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Inv Lecture 4.pdfInvestments Prof. Andrea Burasch...
Inv_Lecture_4.pdfInvestments Prof. Andrea Buraschi Lecture 4
Inv Lecture 4.pdfInvestments Prof....
Inv_Lecture_4.pdfInvestments Prof. Andrea Buraschi Lecture 4
Page 16
Example 2: Opposite
Suppose current rates were reversed:
6
‐
month: r
.5
=0.33%
and 1
‐
year: r
1
=0.16%.
What is the in 6M for 6M forward rate?
Interpretation? Negative forward rates?
%
01
.
0

0001
.
0
1
2
/
0033
.
0
1
/2)
0016
.
0
(1
2
f
2
.5
.5
Page 17
Terminology: long versus short
You are long the forward if you have locked in to invest at the
forward rate. Payoffs are similar to buying (going long) a
bond
Win if rates decrease (you’ve locked in at a higher rate) and you lose if
rates increase
The other side (short) is guarantee to pay the forward rate.
Exposed to floating rate risk.
Like shorting a bond.
Alternative to forward contract: do nothing and borrow at
floating rate.
Page 18
Different Forward Rates
Forward rates for borrowing/lending for 6 months
starting in k years:
6
‐
month spot rates in the future
Forward rate for borrowing/lending for j
‐
years starting
6 months from now:
Spot rate curve, in 6
‐
months
m
1,...,
k
for
f
.5
k
n
1,...,
j
for
f
j
.5
Page 19
The general formula for the 6
‐
month rate, m
‐
years in the future
is:
Where r
m
is the m
‐
year spot rate
Where did this come from?
General formula for 6month forward rates
1
/2)
r
1
(
/2)
r
1
(
2
f
2m
m
1
2m
5
.
m
.5
m
Page 20
Interpretation of forward rates
m
f
.5
m
f
.5
is the rate you can lock in now for 6
‐
month
borrowing/lending starting in
m
years
Forward rates contain information about the market’s guess of
what the 6
‐
month rate will be in the future
Forward rates tell us something about future spot rate!
Page 21
Does today’s forward rate,
.5
f
.5
(t), contain information about
future 6
‐
month spot rates, r
.5
(t+1)?
Hypothesis:
where I(t)=information at time t
Hypothesis: Forward rates forecast future spot rates.
]
I(t)
1)
(t
E[r
(t)
f
.5
.5
.5
Expectations theory of interest rates
Page 22
How would you specify a regression for testing the expectations
hypothesis?
In practice, the regression is typically specified as:
Forward rates contain information about future spot rates, but the
forecast is not perfect
1)
e(t
(t)]
r
(t)
f
[
β
α
(t)
r
1)
(t
r
.5
.5
.5
1
0
.5
.5
Testing the Expectations Hypothesis
R
2
U.S.
.550 (0.129)
.028
Japan
.552 (0.028)
.086
Page 23
Expectation hypothesis: 6
‐
month spot and forward rates.
What about the whole curve?
Active bond managers are interested in what the yield (spot)
curve will look like in the future.
How can it change?
Parallel shifts
Twists: i.e. steepen or flatten.
The future yield (spot) curve
Page 24
The forward yield curve
A
B
A
B
Flattening Twist
Steepening Twist
Under which scenario would you rather be in portfolio A instead of B? Why?
r
n
r
n
maturity
maturity
Future spot Curve
Current Spot Curve
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