Inv Lecture 4.pdf-Investments Prof. Andr...
Inv_Lecture_4.pdf-Investments Prof. Andrea Buraschi Lecture 4
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Inv Lecture 4.pdf-Investments Prof....
Inv_Lecture_4.pdf-Investments 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 6-month 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
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.
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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