FNCE 30001 InvestmentsSemester 2, 2011
12 & 14 October 2011Week 10: The Term Structure of Interest
RatesRatesProfessor Rob Brown
FNCE 30001 Investments 10.0
Lecture 9: The Term Structure of Interest Rates
Overview of Lecture1. Zero Rates, Forward Rates and Actual Rates,2. What Determines the Forward Rate?3. The Term Structure of Interest Rates (TSIR): Definition 3. T e Te St ct e o te est ates (TS ): e t o4. TSIR Explanations (1): The Expectations Hypothesis5. TSIR Explanations (2): The Liquidity Premium Hypothesis5. TSIR Explanations (2): The Liquidity Premium Hypothesis6. Interpreting the Slope of the TSIR
Reading: Bodie et al Chapter 15Reading: Bodie et al, Chapter 15.
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1. Zero Rates, Forward Ratesd A l Rand Actual Rates
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Zero Rates Forward Rates and Actual RatesZero Rates, Forward Rates and Actual Rates
Zero rate: the interest rate for the period from today (time 0) to a future date. Symbol: z.
30 1 2 3
z01z02
z03
The arrows go in both directions because the interest rate applies to both borrowing and lending.
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Zero Rates Forward Rates and Actual RatesZero Rates, Forward Rates and Actual Rates
F d h i d ( i 0) f hForward rate: the interest rate, set today (time 0), for the period from one future date to another future date. Symbol: f.
0 1 2 3
f12f23
f13
The arrows go in both directions because the interest rate applies to both borrowing and lending.
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Zero Rates Forward Rates and Actual RatesZero Rates, Forward Rates and Actual Rates
Example: f13 is the interest rate set today (time 0) and applying from time 1 until time 3.
Th i if i h l k i h i That is, if someone wishes to lock in the interest rate on a loan to begin at time 1 and end at time 3, they can go to the forward market and get a forward contract and thethe forward market and get a forward contract and the interest rate will be set at f13 .
FNCE 30001 Investments 10.5
Zero Rates Forward Rates and Actual RatesZero Rates, Forward Rates and Actual Rates
Actual (future) rate: the market interest rate at a future time. ( )Symbol: r.
For example, r13 means the interest rate applying from time 1 to time 3. We wont know the value of r13 until we get to time 1.
By definition, r01= z01; r02= z02; r03= z03 etc
0 1 2 30 1 2 3
The arrows go in both directions because the interest rate applies to both borrowing and lending
r12 r23r01
FNCE 30001 Investments 10.6
applies to both borrowing and lending.
Zero Rates Forward Rates and Actual RatesZero Rates, Forward Rates and Actual Rates
Discount factors
As we know, there is a discount factor associated with each zero rate.For example, d04 is defined as:
1
A d th r i for rd di t f t r i t d ith h 04 404
1 .1
dz
And there is a forward discount factor associated with each forward rate.For example d is defined as:For example, d14 is defined as:
14 3141 .
1d
f
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141 f
2. What Determines the Forward R ?Rate?
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What Determines the Forward Rate?What Determines the Forward Rate?
The forward rate can be determined from the current zero rates.Example: Forward rate f35Suppose I have $X that I want to invest for 5 years. Then:1. The obvious thing to do is to lend $X for a term of 5 years (ie buy
5 )a 5-year zero).But there are lots of other things I could do. For example, I could:
d b2. (a) Lend $X for a term of 3 years (ie buy a 3-year zero) AND(b) Buy a forward contract to buy a 2-year zero at time 3.
FNCE 30001 Investments 10.9
What Determines the Forward Rate?What Determines the Forward Rate?
Example: Forward rate f35 (contd.)
0 2 3 41 5
f
(1) z05
(2) f35(2) z03
Effectively, (1) and (2) are the same thing.Therefore, the return on (1) and (2) should be the same.If the returns are not the same there is an arbitrage (a free lunch).
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What Determines the Forward Rate?What Determines the Forward Rate?
Example: Forward rate f35 (contd.)1. Lending $X for a term of 5 years (ie buying a 5-year zero).
At the end of the 5th year I will have $X (1+z05)5.2. (a) Lending $X for a term of 3 years (ie buying a 3-year
zero).At the end of the 3rd year I will have $X (1+z03)3.(b) Buying a forward contract to buy a 2-year zero at time 3.At the end of the 5th year I will have $X (1+z03)3 (1+f35)2.
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What Determines the Forward Rate?What Determines the Forward Rate?
