Chapter 6Risk Structure of Long-Term Bonds

in the United States

Interest Rates and Recessions

1988-2016

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Recession Baa State &Local Govt 10-yr Treas Aaa

Treasury Yield Curves

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Sept. 2016

• Default risk —occurs when the issuer of the bond is unable or unwilling to make interest payments or pay off the face value

– U.S. T-bonds are considered default free

– Risk premium—the spread between the interest rates on bonds with default risk and the interest rates on T-bonds

• Liquidity—the ease with which an asset can be converted into cash

• Income tax considerations

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Interest Rates and Recessions 1988-2016

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Recession Baa Fed Funds 10-yr Treas

Fact 1: Interest rates for

different maturities move

together over time

Term Structure Facts to be Explained1. Interest rates for different maturities move together over time

2. Yield curves tend to have steep upward slope when short rates are

low and downward slope when short rates are high

3. Yield curve is typically upward sloping

Three Theories of Term Structure

1. Expectations Theory

2. Segmented Markets Theory

3. Liquidity Premium Theory

A. Expectations Theory explains 1 and 2, but not 3

B. Segmented Markets explains 3, but not 1 and 2

C. Solution: Combine features of both Expectations Theory and Segmented

Markets Theory to get Liquidity Premium (Preferred Habitat) Theory and

explain all facts

Treasury Yield Curves

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June 07 Sept. 2016

Fact 2: Yield Curves slope upward when short-term

rates are low and downward when short-term rates are

high

Fact 3: Yield Curves are typically upward sloping

Yield Curve &

the 3 Components of NIM

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Interest Rate

Risk Spread

Credit

Spread

1-year CD

@ 3.0%

5-year loan

@ 7.5%

Yield Curve &

the 3 Components of NIM

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@ 3.0%

5-year loan

@ 7.5%

“Carry Trade”

-Borrow short-term

-Lend long-term

$1 Million example (wholesale market)

Borrow 1 Year at 4% ($40,000)

Lend 5 Years at 6% ($60,000)

Earn $20,000

Risk

Return

Tradeoffs

Risk Sharing;

Asset Transformation

Selling low-risk assets

to fund the purchase of

higher-risk assets

Expectations Theory

Key Assumption: Bonds of different maturities are perfect

substitutes

Implication: RETe on bonds of different maturities are equal

Investment strategies for two-period horizon

1. Buy $1 of one-year bond and when it matures buy another

one-year bond

2. Buy $1 of two-year bond and hold it

Expected return from strategy 2

(1 + i2t)(1 + i2t) – 1 1 + 2(i2t) + (i2t)2 – 1

=1 1

Since (i2t)2 is extremely small, expected return is approximately

2(i2t)

Expected Return from Strategy 1

(1 + it)(1 + iet+1) – 1 1 + it + iet+1 + it(iet+1) – 1

=1 1

Since it(iet+1) is also extremely small, expected return is

approximately

it + iet+1

From implication above expected returns of two strategies are equal: Therefore

2(i2t) = it + iet+1

Solving for i2t

it + iet+1i2t =

2

More generally for n-period bond:

it + iet+1 + iet+2 + ... + iet+(n–1)int =n

In words: Interest rate on long bond = average short rates expected to occur over life of long bond

With $10,000 min,

or

Premium Checking

With $100,000 min

Type Term Min Bal Rate APY* Rate APY* Rate APY*

Investor's Indexed 36 Month $5,000 5.45% 5.60%

Rate Bump 24 Month $5,000 4.35% 4.45% 4.64% 4.75%

Specials 8 Month $5,000 4.88% 5.00% 5.02% 5.15% 5.16% 5.30%

16 Month $5,000 4.93% 5.05% 5.07% 5.20% 5.21% 5.35%

Regular 60 Month $500 4.64% 4.75% 4.78% 4.90% 4.93% 5.05%

48 Month $500 4.59% 4.70% 4.74% 4.85% 4.88% 5.00%

36 Month $500 4.55% 4.65% 4.69% 4.80% 4.83% 4.95%

30 Month $500 4.50% 4.60% 4.64% 4.75% 4.78% 4.90%

24 Month $500 4.50% 4.60% 4.64% 4.75% 4.78% 4.90%

18 Month $500 4.45% 4.55% 4.59% 4.70% 4.74% 4.85%

12 Month $500 4.45% 4.55% 4.59% 4.70% 4.74% 4.85%

9 Month $500 4.31% 4.40% 4.45% 4.55% 4.59% 4.70%

6 Month $500 4.16% 4.25% 4.31% 4.40% 4.45% 4.55%

3 Month $500 3.97% 4.05% 4.11% 4.20% 4.26% 4.35%

Smart Saver 30 Month $250 4.26% 4.35% 4.40% 4.50%

18 Month $250 4.21% 4.30% 4.35% 4.45%

Smart Saver Plus 12 Month $250 4.21% 4.30% 4.35% 4.45%

UWCU CD interest rates

4.454.50

4.554.59

4.64

4%

5%

Term to Maturity

Yield to

Maturity

Example: 5 year holding period, $100

2 options:

Buy 5-yr CD at 4.64%,…FV = 100*(1+.0464)5 = $125.45

Buy 1-yr CD at 4.45% and a 4-yr CD next year

FV = 100*(1.0445)(1.0469)4 = $125.45

If perfect substitutes

(1+i1)(1+i4,t+1)4 = (1+i5)

5

i4,t+1 = [(1+i5)5]1/4 - 1

[ 1+i1 ]

i4,t+1 = [(1.0464)5]1/4 - 1

[ 1.0445 ]

i4,t+1 = 4.69%

4.69

In General

in,t+1 = [(1+in+1)n+1]1/n - 1

[ 1+i1 ]

Segmented Markets Theory

Key Assumption: Bonds of different maturities are not substitutes at

all

Implication: Markets are completely segmented: interest rate at each

maturity determined separately

Explains Fact 3 that yield curve is usually upward sloping

People typically prefer short holding periods and thus have higher

demand for short-term bonds, which have higher price and lower

interest rates than long bonds

Does not explain Fact 1 or Fact 2 because assumes long and short

rates determined independently

4.454.50

4.554.59

4.64

4%

5%

Term to Maturity

Yield to

Maturity

1 yr 2 yr 3 yr 4 yr 5 yr

Segmented Markets Theory

Different investors have different holding periods

•Banks have S.T. holding periods

•Insurance Co.s have L.T. holding periods

Strong Demand

Weak Demand

If bond maturity = holding period

Then no IRR, no DPB , no uncertainty

So Return = YTM = i

Liquidity Premium Theory

Key Assumption: Bonds of different maturities are substitutes, but are not perfect substitutes

Implication: Modifies Expectations Theory with features of Segmented Markets Theory

Investors prefer short rather than long bonds must be paid positive liquidity (term) premium, lnt, to hold long-term bonds

Results in following modification of Expectations Theory

it + iet+1 + iet+2 + ... + ie

t+(n–1)int = + lnt

n

Relationship Between the Liquidity Premium and

Expectations Theories

Econ 330

Homework 5Due Friday, September 30, in discussion

Chapter 6

Questions & Applied Problems 7, 10, 16, 19, 21, 22, 24, 25