06-Liquidity Preference Theory

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06-Liquidity Preference Theory
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Expectations Theory Review

• Given that
• Expectations Theory
• Given that we want to invest for two years, we
  should be indifferent between either strategy.
• On average, either strategy gives the same
  return.

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Expectations Theory Review

• The yield curve is usually upward sloping.
• According to Expectations Theory The market
  usually expects interest rates to increase.
• But interest rates are stationary they decrease
  from one period to the next about as often as
  they increase.

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Should You Be Indifferent?

• Both bonds are default-free
• Does one strategy expose you other kinds of risk?
• If so, then the return from this strategy should
  be higher to entice investors to buy these bonds.
• The price of this strategy should be lower.

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Should you Be Indifferent? View1

• Youre locked in to get the return with the two
  year bond
• There is uncertainty regarding the actual return
  youll get by buying the one year bond and
  rolling it over.
• Perhaps buying the one-year bond is perceived as
  more risky than just locking in and buying the
  two-year bond.

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Should you Be Indifferent? View2

• Suppose that in 1 year, there is a chance you may
  need to liquidate and get cash to pay off some
  financial obligation.
• In the example, initially,

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Should you Be Indifferent? View2

• Suppose at time t1, 1-year rates jump to 14
• What do you get back from each strategy?
• Strategy of rolling over short-term bonds
• Face value back from the bond (1000)
• Return 1000/909.09 -1 10

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Should you Be Indifferent? View2

• What is price of 2-year bond?
• It only has 1-year left until it matures
• 1-yr rates are 14
• Price 1000/1.14 877.19
• Return 877.19/826.45 -1 6.14

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Should you Be Indifferent? View2

• With the two year bond, you are exposed to
  greater risk if you need to cash out of the
  investment strategy before the end of the 2nd
  year, that is, if you need liquidity.
• Perhaps buying the two-year bond is perceived as
  more risky than buying the one-year bond and
  rolling over the proceeds.

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Liquidity Preference Theory

• Liquidity Preference Theory
• View 2 dominates View 1
• Long term default-free bonds are considered to be
  more risky that short-term bonds, since in the
  short term, if liquidity is needed, the return
  from long term bonds is more uncertain.

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Liquidity Preference Theory

• What about forward rates?
• Forward rates by definition always satisfy
• Hence, if
• then

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Liquidity Preference Theory

• According to the LPT

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Example

• Suppose at time t, the market expects
• It follows that on average, the market expects

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Example

• Suppose as of time t
• YTM on a 1-year zero is 10 ( )
• YTM on a 2-year zero is 12 ( )
• What are ?

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Longer Term Bonds

• For a three-year bond, it is always true that
• by the definition of forward rates.

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Longer Term Bonds

• Liquidity Preference Theory says that
• forward rates are greater than expected future
  short-term rates since forward rates include the
  liquidity premium.

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Longer Term Bonds

• This implies that
• The liquidity preference theory says that the
  n-period spot rate is greater than the average of
  the one period rates expected to occur over the
  n-period life of the bond.

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Example

• Expected one-period spot rates
• Then

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Example

• A flat trend in expected short-term rates
  produces an upward sloping yield curve, because
  of the liquidity premium.
• In general, ln increases with n.

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Example

• You work for the bond trading desk of a large
  investment bank.

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Example

• 2-year forward rate
• (1.09)(1f2)(1.105)2
• f2 12.02
• 2-year risk premium

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Example

• A client, who is concerned about interest rate
  risk, has asked for your help in constructing a
  forward loan. She wants to enter into a contract
  to
• borrow 50 thousand from your firm a year from
  now
• to be repaid one year after.
• What is the lowest interest rate you could charge
  the client and make a profit on the transaction
  for your services?
• Show how you would structure your holdings of
  zero-coupon bonds so that your firm can exactly
  match the cash flows required by the loan.

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Example

• Assume face value of bonds 1000
• Buy 50 1-yr zero bonds.
• Price 50,000/1.09 45,872
• Fund purchase by borrowing 45,872 at 10.5
• In one year,
• bonds pay you 50,000
• Give cash to client

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Example

• In two years,
• liability has grown to
• 45,872(1.105)2 56,011
• Client owes you 50,000 interest
• As long as interest gt 6,011, you have made a
  profit
• 6,011/50,000 12.02

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Example

• But 12.02 is the 2-year forward rate
• Not a coincidence.
• You can always lock in future loans at the
  forward rate.
• As long as your client is willing to pay more
  than 12.02, you have made a profit.

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Example

• Why would your client be willing to lock in at
  any rate above 12.02?
• The client could lock in her own rate of 12.02
• May not be able to do so as efficiently as the
  bank.
• The bank makes a business of buying and selling
  bonds. The client does not.
• The client is paying a fee for the services of
  the bank.

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Example

• But if, the client expects
  to pay a higher rate on average. Why is she
  willing to do this?
• Because she is hedged against the state that
  rates jump to 17.

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Yield Curve and Recessions
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Yield Curve and Recessions

• Why does a flat yield curve predict recessions?
• Assuming risk-premia are constant, a flatter
  yield curve indicates the market expects
  short-term rates to be lower in the future than
  they are now.
• Why do forecasts of low short-term rates also
  indicate recessions?

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Yield Curve and Recessions

• Why do forecasts of low short-term rates also
  indicate recessions?
• during recessions, supply curve shifts left
  firms dont need as much debt
• during recessions, inflationary pressures are
  lower
• Demand curve shifts right
• Supply curve shifts left