Example: Forward rate f35 (contd.)
To prevent arbitrage we require that:
5 3 205 03 35$ 1 $ 1 1which implies that:X z X z f
1 2505
35 3
p
11
zf
3
031+z
The general formula (for ) when the current date is time 0:t T
1 ( )
0
0
1
1
T tTT
tT tt
zf
z1.
FNCE 30001 Investments 10.12
0tz
What Determines the Forward Rate?What Determines the Forward Rate?
Numerical ExampleThe zero rate for t = 5 years (z05) is 7.25% pa.The zero rate for T = 8 ears (z ) is 8 755% paThe zero rate for T = 8 years (z08) is 8.755% pa.What is the forward rate (pa) for the period from t = 5 to T = 8? (ie what is f58?)Answer 1
0
0
11
1
T T tT
tT tt
zf
z
18 8 5
58 51.0875
11 0725
f
1/3
1.0725
1.37862967 111 297% pa
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11.297% pa
What Determines the Forward Rate?What Determines the Forward Rate?
We can rearrange:1
1
0
0
11
1
T T tT
tT tt
zf
z
to find that:
1 1 1T t T tf What is the 0 01 1 1 .T t tTz z f
1 1 1Hence:intuition here?
0 0
0 0
Hence: 1 1 1T t T tT t tT
T t tT
z z fie d d d
00
TtT
t
ddd
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3. The Term Structure of Interest R D fi i iRates: Definition
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The Term Structure of Interest Rates: Definition
Th f i (TSIR) f h diff The term structure of interest rates (TSIR) refers to the different interest rates that, at a given time, apply to different investment terms.
Various curves describe the relationship(s) between interest rate and term. The three most often used interest rate curves are:
z : zero rate curves;f : forward rate curves (for one-period investments); andy : yield curves.
These represent investors views about the interest rates on: b d current zero-coupon bonds; future zero-coupon bonds; and current coupon bonds
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current coupon bonds.
The Term Structure of Interest Rates: Definition
Flat curve: f = z = y ;Rising curve: f > z > y ; andFalling curve: f < z < y .
We will use term structure of interest rates to mean todays f f h i iset of zero rates for the various terms to maturity.
We established these r l ti n hip in W k 8relationships in Week 8
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4. TSIR Explanations (1):Th E i H h iThe Expectations Hypothesis
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TSIR Explanations (1): The Expectations Hypothesis
Usually, long-term interest rates are higher than short-term interest rates why?B i l i l h hBut sometimes, long-term interest rates are lower than short-term interest rates why?
It is critical to know the term structure to price bonds It is critical to know the term structure to price bonds. Two major explanations:
Th E p t ti H p th i The Expectations Hypothesis The Liquidity Premium Hypothesis.
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TSIR Explanations (1): The Expectations Hypothesis
Assume that investors are risk neutral. By definition, risk neutral investors ignore risk. They care
l b donly about expected returns. Faced with a choice between two investments, a risk neutral
investor will always choose the one with the higher expectedinvestor will always choose the one with the higher expected return even if it is much riskier and the expected return is only a even if it is much riskier and the expected return is only a
little higher.
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TSIR Explanations (1): The Expectations Hypothesis
C id h f ll i h i $X f 3 Consider the following three ways to invest $X for 3 years:1. Buy a 3-year zero today;2 I iti ll shorter th th i tm t h riz2. Initially, go shorter than the investment horizon:
a. Buy a 2-year zero today andb At the end of the 2 years collect the par value andb. At the end of the 2 years, collect the par value, and
then buy a 1-year zero.3. Initially, go longer than the investment horizon:y, g g
a. Buy a 4-year zero today andb. Sell it at the end of 3 years.
The return from Strategy 1 is certain why? But the returns from Strategies 2 and 3 are risky why?
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TSIR Explanations (1): The Expectations Hypothesis
S 1Strategy 1 The sum that will be accumulated by Strategy 1 is:
S = $X (1+ )3S1 = $X (1+ z03)3.Strategy 2 The sum that will be accumulated by Strategy 2 is: The sum that will be accumulated by Strategy 2 is:
S2 = $X (1 + z02)2 (1 + r23). Today (time 0), r23 is unknown, but investors today expect itToday (time 0), r23 is unknown, but investors today expect it
to be E(r23). So, the sum expected to be accumulated by Strategy 2 is:
E(S2) = $X (1 + z02)2 [1+E(r23 )]
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TSIR Explanations (1): The Expectations Hypothesis
C i S i 1 d 2Comparing Strategies 1 and 2: If S1 > E(S2) then risk-neutral investors will choose Strategy 1.
