06-Liquidity Preference Theory

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.

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.

Should you Be Indifferent? View#1

You’re locked in to get the return with the two year bond

There is uncertainty regarding the actual return you’ll 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.

Should you Be Indifferent? View#2

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, %.1211 etYTM

Should you Be Indifferent? View#2

Suppose at time t+1, 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? View#2

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%

Should you Be Indifferent? View#2

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.

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

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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

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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, n 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)(1+f2)=(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.

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 > 6,011, you have made a

profit

– 6,011/50,000 = 12.02%

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.

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.

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

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?

Yield Curve and Recessions

Why do forecasts of low short-term rates also indicate recessions?

1) during recessions, supply curve shifts left – firms don’t need as much debt

2) during recessions, inflationary pressures are lower1) Demand curve shifts right

2) Supply curve shifts left