1

$425

$391.81

2.083

1

$425

2


4. Sell the final coupon and principal …


Principal Sum of $10,000 April 15, 2015with interest calculated at 8.5%

$425 April 15,

2015



… 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



5. Which determines the zero coupon yield

$9,144.51

2Yd

1

$10,425

3

13

$9,144.51

$10,4252Yd

$10,425April 15, 2015

0.0893Yd


0 6 12 18 247.0%

7.5%

8.0%

8.5%

9.0%

8.0%

8.3%

8.9%

Coupon Rate

8.9%Yield Curve


0 6 12 18 247.0%

7.5%

8.0%

8.5%

9.0%

8.0%

8.3%

8.9%

Yield Curve



Bloomberg shows 24 month 9% T-Note trading at a yield of

8.92% Calculate the 24 month zero-coupon yield

*hypothetical data


0 6 12 18 24 307.0%

7.5%

8.0%

8.5%

9.0%

9.5%

8.0%

8.3%

8.9%

Yield Curve

Bonds III

v: bonds 14: term structure of interest rates. chapter 14: term structure of interest rates term...

Documents

rates oltheten waspi

deriving term structure

yield curve yield

function of term

lower rates

decreasing rates

increasing rates

higher rates