If E(S ) > S th ri k tr l i t r ill h Str t 2If E(S2) > S1 then risk-neutral investors will choose Strategy 2. Therefore, in equilibrium, S1 = E(S2). That is $ X (1+ z )3 = $X (1 + z )2 [1+E(r )] That is, $ X (1+ z03) = $X (1 + z02) [1+E(r23 )]. Hence (1+ z03)3 = (1 + z02)2 [1+E(r23 )]. Generalising from this example, for two future dates t and TGeneralising from this example, for two future dates t and T
(where t < T ):(1+ z0T)T = (1 + z0t)t [1+E(rt T )]T t.
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TSIR Explanations (1): The Expectations Hypothesis
Strategy 3
The sum that will be accumulated by Strategy 3 is:
4
043
34
$ 1.
1X z
Sr
Today (time 0), r34 is unknown, but investors today expect it to be E(r34).
b d b So, the sum expected to be accumulated by Strategy 3 is:
4
04$ 1EX z
S 3 34E 1 ES r
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TSIR Explanations (1): The Expectations Hypothesis
Comparing Strategies 1 and 3:
If S1 > E(S3) then risk-neutral investors will choose Strategy 1.1 ( 3) gyIf E(S3) > S1 then risk-neutral investors will choose Strategy 3.
Therefore, in equilibrium, S1 = E(S3)., q , 1 ( 3) That is,
4$ 1X z
3 04
03344
$ 1$ 1
1 E
1
X zX z
r
43 04
0334
1Hence 1
1 Ez
zr
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TSIR Explanations (1): The Expectations Hypothesis
Comparing Strategies 1 and 3 (contd.):
Generalising from this example, for two future dates t and T( h t < T )(where t < T ):
0
01
1T
t Tt T t
zz
Rearranging this equation, we find: 1 E T ttTr
0 01 1 1 Ehi h i h l f d h
T tT tT t tTz z r
which is the same result we found when we compared Strategies 1 and 2.
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TSIR Explanations (1):TSIR Explanations (1): The Expectations Hypothesis
Interpretation:
If the expected returns are the same, risk-neutral investors do h h h f h i inot care whether the term of their investment:
Matches their investment horizon (Strategy 1)I h h h i i h i (S 2) Is shorter than their investment horizon (Strategy 2)
Is longer than their investment horizon (Strategy 3).
This is because, by definition, they do not care about risk.If the expected returns are the same, they place no value on the fact that Strategy 1 is less risky than Strategies 2 and 3.
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TSIR Explanations (1): The Expectations Hypothesis
Compare this equation:p q(1+ z0T)T = (1 + z0t)t [1+E(rt T )]T t
with this one we covered earlier:Assumes risk neutrality
(1 + z0T )T = (1 + z0t )t (1 + ft T )T t Assumes there are no arbitrage opportunities
Thus, according to the expectations hypothesis:E(rt T ) = ft T
This is the heart of the Expectations Hypothesis: Th k d f h hThe market sets todays term structure of zero rates such that the resulting forward rates are equal to the markets expectations of future interest rates.
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f
TSIR Explanations (1): The Expectations Hypothesis
Thousands of thingsg
Expected future interest rates
Todays zero rates (ie todays term structure)
Todays forward rates
Trade bonds
Do forwards = expected?
Trade bonds
Equilibrium TSIR
YES NO
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Equilibrium TSIR
TSIR Explanations (1): The Expectations Hypothesis
ll h d h h hRecall that according to the expectations hypothesis:
0 01 1 1 E T tT tT t tTz z r Suppose t = 2 and T = 3. Then:
3 21 1 1 Ez z r
But the expectations hypothesis also maintains that when 1 d T 2 h
03 02 231 1 1 Ez z r
t = 1 and T = 2 then:
202 01 121 1 1 Ez z r 303 01 12 23So 1 1 1 E 1 Ez z r r
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TSIR Explanations (1): The Expectations Hypothesis
l f h f h Generalising from this gives us a more convenient statement of the expectations hypothesis.
For any given term to maturity of T, the hypothesis states that the current y g y , ypzero rate for that term (z0T) is set by the market such that:
0 01 12 23 11 1 1 E 1 E ... 1 ETT T Tz z r r r
0 01 12 23 1,
1
0 01 12 23 1
...
