BKM Chapter 15

Question 1

Relationship between interest rates and maturity

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Answer 1

interest rates increase as maturity increases

Question 2

Yield curve

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Answer 2

relationship between YTM and maturity

Question 3

Uses for the yield curve (2)

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Answer 3

1. bond valuation

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

Question 4

Spot rates

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Answer 4

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

Question 5

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

(BKM - 15)

Answer 5

sum of individual coupon values should equal the total bond value

if it does not, arbitrage opportunity exists

1. bond stripping
2. bond reconstitution

Question 6

Bond stripping

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Answer 6

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)

Question 7

Bond reconstitution

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Answer 7

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)

Question 8

Pure yield curve

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Answer 8

yield curve for zero-coupon bonds

Question 9

On-the-run yield curve

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Answer 9

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

Question 10

Short rates

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Answer 10

rate for a specific period length at different points in time

Question 11

Expected future short rate formula

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Answer 11

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

y(n) = YTM for n-period maturity 
r(n) = short rate

Question 12

Forward rate description

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Answer 12

“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

Question 13

Forward rate formula (3)

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Answer 13

(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

Question 14

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

(BKM - 15)

Answer 14

interest rate uncertainty

Question 15

Liquidity premium definition & formula

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Answer 15

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

liquidity premium = forward rate - expected future short rate

Question 16

Liquidity premiums desired by short-and long-term investors

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Answer 16

short-term: positive liquidity premium
long-term: negative liquidity premium

(to invest in short-term bonds)

Question 17

Reasons forward rates can be high (2)

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Answer 17

1. investors expect rising interest rates

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

Question 18

Theories of interest rate term structure (2)

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Answer 18

1. expectations hypothesis

2. liquidity preference theory

Question 19

Expectations hypothesis assumptions (3)

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Answer 19

1. forward rate = expected future short rate
2. liquidity premiums = 0
3. upward-sloping yield curve indicates expectation of increasing interest rates

Question 20

Liquidity preference theory

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Answer 20

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

Question 21

Implication of liquidity preference theory

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Answer 21

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

Question 22

Relationship between yield curve and forward rates

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Answer 22

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

Question 23

Problems with constant liquidity premium assumption (2)

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Answer 23

1. difficult to obtain precise estimates of liquidity premiums
2. no reason to assume liquidity premiums are constant

Question 24

Nominal interest rate

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Answer 24

nominal interest rate = real interest rate + inflation rate

Question 25

Causes for changes in interest rates (3)

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Answer 25

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)

Question 26

Forward contracts

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Answer 26

arrangements that effectively lock in a future interest rate

Question 27

Synthetic forward loan (investor = borrower)

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Answer 27

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

Question 28

When is it advantageous to lend and borrow a synthetic forward loan?

(BKM - 15)

Answer 28

lend: if believe interest rates will fall
borrow: if believe interest rates will rise