yield curves and term structure of interest rates
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8/4/2019 Yield Curves and Term Structure of Interest Rates
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Yield Curves and Term Structure of
8/4/2019 Yield Curves and Term Structure of Interest Rates
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Topics
to
be
covered Current Yield
Yield to Maturit
Relationship between Bond Prices, Time to Maturity &
The Yield Curve Theories of Term Structure of Interest Rates
Uses of Yield Curve
Numerical Questions
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Current
Yield The current yield on a bond is the annual interest due
on it divided by the bond’s market price
Current Yield = Annual Interest or Coupon / Market Price
of money, or the complete series of expected future
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Yield
to
Maturity Yield to Maturity (YTM) refers to the internal rate of return
of the bond, i.e. discount rate at which present value of
inflows is equal to outflows.
Inflows refers to interest received on bonds and the
redemption price on maturity
Outflows refer to the price at which the bonds can be
purchased from the market, i.e. the current market price
YTM re resents the ield on the bond rovided the bond
is held to maturity and the intermittent coupons are re‐
invested at the same YTM rate
YTM = (((Maturity Value – Purchase Price)/ Years to
+ * +
Price*0.6)
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Relationship between Bond Prices, Time
to
Maturity
&
Interest
Rates Price yield relationship between bonds is not a straight line, but
is convex. This means that price changes for yield changes are
no symme r ca , or ncrease an ecrease n y e The sensitivity of price to change in yield is not uniform across
on s. ere ore, or a same c ange n y e , epen ng on e
kind of bond one holds, the changes in price will be different
,
sensitivity. Price sensitivities are higher for longer tenor bonds,
stability for a wide range of changes in yield Lower the cou on hi her the rice sensitivit . Other thin s
remaining the same, bonds with higher coupon exhibit lower
price
sensitivity
than
bonds
with
lower
coupons
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The
Yield
Curve Graphical representation between YTM and term to maturity is
called the yield curve
‘
rates’ because it relates yields to the term (maturity) of each
bond
It helps the investors to understand the current and future
market trends and thus helps them in decision making Types of yield curves: ‐
Rising yield curve – it indicates that long term bonds generally have
Downward sloping yield curve (inverted yield curve) – it indicates
that bonds with longer maturity have lower yield. This yield curve is
attributed to the expectation of fall in short term interest rates
Hump shaped yield curve
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Theories of Term Structure of Interest
Rates The most commonly known theories that attempt an
interpretation of the shape of the yield curve are: ‐
– holding period, returns will be equal for all bonds. The notion that asserts that the slope of the yield curve is attributable to expectations
. term bonds are attributed to expectations of future increase in rates,
while relatively low yields on long term bonds (downward sloping
The liquidity preference hypothesis – The reason for upward sloping in
the curve is investor demand for higher expected returns on assets that are perceived as riskier. The preference of investors for greater liquidity
makes them willing to hold these shorter bonds even if they do not offer expected returns as high as those of long term bonds. The risk
premium required to hold longer term bonds is called a liquidity
premium. Even if rates are expected to remain unchanged, the yield
curve will slope upwards due to liquidity premium
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Theories of Term Structure of Interest
Rates The preferred habitat hypothesis – this hypothesis recognizes that
the market is segmented and that expectations of investors are not
.
categories of investors exist, and that each of these categories
prefers to invest at certain segments of the yield curve. This theory
suggests that depending on demand and supply at varying tenors of
the yield curve, investors will have to receive or pay, premiums or
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Theories of Term Structure of Interest
Rates
– SummaryTerm Structure Hypothesis
Flat Yield Curve Upward Sloping Curve
Downward Sloping Curve
Humped
Ex ectations Short term Short term Short term Short term
Hypothesis interest rates are
not expected to
change
interest rates are
expected to
increase
interest rates are
expected to
decrease
interest rates are
expected to
initially increase
and then decrease
Liquidity
Preference
There is no
li uidit remium
Liquidity premium
is ositive with
Liquidity premium
is ne ative with
Liquidity premium
is ositive u to
Hypothesis
on long term rates
as compared to
short term rates
increase in term
increase in term
certain term after
which it turns
ne ative
Preferred Habitat
HypothesisDemand and
supply are
Excess of supply
over demand in
Excess of supply
over demand in
Excess of supply
over demand in
maturities
term
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Uses
of
Yield
Curve Forecasting Interest Rates
Useful to Financial Intermediaries
Detecting over priced and under priced securities
‐
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Numerical
Questions Example 1 – A GOI bond of INR 100 each has a coupon rate of
8% p.a. and maturity period is 10 years. If current market price is
,
Solution – YTM = (((Maturity Price – Purchase Price)/Years to
Maturity) + Coupon) / (Maturity Price * 0.4 + Purchase Price * 0.6)
YTM = (((100‐110)/10)+8)/(100*0.4+110*0.6)
YTM
=
6.60%
Example 2 – A bond of face value INR 1000 (coupon rate 10%
. .
INR 1050. Determine YTM? Solution – YTM = Maturit Price – Purchase Price Years to
Maturity) + Coupon) / (Maturity Price * 0.4 + Purchase Price * 0.6)
YTM = (((1000‐1050)/20)+100)/(1000*0.4+1050*0.6)
= .
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Numerical
Questions xamp e – r. erma s cons er ng nvest ng n a on w c
is currently selling for INR 8,785.07. The bond has 4 years to
maturity, a INR 10,000 face value and 8% coupon rate. The next
annual interest payment is due 1 year from today. The discount factor for investment of similar risk is 10%.
. . purchase this bond at its current market price?
b) Calculate YTM of the bond? Based on this calculation, should
r. erma purc ase s on
Solution –
the cash flows, Thus, Intrinsic Value = 800/(1.10^1) + 800/(1.10^2) + 800/(1.10^3) +
.
Intrinsic Value = 9,366.03. Since its intrinsic value is higher than
the
market
price,
the
bond
is
underpriced
and
Mr.
Vermashould purchase this bond at the current market price
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Numerical
Questions Solution –
b YTM = (((Maturity Price – Purchase Price)/Years to Maturity)
+ Coupon) / (Maturity Price * 0.4 + Purchase Price * 0.6)
YTM = (((10000‐8785.07)/4)+800)/(10000*0.4+8785.07*0.6)
YTM = 11.91%. Since YTM is greater than the discount rate, Mr.
Verma should purchase this bond
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Numerical
Questions Example 4 –
Particulars Bond A Bond BMarket Price 95 95
Face Value 100 100
Maturity 5 years 10 years
Coupon 10% 10%
a) Calculate YTM?
b) If yield increases by 1%, calculate the bond price of bond A
and bond B?
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Numerical
Questions Example 5 – Let us consider two bonds – Bond A (coupon
12.5%) and Bond B (zero coupon bond). Bond A and Bond
B has maturity of 7 years with YTM of 15%.
a) Calculate the market price of these bonds?
b) Also analyse the impact of change in interest rates by 1%
on the market price of these bonds?