Albert Bandura’s Social Cognitive Learning Theory: Self Efficacy Expectations.
06-Liquidity Preference Theory. Expectations Theory Review Given that Expectations Theory: – Given...
-
date post
19-Dec-2015 -
Category
Documents
-
view
226 -
download
0
Transcript of 06-Liquidity Preference Theory. Expectations Theory Review Given that Expectations Theory: – Given...
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.
%12%10 111 ett YTMYTM
22 )1()12.1)(10.1( tYTM
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%
%1411 tYTM
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.
221,11 )1()1)(1( t
ett YTMYTMYTM
Liquidity Preference Theory
What about forward rates? Forward rates by definition always satisfy
Hence, if
then
2221 )1()1)(1( tt YTMfYTM
221,11 )1()1)(1( t
ett YTMYTMYTM
21,1 fYTM et
Example
Suppose at time t, the market expects:
It follows that on average, the market expects
yprobabilit 50% with
yprobabilit 50% with
%8
%12
11
11
t
t
YTM
YTM
%1011 etYTM
Example
Suppose as of time t:– YTM on a 1-year zero is 10% ( )– YTM on a 2-year zero is 12% ( )– What are ? 22 and f
%36.4%10%36.14
%36.14
)12.1()1)(10.1(
2
2112
22
e
tYTMf
f
%101 tYTM
%122 tYTM
Longer Term Bonds
For a three-year bond, it is always true that
by the definition of forward rates.
tt
tt
YTMffYTM
YTMffYTM
3321
33321
3
)1()1)(1)(1(
implies ionapproximat an to which
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.
et
et YTMfYTMf 213112 ,
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.
3321111
3321
et
ett
tt YTMYTMYTM
YTMffYTM
Example
Expected one-period spot rates
Then
%3.1%,1%,5.0
%4%,4%,4%,4
432
3121111
et
et
ett YTMYTMYTMYTM
%7.44/%)3.5%5%5.4%4(
%5.43/%)5%5.4%4(
%25.42/%)5.4%4(
%3.5%3.1%4
%5%1%4
%5.4%5.%4
4
3
2
4
3
2
t
t
t
YTM
YTM
YTM
f
f
f
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.
%7.4
%5.4
%25.4
4
3
2
t
t
t
YTM
YTM
YTM
Example
You work for the bond trading desk of a large investment bank.
%5.10
%9
2
1
t
t
YTM
YTM
? is What
rate? forward yr-2 is What
is What
yprobabilit :2 State
yprobabilit :1 State
t
et
t
t
YTM
YTM
YTM
2
11
11
11
?
)%50(%3
)%50(%17
Example
2-year forward rate:– (1.09)(1+f2)=(1.105)2
– f2= 12.02%
2-year risk premium:
%10)17.0(50.0)03.0(50.011 etYTM
%02.2%10%02.122
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
%5.10%9 21 tt YTMYTM
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%.
%1011 etYTM
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?