Therefore:
1 1 E 1 E ... 1 E 1
T T T
T
T T T
z z
z z r r r
This is a geometric average of the zero and the expected rates.
0 01 12 23 1,1 1 E 1 E ... 1 E 1T T Tz z r r r If the expectations hypothesis is true, then the expected rates are equal to the
forward rates.
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TSIR Explanations (1): The Expectations Hypothesis
Th t i th p t ti h p th i b t t d thi That is, the expectations hypothesis can be stated this way:The current zero rate for a term of T years is a function of the current zero rate for Year 1 and the expected one yearthe current zero rate for Year 1 and the expected one-year rates for Year 2, Year 3, Year 4, etc up to T years.
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TSIR Explanations (1): The Expectations Hypothesis
Example 1
Suppose the expectations hypothesis is true. Todays one-year zero rate (z01) is 10.0%.The expected one-year rates are:
Year 1: E(r12) = 12.0%Year 2: E(r23) = 13.0%Year 3: E(r34) = 13.4%Year 4: E(r45) = 13.5%
What is todays term structure of interest rates?
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TSIR Explanations (1): The Expectations Hypothesis
Answer to Example 1According to the expectations hypothesis, the market will set todays zero rates such that todays forward rates equal expected future ratesrates such that today s forward rates equal expected future rates.Therefore f12 = E(r12) = 12.0%. 2021B d fi iti 1zf
0212
012
02
By definition 11
1Th f 0 12 1
zf
z
z
02
02
Therefore 0.12 11.10
which solves to give 0.10995 10.995%
z
z
By similar reasoning we can find z03, z04 and z05.
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TSIR Explanations (1): The Expectations Hypothesis
Or, just applying the formula:
10 01 12 23 1,1 1 E 1 E ... 1 E 1TT T Tz z r r r 0 0 3 ,1 2
we get
T T Tz z
1 202
1 303
1.10 1.12 1 10.995% pa
1.10 1.12 1.13 1 11.660% pa
z
z
031 4
04
1.10 1.12 1.13 1 11.660% pa
1.10 1.12 1.13 1.134 1 12.092% pa
z
z
1 505 1.10 1.12 1.13 1.134 1.135 1 12.372z % pa
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TSIR Explanations (1): The Expectations Hypothesis
Example 2
Given these expectations, an investor wonders what next ill l k likyears term structure will look like.
Assuming that the expectations hypothesis is true, and expectations are fulfilled (that is at the start of next year theexpectations are fulfilled (that is, at the start of next year, the one-year rate is indeed 12% pa, as expected), what should be the term structure next year?y
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TSIR Explanations (1): The Expectations Hypothesis
Answer to Example 2We can summarise the results so far in the following table:
Term Now (ie at t = 0)Start of next year
(ie at t = 1) At t = 2 At t = 3 At t = 4
g
1 year z01=10.000% z12 = 12.000% 13.000% 13.400% 13.500%2 years z02=10.995% E(z13)3 years z03=11.660% E(z14)4 years z04=12.092% E(z15)5 12 372%5 years z05=12.372%
We want to calculate E(z13), E(z14) and E(z15).
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TSIR Explanations (1): The Expectations Hypothesis
Answer to Example 2 (contd.)
