Financial Investments & Pricing Overview
1
T
e
r
m
S
t
r
u
c
t
u
r
e
A
.
C
a
g
g
i
a
,
M
.
A
r
m
a
n
i
n
i
F
i
n
a
n
c
i
a
l
I
n
v
e
s
t
m
e
n
t
s
&
P
r
i
c
i
n
g
2
0
1
5
/
2
0
1
6
2
S
P
O
T
v
s
.
F
O
R
W
A
R
D
S
P
O
T
R
A
T
E
(
S
t
)
:
i
s
t
h
e
a
n
n
u
a
l
i
n
t
e
r
e
s
t
r
a
t
e
t
h
a
t
c
a
n
b
e
l
o
c
k
e
d
t
o
d
a
y
f
o
r
t
h
e
n
e
x
t
t
y
e
a
r
s
.
F
O
R
W
A
R
D
R
a
t
e
(
F
t
)
:
i
s
t
h
e
a
n
n
u
a
l
i
n
t
e
r
e
s
t
r
a
t
e
t
h
a
t
c
a
n
b
e
e
x
t
r
a
p
o
l
a
t
e
d
t
o
d
a
y
f
r
o
m
t
h
e
m
a
r
k
e
t
a
n
d
a
p
p
l
i
e
d
t
o
a
f
u
t
u
r
e
p
e
r
i
o
d
s
t
a
r
t
i
n
g
i
n
t
y
e
a
r
s
f
r
o
m
n
o
w
.
3
S
P
O
T
v
s
.
F
O
R
W
A
R
D
R
a
t
e
s
(
c
o
n
t
i
n
u
e
d
)
T
e
r
m
S
t
r
u
c
t
u
r
e
The term structure of interest rates (risk free)
shows the existing relationship between spot
rates (also “Zero Rates”) and the time to maturity
of (risk free) bonds
T
o
c
a
l
c
u
l
a
t
e
t
h
e
z
e
r
o
r
a
t
e
s
f
r
o
m
t
h
e
p
r
i
c
e
o
f
c
o
u
p
o
n
b
o
n
d
s
w
e
u
s
e
t
h
e
B
o
o
t
s
t
r
a
p
p
i
n
g
:
t
h
i
s
i
s
a
r
e
c
u
r
s
i
v
e
m
e
t
h
o
d
t
o
c
a
l
c
u
l
a
t
e
z
e
r
o
r
a
t
e
s
f
r
o
m
m
a
r
k
e
t
p
r
i
c
e
s
,
m
a
t
u
r
i
t
y
a
f
t
e
r
m
a
t
u
r
i
t
y
4
L
i
n
e
a
r
a
s
s
u
m
p
t
i
o
n
Note that conventionally we calculate spot rates on the curve using the
linear assumption between known rates
So to find
r
t
when both
r
d
d
and
r
u
u
are known we assume a linear
are known we assume a linear
relationship
relationship
5
6
Y
i
e
l
d
C
u
r
v
e
Show the relationship between IRR (o YTM) and residual
life of the assets.
7
Y
i
e
l
d
C
u
r
v
e
(
h
t
t
p
:
/
/
w
w
w
.
s
m
a
r
t
m
o
n
e
y
.
c
o
m
/
I
n
v
e
s
t
i
n
g
/
B
o
n
d
s
/
T
h
e
-
L
i
v
i
n
g
-
Y
i
e
l
d
-
C
u
r
v
e
-
7
9
2
3
/
)
8
M
o
d
e
l
i
n
g
o
n
E
x
p
e
c
t
a
t
i
o
n
s
(
F
i
s
h
e
r
,
1
8
9
6
;
L
u
t
z
,
1
9
4
0
)
Assume that an investor should expect to earn
the same from equivalent strategies.
Suggest that spot rates reflect market
expectations of forward rates.
9
L
i
q
u
i
d
i
t
y
P
r
e
m
i
u
m
(
H
i
c
k
s
,
1
9
4
6
)
Assume that investors demand a yield premium
to compensate for investing on longer maturities.
Investors are risk adverse and prefer short term
investments to longer ones, as the formers are
more liquid than the latters.
To attract investors then the long date assets
have to bear an higher yield than the short dated
ones.
10
M
a
r
k
e
t
S
e
g
m
e
n
t
a
t
i
o
n
(
C
u
l
b
e
r
t
s
o
n
,
1
9
5
7
;
M
o
d
i
g
l
i
a
n
i
–
S
u
t
c
h
,
1
9
6
6
)
Explain the term structure of yield as a series of
preference zones for maturities chosen by
certain investors.
