presentation
GROUP2
MAI THI QUYEN – MAMAIU16049
NGUYEN THANH KHANG – MAMAIU16036
THIEU THI THUY VAN – MAMAIU16059
Presentation
overview
4.1 The yield curve
4.2 The term structure
4.3 Forward rates
4.4 Term structure explanations
4.5 Expectations dynamics
4.6 Running present value
4.7 Floating rate bonds
4.8 Duration
4.9 Immunization
4.1
YIELD CURVE: a plot of the interest rates ( yield to maturity )
for particular types of bond with different terms to maturity,
but the same risk, liquidity and tax treatments
_Yield curve are classified in terms of their shapes and are
used to explain the condition in financial markets and the
economy
Theyieldcurve
TYPES OF YIELD CURVE
_Normal yield curve
_Steep yield curve
_ Flat yield curve
_ Inverted yield curve
Different shapes appear under different economic
condition
4.2 the
term
structu
re
SPOT RATE, DISCOUNT FACTOR,
PRESENT VALUE.
Spot rate
is the rate of interest , expressed in yearly term, charged for
money held from the present time (t=0) until time t.
KEY TAKEAWAYS:
*The spot rate reflects current market supply and demand
for an asset.
*The spot rates for particular currency pairs and
commodities are widely publicized and followed.
*Contracts for delivery will often reference the spot rate at
the time of signing.
Spot rate
DISCOUNT FACTOR
and
PRESENT VALUE
Once the spot rates has been determined ,
it is natural to defined the corresponding
discount factor dt for each time point.
These are the factors by which future cash
flows must be multiplied to obtain an
equivalent present value. For the various
compouding conventions, they are defined
as follow:
Discount factor
Using the spot rate curve of figure below,
let us find the value of an 8% bond maturing in 10
years
example
Using the spot rate curve of figure below,
let us find the value of an 8% bond maturing in 10
years
example
4.3 FORWARD
RATE
Forward rates
-The forward rate between time t1 and
t2 with t1< t2 is denoted by f(t1,t2). It is
the rate of interest charged for
borrowing money at time t1, which is to
be repaid ( with interest) at time t2
_ Forward rates are calculated from the
spot rate.
_In the context of bonds, forward rates
are calculated to determine future
values.
4.4 TERM
STRUCTURE_
EXPLANATIONS
THE EXPECTATION THEORY
LIQUIDITY PREFERENCE THEORY
MARKET SEGMENTATION THEORY
Term Structure Theories
Any study of the term structure is incomplete without its background
theories. They are pertinent in understanding why and how are the
yield curves
so shaped.
#1 – The Expectations Theory/ Pure Expectations Theory
This theory states that current long-term rates can be used to
predict
short term rates of future. It simplifies the return of one bond as a
combination of the return of other bonds.
For example: a 3-year bond would yield approximately the same
return as three 1-year bonds.
Term Structure Theories (cont)
Any study of the term structure is incomplete without its background
theories. They are pertinent in understanding why and how are the yield
curves
so shaped.
.#2 – Liquidity Preference Theory
This theory perfects the more commonly accepted understanding of
liquidity preferences of investors. Investors have a general bias towards
short
term securities which have higher liquidity as compared to the long term
securities which get one’s money tied up for long. Key points of this
theory
are:
• Price change for a long term debt security is more than that for a short
term debt security.
• Liquidity restrictions on long term bonds prevent the investor from
selling it whenever he wants.
• The investor requires an incentive to compensate for the various risks
he is exposed to, primaril price risk and liquidity risk.
• Less liquidity leads to an increase in yields while more liquidity leads to
falling yields, thus
defining the shape of upward and downward slope curves.
Term Structure Theories (cont)
Any study of the term structure is incomplete without its background
theories. They are pertinent in understanding why and how are the yield curves
so shaped.
#3 – Market Segmentation Theory
This theory related to the supply-demand dynamics of a market. The yield
curve shape is governed by the following aspects:
• Preferences of investors for short term and long term securities.
• An investor tries to match the maturities of his’ assets and liabilities. Any mismatch
can lead to
capital loss or income loss.
• Securities with varying maturities form a number of different supply and demand
curves which then eventually inspire the final yield curve.
• Low supply and high demand lead to an increase in interest rates..
a. Spot rate forecasts
4.5EXPECTATION_
DYNAMICS
Expectation theory forms the basis of the concept of expectation dynamics,
which is a particular model of how spot rates might
change with time.
Expectation Dynamic is only a model, and
future rates will most likely deviate from the values its delivers; but it
provides a logical simple prediction of future rate.
a. Spot rate forecasts
4.5EXPECTATION_
DYNAMICS
b. Discount factor
SIMPLE YOUR
C R E AT I V I T Y
SIMPLE YOUR
C R E AT I V I T Y
C. Short rates
SIMPLE YOUR
C R E AT I V I T Y
SIMPLE YOUR
C R E AT I V I T Y
SIMPLE YOUR
C R E AT I V I T Y
CONTINUE…
d.
Invariance
As a special case, if the current spot rate is flat say, at 12% then
according to expectation dynamic, the spot rate curve next year will
also be
flat at 12%. The invariance theorem states that if spot rate evolve
according
to expectations dynamics, the interest rate market for several years
is
independent of how those funds are invested
4.6 RUNNING
PRESENT VALUE
_Present value can be calculated by the running method, which states from
the final cash flow and works backward toward the first cash flow.
._At any stage k of the process, the present value is calculated by
discounting the next period’s present value using the short rate at time k that
is implied by the term structure.
_This backward moving method of evaluation is fundamental to advance
methods of calculation in various areas of investment science.
EXAMPLE
4.6 RUNNING
PRESENT VALUE
4.7
FLOATING RATE
BONDS
•A floating rate note or bond has a fixed face value and
fixed
maturity.
•But its coupon payments are tied to current ( short) rates
of
interest.
•It has interest rates are varied by period. The interest rate
adjustment period can be 6 months, 1 year, 1 and a half
years, ... clearly agreed on the bond, while the interest
rate changes depends on the average indicators in the
market at the time. This interest rate change is prescribed
by the issuing company
FLOATING BOND
•Consider, a floating rate bond that makes coupon payments
every 6 months. When the bond is issued, the coupon rate
for the first 6 months is set equal to the current 6-month
interest rate. At the end of 6 months a coupon payment at that
rate is paid.
•The coupon is the rate times the face value divided by 2
(because of the 6-month schedule). Then, after that payment,
the rate is reset.The process continues until maturity
•Clearly, the exact values of future coupon payments are
uncertain until 6 months before they are due. Therefore,
that it may be difficult to assess the value of such a bond In fact
at the reset times, the value is easy to deduce-it is equal to par.
FLOATING BOND
4.8
DURATION
•Given the spot rates s1, s2,…
imagine that these rates all change together by an additive amount λ.
Then the new spot rates are s1 + λ, s2 + λ …, for the new spot rates are for the
same periods as before. This parallel shift of the spot rate curve generalizes
a change in the yield because if the spot rate curve were flat, all spot rates
would be equal to the common value of yield
90%
4.8
DURATION
90%
4.8
DURATION
90%
4.8
DURATION
90%
4.8
DURATION
90%
4.9
IMMUNIZATION
90%
4.9
IMMUNIZATION
4.9
IMMUNIZATION
THANK YOU !