Lecture 1
Yield to
maturity Rate of return
YTM is the interest rate that matches A coupon band bought at time t and
/ price with the sold at t has
present
-11
today 's value
RET Re C + Pe Pt
future
= = -
value of all cash flows .
c- + i
Pt
PV CF
Pete
=
"
=
( +
,
-
Pt
Citi )
p , Pt
Credit market instruments
=
ic +
ge
where ic and
= current
yield
1 simple loan
2 Fixed
ge = rate of expected capital gain .
payment loan
-
3 coupon bond key facts maturity and returns
4 Discount ( ) bond
1 If return =
yield then
ze ro -
coupon
maturity =
holding period and vice
Relation YTM
price and versa .
1 Price and YTM a re
negatively related 2 If maturity >
holding period and
P t
"
2 the bond traded
"
at then it then
resulting in capital
If is
par ,
,
loss
price equal to its face value and
.
is
the YTM
3 The effect of interest rate changes
equals the coupon rate
is
larger for long maturities
3
.
YTM rate
>
coupon if bond price
4 The change in return becomes
larger
is below
par
when maturity increases if
Consol interest rate
changes .
A perpetuity or consol is a bond without 5 Bond with high initial interest rate
date ,
maturity so
principal is not payed and/or coupon rate can end up
continue
back and coupon payments with a
negative rate of return
forever .
if it .
Pc = C
Interest rate risk
ic
This approximation
longer term bonds react
stronger to
gives an
easy for
changes in interest For
any bond
the YTM bond
.
of a which is m o re
,
which is held for the entire maturity ,
precise if price is near
par and
long
there is no interest rate risk .
maturity .
Fisher equation
'
c- = r + He ,
ir = r =
i -
IT
when the real interest rate is lower ,
people a re m o re willing to borrow .
S. Veeling
, Demand shift
This can be caused
by the
following
Demand and
supply analyses bonds
for
factors :
If prices a re low and so interest high then
1
, ,
wealth if wealth
:
economy grows ,
demand is
higher and supply tower .
of individuals increases so that
If excess
supply ,
the price drops and in
demand for bonds increases and
case
of demand the price rises
Bd
excess .
shifts to the right .
Supply shift
2 Expected return of bonds relative to
This other assets if the bonds become
can happen in case
of :
:
1 Expected profitability of investments : less attractive
,
Bd shifts to the left
In times
of business cycle expansion ,
*
if expected interest rate ⇐p )
investment opportunities increase and
increases
,
so ie T ,
then Pete
BS shifts to the
right and as a result expected return
.
,
2 te
Expected inflation : i n c re a s e in
Re Iv and Bd shifts to the left .
leads to r = i -
ite t So the real
if expected inflation ITET then
.
*
,
and
cost
of borrowing decreases
ir=r ite t Bd
by = i and
-
BS T which shifts BS to the right .
shifts to the left .
3 Government deficit : an increase
3 Risk when
investing to bonds relative
shifts Bs to the right as
they
to other assets :
if risk in bonds
need to borrow
money .
increases
,
Bd Tv and shifts to the
left .
4 liquidity of bonds relative to other
assets :
if it becomes easier relative
to other assets to tur n the asset into
cash at low cost and small value
loss the demand for bonds increases
,
and Bd shifts to the right .
S. Veeling
, Lecture 2
Real and nominal interest rates
Fisher : r= i -
ite
gives an approximation .
Precisely :
Inflation -
indexed bonds
itr = iti The
coupon payments as well as face value
I1-1TE
a re
adjusted for inflation . If inflation
> it i =
I + r + we + rite
fluctuates ,
these bonds a re saver as
If r and ite a re small ,
it rtite
they are constant in real terms .
Unstable countries provide these bonds
Fisher effect in the US 1953 -2017
to attract funding Also stable countries
Usually te i
positively related
.
and a re .
these bonds which market
i ss u e
gives
•
stable
,
The real interest rate is
kept .
estimates of future inflation .
Those
so the nominal interest rate should
if
we used
for wage negotiations and
be low and stable so should be the 1T ?
bank because it tells them
by the central
inflation stable results in
keeping low and
if the market believes in their ability .
low nominal interest .
Quantitative
easing
Example : Business cycle expansion a policy in w h i ch the UK government
→ as expected profitability increase , bought a lot
of mostly long-term
companies want to borrow bonds This increased the
money .
government .
Bs T shift to the right price of bonds and so decreased the
,
wealth to interest rates
as increases want
*
people
.
,
buy B☐ T shift to the
more bonds .
, right
normally ,
the supply effect is
larger ,
therefore P v1 and i T .
Also explained
•
i He expected to
by r + IT as is
=
i n c re a s e in a business cycle expansion .
