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Transcript of 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
Chapter 14: Term Structure of Interest Rates © Oltheten & Waspi 2012
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
Chapter 14: Term Structure of Interest Rates © Oltheten & Waspi 2012
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
Chapter 14: Term Structure of Interest Rates © Oltheten & Waspi 2012
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
Chapter 14: Term Structure of Interest Rates © 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
0 5 10 15 20 25 30 350%
1%
2%
3%
4%
5%
6%
7%
8%
20062005
1999
Chapter 14: Term Structure of Interest Rates © Oltheten & Waspi 2012
Inverted Yield Curve
0 5 10 15 20 25 30 350%
1%
2%
3%
4%
5%
6%
7%
200720062000
Chapter 14: Term Structure of Interest Rates © Oltheten & Waspi 2012
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
Don’t have to worry about these any more
Chapter 14: Term Structure of Interest Rates © 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
Yield Curve
© Oltheten & Waspi 2012
0 6 12 18 247.0%
7.5%
8.0%
8.5%
9.0%
Chapter 14: Term Structure of Interest Rates © 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
Yield Curve
© Oltheten & Waspi 2012
0 6 12 18 247.0%
7.5%
8.0%
8.5%
9.0%
Chapter 14: Term Structure of Interest Rates © 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 month8.5%
Yield: 8.9%
12 month0%
Yield: 8.3%
Chapter 14: Term Structure of Interest Rates © Oltheten & Waspi 2012
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
Chapter 14: Term Structure of Interest Rates © Oltheten & Waspi 2012
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
Chapter 14: Term Structure of Interest Rates
1. ... for a total of $9,944.97
© Oltheten & Waspi 2012
$9,148.52
2.089
1
$10,4253
$406.89
2.089
1
$425
$389.56
2.089
1
$4252
Chapter 14: Term Structure of Interest Rates
2. Remove the coupons
Department of the Treasury
Principal Sum of $10,000 due April 15, 2015with interest calculated at 8.5%
$425April 15, 2015
$425April 15, 2014
$425October 15,
2014
© Oltheten & Waspi 2012
Chapter 14: Term Structure of Interest Rates © Oltheten & Waspi 2012
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
Chapter 14: Term Structure of Interest Rates
4. Sell the final coupon and principal …
Department of the Treasury
Principal Sum of $10,000 April 15, 2015with interest calculated at 8.5%
$425 April 15,
2015
© Oltheten & Waspi 2012
Chapter 14: Term Structure of Interest Rates
… 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
© Oltheten & Waspi 2012
Chapter 14: Term Structure of Interest Rates © Oltheten & Waspi 2012
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
Chapter 14: Term Structure of Interest Rates © Oltheten & Waspi 2012
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
Chapter 14: Term Structure of Interest Rates © Oltheten & Waspi 2012
0 6 12 18 247.0%
7.5%
8.0%
8.5%
9.0%
8.0%
8.3%
8.9%
Yield Curve
Chapter 14: Term Structure of Interest Rates © 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
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