Time has in effect moved on 1 year from 0 to 1t t
1
Time has, in effect, moved on 1 year from 0 to 1.So the relevant formula now is:
T
t t
1 12 23 34 1,E 1 1 E 1 E ... 1 E 1T T Tz z r r rHence:
1/2131/3
Hence:
E 1.12 1.13 1 12.4989% paz
1/314
1/415
E 1.12 1.13 1.134 1 12.7985% pa
E 1.12 1.13 1.134 1.135 1 12.9734% pa
z
z
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5
TSIR Explanations (1): The Expectations Hypothesis
Answer to Example 2Adding these results to the table:g
Term Now (ie at t = 0)Start of next year
(ie at t = 1) At t = 2 At t = 3 At t = 4(ie at t = 0) (ie at t = 1)1 year z01=10.000% z12 = 12.000% 13.000% 13.400% 13.500%2 years z02=10.995% E(z13) = 12.4989%2 years z02 10.995% E(z13) 12.4989%3 years z03=11.660% E(z14) = 12.7985%4 years z04=12.092% E(z15) = 12.9734%y z04 (z15)5 years z05=12.372%
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TSIR Explanations (1): The Expectations Hypothesis
This means the TSIR is forecast to rise and flatten next year:14.000
10.000
12.000
6.000
8.000
R
A
T
E
(
%
p
a
)
TSIR this yearTSIR next year
2 000
4.000
0.000
2.000
0 1 2 3 4 5 6
TERM (YEARS)
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TERM (YEARS)
TSIR Explanations (1): The Expectations Hypothesis
S o , if w e h av e a fo re cast o f n ex t y e a rs (t im e 1 's) te rm stru c tu re y ( )w e c an d ed u ce n ex t y e a r 's fo rw ard cu rv e .T h e fo rm u la w h en th e cu rren t d a te is t im e 1 is :
1 ( )11
11
11, w h ich im p
1
T tTT
tT tt
zf
zl ie s : 1 tz
2
2 3 2 31 .1 2 4 9 8 9
1 1 3 .0 0 0 % E1 .1 2 0 0 0
f r
3
3 4 3 42
1 .1 2 0 0 01 .1 2 7 9 8 5
1 1 3 .4 0 0 % E1 .1 2 4 9 8
f r
4
4 5 4 531 .1 2 9 7 3 4
1 1 3 .5 0 0 % E1 1 2 7 9 8 5
f r
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1 .1 2 7 9 8 5
4. TSIR Explanations (2):Th Li idi P i H h iThe Liquidity Premium Hypothesis
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TSIR Explanations (2): The Liquidity Premium Hypothesis
The Main Weakness of the Expectations HypothesisThe Main Weakness of the Expectations Hypothesis The expectations hypothesis assumes that investors are risk neutral.
Ri k li i h d d i i Fi Risk neutrality is not the standard assumption in Finance. If all investors were risk neutral, then (for example):
i h l h di ifi d f li f h in the long term, the return on a diversified portfolio of shares would be the same as the interest rate on bank deposits;no homeo ner o ld ins re their home g inst fire no homeowner would insure their home against fire.
This is a pretty strange world!
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TSIR Explanations (2): The Liquidity Premium Hypothesis
The standard assumption in finance is risk aversion. That is, investors regard risk as undesirable.
Thus, bearing risk must be compensated by a higher expected return.
If ll i i k h (f l ) If all investors were risk averse, then (for example): in the long run, the return on a diversified portfolio of
h r ill d th i t r t r t b k d p itshares will exceed the interest rate on bank deposits; at least some homeowners will insure against fire.
Thi i h lik h ld li i ! This is much more like the world we live in! The liquidity premium hypothesis assumes that investors
are risk averseFNCE 30001 Investments 10.44
are risk averse.
TSIR Explanations (2): The Liquidity Premium Hypothesis
Consider again the following three ways to invest $X for 3 years:1 B 3 d1. Buy a 3-year zero today;2. Initially, go shorter than the investment horizon:
B 2 d da. Buy a 2-year zero today andb. At the end of the 2 years, collect the par value, and then
b 1 r z rbuy a 1-year zero.3. Initially, go longer than the investment horizon:
B 4 d da. Buy a 4-year zero today andb. Sell it at the end of 3 years.
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TSIR Explanations (2): The Liquidity Premium Hypothesis
With risk-neutral investors (ie the expectations hypothesis), the market will set interest rates such that the returns from Strategies 1 2 and 3 are equal:Strategies 1, 2 and 3 are equal:
43 2 04
03 02 2334
11 1 1 E
1 Ez
z z rr
Suppose instead that investors are risk averse. S pp l th t e er i t r i thi m rk t h 3 r
341 E r
Suppose also that every investor in this market has a 3-year investment horizon.
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TSIR Explanations (2): The Liquidity Premium Hypothesis
Th Then:
1 23
3 2 0311 1 1 1 dz
3 2 0303 02 23 02
23
4 1 43 304
1 1 1 E 1 and1 E
11 1 1 E 1
zz z r z
r
z
Thus, because of risk aversion, both the 2-year rate (z02) and
3 30403 04 03 34341 1 1 E 11 Ezz z z rrThus, because of risk aversion, both the 2 year rate (z02) andthe 4-year rate (z04) will be higher than in a risk-neutral world.
Investors have to be offered higher interest rates to induce them to go shorter (2 years) and longer (4 years) than their horizon.
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TSIR Explanations (2):
B i i lik l h ll i (l d ) ld h
The Liquidity Premium Hypothesis
But it is most unlikely that all investors (lenders) would have the same investment horizon (3 years).
Some investors (lenders) would have a 2-year horizon some aSome investors (lenders) would have a 2-year horizon, some a 3-year horizon, some a 4-year horizon etc.