S. Veeling
Yield to
maturity Rate of return
YTM is the interest rate that matches A coupon band bought at time t and
/ price with the sold at t has
present
-11
today 's value
RET Re C + Pe Pt
future
= = -
value of all cash flows .
c- + i
Pt
PV CF
Pete
=
"
=
( +
,
-
Pt
Citi )
p , Pt
Credit market instruments
=
ic +
ge
where ic and
= current
yield
1 simple loan
2 Fixed
ge = rate of expected capital gain .
payment loan
-
3 coupon bond key facts maturity and returns
4 Discount ( ) bond
1 If return =
yield then
ze ro -
coupon
maturity =
holding period and vice
Relation YTM
price and versa .
1 Price and YTM a re
negatively related 2 If maturity >
holding period and
P t
"
2 the bond traded
"
at then it then
resulting in capital
If is
par ,
,
loss
price equal to its face value and
.
is
the YTM
3 The effect of interest rate changes
equals the coupon rate
is
larger for long maturities
3
.
YTM rate
>
coupon if bond price
4 The change in return becomes
larger
is below
par
when maturity increases if
Consol interest rate
changes .
A perpetuity or consol is a bond without 5 Bond with high initial interest rate
date ,
maturity so
principal is not payed and/or coupon rate can end up
continue
back and coupon payments with a
negative rate of return
forever .
if it .
Pc = C
Interest rate risk
ic
This approximation
longer term bonds react
stronger to
gives an
easy for
changes in interest For
any bond
the YTM bond
.
of a which is m o re
,
which is held for the entire maturity ,
precise if price is near
par and
long
there is no interest rate risk .
maturity .
Fisher equation
'
c- = r + He ,
ir = r =
i -
IT
when the real interest rate is lower ,
people a re m o re willing to borrow .
S. Veeling
, Demand shift
This can be caused
by the
following
Demand and
supply analyses bonds
for
factors :
If prices a re low and so interest high then
1
, ,
wealth if wealth
:
economy grows ,
demand is
higher and supply tower .
of individuals increases so that
If excess
supply ,
the price drops and in
demand for bonds increases and
case
of demand the price rises
Bd
excess .
shifts to the right .
Supply shift
2 Expected return of bonds relative to
This other assets if the bonds become
can happen in case
of :
:
1 Expected profitability of investments : less attractive
,
Bd shifts to the left
In times
of business cycle expansion ,
*
if expected interest rate ⇐p )
investment opportunities increase and
increases
,
so ie T ,
then Pete
BS shifts to the
right and as a result expected return
.
,
2 te
Expected inflation : i n c re a s e in
Re Iv and Bd shifts to the left .
leads to r = i -
ite t So the real
if expected inflation ITET then
.
*
,
and
cost
of borrowing decreases
ir=r ite t Bd
by = i and
-
BS T which shifts BS to the right .
shifts to the left .
3 Government deficit : an increase
3 Risk when
investing to bonds relative
shifts Bs to the right as
they
to other assets :
if risk in bonds
need to borrow
money .
increases
,
Bd Tv and shifts to the
left .
4 liquidity of bonds relative to other
assets :
if it becomes easier relative
to other assets to tur n the asset into
cash at low cost and small value
loss the demand for bonds increases
,
and Bd shifts to the right .
S. Veeling
, Lecture 2
Real and nominal interest rates
Fisher : r= i -
ite
gives an approximation .
Precisely :
Inflation -
indexed bonds
itr = iti The
coupon payments as well as face value
I1-1TE
a re
adjusted for inflation . If inflation
> it i =
I + r + we + rite
fluctuates ,
these bonds a re saver as
If r and ite a re small ,
it rtite
they are constant in real terms .
Unstable countries provide these bonds
Fisher effect in the US 1953 -2017
to attract funding Also stable countries
Usually te i
positively related
.
and a re .
these bonds which market
i ss u e
gives
•
stable
,
The real interest rate is
kept .
estimates of future inflation .
Those
so the nominal interest rate should
if
we used
for wage negotiations and
be low and stable so should be the 1T ?
bank because it tells them
by the central
inflation stable results in
keeping low and
if the market believes in their ability .
low nominal interest .
Quantitative
easing
Example : Business cycle expansion a policy in w h i ch the UK government
→ as expected profitability increase , bought a lot
of mostly long-term
companies want to borrow bonds This increased the
money .
government .
Bs T shift to the right price of bonds and so decreased the
,
wealth to interest rates
as increases want
*
people
.
,
buy B☐ T shift to the
more bonds .
, right
normally ,
the supply effect is
larger ,
therefore P v1 and i T .
Also explained
•
i He expected to
by r + IT as is
=
i n c re a s e in a business cycle expansion .
S. Veeling
