yield curves and term structure of interest rates

8/4/2019 Yield Curves and Term Structure of Interest Rates

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Yield Curves and Term Structure of



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



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



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)



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



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



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




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




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



Uses

of

Yield

Curve Forecasting Interest Rates

Useful to Financial Intermediaries

Detecting over priced and under priced securities

‐



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)

= .



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



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



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?



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?

yield curves and term structure of interest rates

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