However, according to the liquidity premium hypothesis, g q y p ypthere is a pattern.
This pattern is: There is a systematic tendency for borrowers to want to b f l n r p i d th l d t t l dborrow for longer periods than lenders want to lend.
That is, investors (lenders) display a preference for liquidity (making shorter-term loans).(making shorter term loans).
Hence, investors (lenders) require extra inducement if they are to make long-term loans.
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TSIR Explanations (2): The Liquidity Premium Hypothesis
According to the liquidity premium hypothesis, the relevant case to look at is where an investor is induced to lend for a term that exceeds the investment horizon:term that exceeds the investment horizon: As in the case where investors have a 3-year horizon but
are induced to buy a 4-year zero:are induced to buy a 4 year zero:
43 04
031
1z
z
0334
43 04
1 E
1Th f 1
zr
z 04
0334 34
34
Therefore: 11 E
where is an extra return (a liquidity premium).
zz
r LL
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34where is an extra return (a liquidity premium).L
TSIR Explanations (2): The Liquidity Premium Hypothesis
404
34 34303
1Therefore: 1 E
1
zL r
z 34 34Ef r
34 34 34which we can rewrite as: Ef r L The liquidity premium hypothesis says that the zero rates
(term structure) set by market participants produce forward
34 34 34f
rates that are equal to the relevant expected rate plus a little bit this little bit being the liquidity premium
Th li idi i b d i i h The liquidity premium may be assumed to increase with term.
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TSIR Explanations (2): The Liquidity Premium Hypothesis
Thousands of thingsg
Expected future interest rates
Todays zero rates (ie todays term structure)
Todays forward rates
Trade bonds
Do forwards = expected + L ?
Trade bonds
Equilibrium TSIR
YES NO
FNCE 30001 Investments 10.51
Equilibrium TSIR
TSIR Explanations (2): The Liquidity Premium Hypothesis
The general effect of having a liquidity premium is that there is a bias towards longer-term interest rates being higher than would be justified purely on the basis of expectations of future interestbe justified purely on the basis of expectations of future interest rates.
Note that the liquidity premium hypothesis builds on theNote that the liquidity premium hypothesis builds on the foundation of the expectations hypothesis; both hypotheses maintain that expectations are important.yp p p
To avoid confusion, they are sometimes renamed:expectations hypothesis pure expectations hypothesisexpectations hypothesis pure expectations hypothesisliquidity premium hypothesis biased expectations hypothesis
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TSIR Explanations (2): The Liquidity Premium Hypothesis
Suppose a time came when lenders had a longer-terminvestment horizon than borrowers.
Wh i h hi h ? When might this happen? Then lenders would need to be induced to lend for short
periodsperiods. The liquidity premium would be negative.
Th t i th r ld b p lt ppli d t l d r h That is, there would be a penalty applied to lenders who wanted to lend for long periods.
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5. Interpreting the Slope of the TSIRTSIR
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Interpreting the Slope of the TSIRInterpreting the Slope of the TSIR
d b l Suppose, today, we observe a particular term structure. Given belief in a theory of the term structure we may be able to infer what
investors expectations are. p For example,
if todays term structure is flat (at 10% pa), then
if we believe in the pure expectations hypothesis, investors must expect interest rates will not change in the future;investors must expect interest rates will not change in the future; but
if we believe in the liquidity premium hypothesis, and also believe that the liquidity premium rises with term, then investors must expect interest rates to fall in the future.
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Interpreting the Slope of the TSIRInterpreting the Slope of the TSIR
Todays TSIRP i
Interest Pure expectations:
All forward rates = 10% paAll expected rates = 10% pa
rate (pa)
10%
LLt,t+1
Rising liquidity premium:All forward rates = 10% paAll expected rates = 10% Lt, t+1
Term (years ahead)
FNCE 30001 Investments 10.56INTERPRETING THE TSIR WITH A RISING LIQUIDITY PREMIUM
Interpreting the Slope of the TSIRInterpreting the Slope of the TSIR
Excluding the possibility of a negative liquidity premium, the slope of the term structure is interpreted as shown in the table:
If todays term structure of
Then market expectations of future interest rates are:
According to the (pure) According to the liquidity interest rates is:
g (p )expectations hypothesis
g q ypremium hypothesis
Increasing Increasing Increasing, Flat or Decreasing
Flat Flat Decreasing
Decreasing Decreasing Decreasing
FNCE 30001 Investments 10.57