Flashcards in BKM Chapter 15 Deck (29)

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1

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Relationship between interest rates and maturity

(BKM - 15)

### interest rates increase as maturity increases

2

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Yield curve

(BKM - 15)

### relationship between YTM and maturity

3

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Uses for the yield curve (2)

(BKM - 15)

###
1. bond valuation

2. to gauge expectations for future interest rates against the market

4

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Spot rates

(BKM - 15)

### YTM on zero-coupon bonds (for the given duration)

5

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General relationship between individual coupon values and total bond value and arbitrage opportunities if this relationship is violated (2)

(BKM - 15)

###
sum of individual coupon values should equal the total bond value

if it does not, arbitrage opportunity exists

1. bond stripping

2. bond reconstitution

6

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Bond stripping

(BKM - 15)

### if bond price < sum of individual coupon values investors can buy the bond then strip each coupon payment into stand-alone zero-coupon bonds and sell (resulting in an arbitrage opportunity)

7

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Bond reconstitution

(BKM - 15)

### if bond price > sum of individual coupon values investors can buy the individual zero-coupon bonds then re-assemble them into a coupon bond and sell (resulting in an arbitrage opportunity)

8

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Pure yield curve

(BKM - 15)

### yield curve for zero-coupon bonds

9

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On-the-run yield curve

(BKM - 15)

### yield curve for recently issued coupon bonds selling at or near par value

10

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Short rates

(BKM - 15)

### rate for a specific period length at different points in time

11

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Expected future short rate formula

(BKM - 15)

###
(1 + r(n)) = ((1 + y(n))^n) / ((1 + y(n-1))^(n-1))

y(n) = YTM for n-period maturity

r(n) = short rate

12

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Forward rate description

(BKM - 15)

### "break-even" interest rate that forces identical returns b/w an n-period zero-coupon bond and an (n-1) period zero-coupon bond rolled over into a 1-yr bond in year n

13

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Forward rate formula (3)

(BKM - 15)

###
(1 + f(n)) = ((1 + y(n))^n) / ((1 + y(n-1))^(n-1))

(1 + f(n)) = price of (n-1) yr zero-coupon bond / price of n-yr zero-coupon bond

forward rate = expected future short rate + liquidity premium

14

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Reason that the forward rate does not necessarily equal the future short rate

(BKM - 15)

### interest rate uncertainty

15

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Liquidity premium definition & formula

(BKM - 15)

###
compensation for uncertainty in bond price due to changes in short rates demanded by investors

liquidity premium = forward rate - expected future short rate

16

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Expected holding period return (HPR)

(BKM - 15)

### expected HPR = change in price / original price

17

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Liquidity premiums desired by short-and long-term investors

(BKM - 15)

###
short-term: positive liquidity premium

long-term: negative liquidity premium

(to invest in short-term bonds)

18

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Reasons forward rates can be high (2)

(BKM - 15)

###
1. investors expect rising interest rates

2. large liquidity premium required for holding longer-term bonds

19

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Theories of interest rate term structure (2)

(BKM - 15)

###
1. expectations hypothesis

2. liquidity preference theory

20

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Expectations hypothesis assumptions (3)

(BKM - 15)

###
assumes:

1. the forward rate = expected future short rate

2. liquidity premiums are 0

3. upward-sloping yield curve indicates expectation of increasing interest rates

21

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Liquidity preference theory

(BKM - 15)

### assumes short-term investors dominate the market, so in general, the forward rate > expected short rate resulting in a positive liquidity premium, on average

22

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Implication of liquidity preference theory

(BKM - 15)

###
means that an upward-sloping yield curve does not mean there is an expectation of increasing interest rates

>> possible to have an upward curve w/declining expected future short rates if the liquidity premium is increasing more than expected future short rates are decreasing

23

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Relationship between yield curve and forward rates

(BKM - 15)

### upward-sloping yield curve must indicate an increase in forward rates (which consist of expected short rates and liquidity premiums)

24

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Problems with constant liquidity premium assumption (2)

(BKM - 15)

###
1. difficult to obtain precise estimates of liquidity premiums

2. no reason to assume liquidity premiums are constant

25

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Nominal interest rate

(BKM - 15)

### nominal interest rate = real interest rate + inflation rate

26

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Causes for changes in interest rates (3)

(BKM - 15)

###
1. increase in nominal interest rates can be driven by real rate increases or changes in inflation

2. rapidly expanding economy generally leads to an increase in rates

3. supply-side shocks can lead to an increase in rates (e.g. interruptions in oil supply)

27

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Forward contracts

(BKM - 15)

### arrangements that effectively lock in a future interest rate

28

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Synthetic forward loan (investor = borrower)

(BKM - 15)

###
buy 1-yr zero-coupon bond for initial CF = - B(1)

sell (1 + f(2)) 2-yr zero-coupon bonds for CF = B(2) * (1 + f(2))

total initial CF = 0

29