BKM Chapter 15 Flashcards
Relationship between interest rates and maturity
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interest rates increase as maturity increases
Yield curve
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relationship between YTM and maturity
Uses for the yield curve (2)
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- bond valuation
2. to gauge expectations for future interest rates against the market
Spot rates
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YTM on zero-coupon bonds (for the given duration)
General relationship between individual coupon values and total bond value and arbitrage opportunities if this relationship is violated (2)
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sum of individual coupon values should equal the total bond value
if it does not, arbitrage opportunity exists
- bond stripping
- bond reconstitution
Bond stripping
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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)
Bond reconstitution
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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)
Pure yield curve
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yield curve for zero-coupon bonds
On-the-run yield curve
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yield curve for recently issued coupon bonds selling at or near par value
Short rates
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rate for a specific period length at different points in time
Expected future short rate formula
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(1 + r(n)) = ((1 + y(n))^n) / ((1 + y(n-1))^(n-1))
y(n) = YTM for n-period maturity r(n) = short rate
Forward rate description
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“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
Forward rate formula (3)
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(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
Reason that the forward rate does not necessarily equal the future short rate
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interest rate uncertainty
Liquidity premium definition & formula
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compensation for uncertainty in bond price due to changes in short rates demanded by investors
liquidity premium = forward rate - expected future short rate
Liquidity premiums desired by short-and long-term investors
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short-term: positive liquidity premium
long-term: negative liquidity premium
(to invest in short-term bonds)
Reasons forward rates can be high (2)
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- investors expect rising interest rates
2. large liquidity premium required for holding longer-term bonds
Theories of interest rate term structure (2)
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- expectations hypothesis
2. liquidity preference theory
Expectations hypothesis assumptions (3)
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- forward rate = expected future short rate
- liquidity premiums = 0
- upward-sloping yield curve indicates expectation of increasing interest rates
Liquidity preference theory
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assumes short-term investors dominate the market, so in general, the forward rate > expected short rate resulting in a positive liquidity premium, on average
Implication of liquidity preference theory
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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
Relationship between yield curve and forward rates
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upward-sloping yield curve must indicate an increase in forward rates (which consist of expected short rates and liquidity premiums)
Problems with constant liquidity premium assumption (2)
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- difficult to obtain precise estimates of liquidity premiums
- no reason to assume liquidity premiums are constant
Nominal interest rate
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nominal interest rate = real interest rate + inflation rate
Causes for changes in interest rates (3)
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- increase in nominal interest rates can be driven by real rate increases or changes in inflation
- rapidly expanding economy generally leads to an increase in rates
- supply-side shocks can lead to an increase in rates (e.g. interruptions in oil supply)
Forward contracts
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arrangements that effectively lock in a future interest rate
Synthetic forward loan (investor = borrower)
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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
When is it advantageous to lend and borrow a synthetic forward loan?
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lend: if believe interest rates will fall
borrow: if believe interest rates will rise