11
C
r
e
d
i
t
R
i
s
k
Moody’s
S
& P
Fitch
D & P
Brief Definition
I
n
v
e
s
t
m
e
n
t
G
r
a
d
e
-
H
i
g
h
C
r
e
d
i
t
w
o
r
t
h
i
n
e
s
s
Aaa
AAA
AAA
AAA
Gilt edge, prime, maximum safety
Aa1
AA+
AA+
AA+
Aa2
AA
AA
AA
Very high grade, high quality
Aa3
AA-
AA-
AA-
A1
A+
A+
A+
A2
A
A
A
Upper medium grade
A3
A-
A-
A-
Baa1
BBB+
BBB+
BBB+
Baa2
BBB
BBB
BBB
Lower medium grade
Baa3
BBB-
BBB-
BBB-
D
i
s
t
i
n
c
t
l
y
S
p
e
c
u
l
a
t
i
v
e
-
L
o
w
C
r
e
d
i
t
w
o
r
t
h
i
n
e
s
s
Ba1
BB+
BB+
BB+
Ba2
BB
BB
BB
Low grade, speculative
Ba3
BB-
BB-
BB-
B1
B+
B+
B+
B2
B
B
B
Highly speculative
B3
B-
B-
B-
P
r
e
d
o
m
i
n
a
n
t
l
y
S
p
e
c
u
l
a
t
i
v
e
-
S
u
b
s
t
a
n
t
i
a
l
R
i
s
k
o
r
i
n
D
e
f
a
u
l
t
CCC+
Caa
CCC
CCC
CCC
Substantial risk, in poor standing
CCC-
Ca
CC
CC
May be in default, extremely speculative
C
C
C
Even more speculative than those above
CI
Income bonds - no interest being paid
DDD
DD
DD
Default
D
D
12
C
r
e
d
i
t
R
i
s
k
The term structure of interest rates, spot vs forward rates, bootstrapping method for zero rates, linear assumption in calculating spot rates, yield curve analysis, and modeling on expectations in financial investments and pricing. Explore the relationship between spot rates and market expectations of forward rates. Learn about liquidity premium in investments.
Download Presentation
Please find below an Image/Link to download the presentation.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author.If you encounter any issues during the download, it is possible that the publisher has removed the file from their server.
You are allowed to download the files provided on this website for personal or commercial use, subject to the condition that they are used lawfully. All files are the property of their respective owners.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author.
E N D
Presentation Transcript
Term Structure A. Caggia, M. Armanini Financial Investments & Pricing 2015/2016 1
SPOT vs. FORWARD SPOT RATE (St): is the annual interest rate that can be locked today for the next t years. FORWARD Rate(Ft): is the annual interest rate that can be extrapolated today from the market and applied to a future period starting in t years from now. 2
SPOT vs. FORWARD Rates (continued) 3
Term Structure The term structure of interest rates (risk free) shows the existing relationship between spot rates (also Zero Rates ) and the time to maturity of (risk free) bonds To calculate the zero rates from the price of coupon bonds we use the Bootstrapping: this is a recursive method to calculate zero rates from market prices, maturity after maturity 4
Linear assumption Note that conventionally we calculate spot rates on the curve using the linear assumption between known rates So to find rt when both rd and ru are known we assume a linear relationship ( ) ( - ) t d r r = + u d r r t d - u d 5
Yield Curve Show the relationship between IRR (o YTM) and residual life of the assets. Upward Sloped Foresee raising interest rates Yield to Maturity Expactations of future rates at same level than current ones Flat Foresee lower interest rates Downward Sloped Maturity 6
Yield Curve (http://www.smartmoney.com/Investing/Bonds/ The-Living-Yield-Curve-7923/) 7
Modeling on Expectations (Fisher, 1896; Lutz, 1940) Assume that an investor should expect to earn the same from equivalent strategies. + = + + 2 1 ( ) 1 ( 1 ( * ) 1 ) S S F 2 2 F + = + + = + + + 3 2 1 ( ) 1 ( ) 1 ( * ) 1 ( 1 ( * ) 1 1 ( * ) 2 ) S S S F F 2 2 3 3 Suggest that spot rates reflect market expectations of forward rates. 8
Liquidity Premium (Hicks, 1946) Assume that investors demand a yield premium to compensate for investing on longer maturities. Investors are risk adverse and prefer short term investments to longer ones, as the formers are more liquid than the latters. To attract investors then the long date assets have to bear an higher yield than the short dated ones. 9
Market Segmentation (Culbertson, 1957; Modigliani Sutch, 1966) Explain the term structure of yield as a series of preference zones for maturities chosen by certain investors. 10
Credit Risk S & P Moody s Fitch D & P Brief Definition Investment Grade - High Creditworthiness Aaa AAA Aa1 AA+ Aa2 AA Aa3 AA- A1 A+ A2 A A3 A- Baa1 BBB+ Baa2 BBB Baa3 BBB- AAA AA+ AA AA- A+ A A- BBB+ BBB BBB- AAA AA+ AA AA- A+ A A- BBB+ BBB BBB- Gilt edge, prime, maximum safety Very high grade, high quality Upper medium grade Lower medium grade Distinctly Speculative - Low Creditworthiness Ba1 BB+ Ba2 BB Ba3 BB- B1 B+ B2 B B3 B- BB+ BB BB- B+ B B- BB+ BB BB- B+ B B- Low grade, speculative Highly speculative Predominantly Speculative - Substantial Risk or in Default CCC+ Caa CCC CCC CCC- Ca CC CC C C C CI DDD DD D D CCC Substantial risk, in poor standing May be in default, extremely speculative Even more speculative than those above Income bonds - no interest being paid 11 DD Default
Credit Risk Sept. 15 Sept. 14 Sept. 13 Past 12 months Av. Aug. Av. July High Low SPREADS ABOVE TREASURY (bp) Average Corporate Aaa: 188 Aa: 210 A: 240 Baa: 262 Average Industrial: Aaa: 154 Aa: 180 A: 227 Baa: 265 Average Public Utility: Aaa: 221 Aa: 239 A: 252 Baa: 259 225 221 222 206 144 206 194 183 207 236 259 204 185 207 237 260 206 173 188 220 247 189 116 130 153 172 127 173 188 220 244 189 161 177 207 231 175 207 150 177 224 263 238 152 178 227 265 238 144 165 209 252 223 99 112 132 164 158 139 162 209 244 223 126 147 193 232 213 243 216 236 247 254 217 235 247 254 207 213 231 243 130 147 173 179 207 213 231 243 196 206 221 229 12
