Bond Return and Valuation

7/28/2019 Bond Return and Valuation

1/19

Bond Return

and

Valuation
http://blog.oureducation.in/


2/19

Chapter Objectives

To understand the basics of bond

To know the concept of bond return and valuation

To learn about the types of bond risk

To understand the bond value theorems

To understand the concept of duration and

immunisation


3/19

Concept of Bond

It is a contract between a borrower and a lender in

which the borrower is required to pay a certain

amount of interest income to the lender.

In general, bonds carry a fixed payment of interest

till the maturity date.

The rate of interest is also known as coupon rate.


4/19

Types of bond

Treasury notes and bonds are debt securities issued

by the Central Government of a country. Treasurynotes maturity range up to 10 years, whereas

treasury bonds are issued for maturity ranging from

10 years to 30 years. Apart from the central Government, various State

Governments and sometimes municipal bodies are

also empowered to borrow by issuing bonds. Theyusually are also backed by guarantees from the

respective Government. These bonds may also be

issued to finance specific projects (like road,

brid e air orts etc.
http://blog.oureducation.in/http://blog.oureducation.in/http://blog.oureducation.in/


5/19

Types of bond

Bonds are also issued by large corporate houses for

borrowing money from the public for a certain

period. These bonds are not exempt from taxes.

Zero coupon bonds (also called as deep-discount

bonds or discount bonds) refer to bonds which do

not pay any interest (or coupons) during the life of

the bonds. The bonds are issued at a discount to the

face value and the face value is repaid at thematurity. The return to the bondholder is the

discount at which the bond is issued, which is the

difference between the issue price and the face


6/19

Types of bond

Convertible bonds offer a right (but not the

obligation) to the bondholder to get the bondconverted into predetermined number of equity

stock of the issuing company, at certain, pre

specified times during its life. In case of callable bonds, the bond issuer holds a

call option, which can be exercised after some pre-

specified period from the date of the issue. Theright is exercised if the coupon rate is higher than

the prevailing interest rate in the market
http://blog.oureducation.in/http://blog.oureducation.in/


7/19

Bond Risk

Bonds are considered to be quite safe but they alsocarry a certain amount of risk.

Types of bond risk:

Interest rate risk: The value of bonds changes due tovariability of the market interest rates.

Default risk: The borrower fails to pay the agreed value ofdebt instrument on time.

Marketability risk: There is difficulty in liquidating the

bonds in the market. Callability risk: There is an uncertainty created in the

returns of the investor by the issuers right to call the bondany time.


8/19

Bond Pricing

The cash inflow for an investor in a bond includesthe coupon payments and the payment on maturity

(which is the face value) of the bond. Thus the price

of the bond should represent the sum total of the

discounted value of each of these cash flows (such a

total is called the present value of the bond). The

discount rate used for valuing the bond is generally

higher than the risk-free rate to cover additionalrisks such as default risk, liquidity risks, etc.

Bond Price = PV (Coupons and Face Value)


9/19

Bond Pricing Basic bond valuation model

n coupon face value

P = ------------ + ---------------------

t=1 (1+y)t (1+y)n

Bond values with semi annual interest

As half yearly interest can be reinvested the value of

such bonds would be more.

2n (coupon/2) face value

P = ------------ + ---------------------

t=1 (1+y/2)t (1+y/2)2n


10/19

Bond Yield Measures

There are several ways of describing a rate of return on

bond. Some of them are:

Holding period return

The current yield

Yield to maturity


11/19

Holding Period Return

It is a return in which an investor buys a bond and

liquidates it in the market after holding it for a

definite period of time.

The formula for calculating holding period of returnis as follows:

It can be calculated on a daily, monthly or annual

basis.

Price gain + Coupon payment

Purchase price


12/19

The Current Yield

It is a measure through which the investors can easily

figure out the rate of cash flow on the investments

made by them every year.

It is calculated as:

Annual Coupon Payment

Purchase Price


13/19

Yield to Maturity It is the rate of return earned by an investor who purchases

a bond & holds till maturity. The YTM is the discount rate

which equals the present value of promised cash flows to

current market price/purchase price.

The following assumptions are used to calculate yield to

maturity: There should not be any default.

The interest payments are reinvested at yield to maturity.

The investor has to hold the bond till its maturity.

It is calculated as:

I + (F-P)/n

YTM = -------------------

(F + P )/2


14/19

Duration of a bond

Duration measures the number of years requiredto recover the true cost of a bond, considering

the present value of all coupon and principal

payments received in the future. The duration ofa bond is expressed as a number of years from

its purchase date.

Thus, the higher the coupon rate of a particularbond, the shorter its duration will be. In other

words, the more money coming in now (because

of a higher rate), the faster the cost of the bond

will be recovered.


15/19

Duration = t * wt

The weights (Wt) associated for each period are

the present value of the cash flow at each periodas a proportion to the bond price, i.e.

PV of cash flow

Wt =-----------------------------

Bond price

Duration of a bond


16/19

Bond Value Theorems

These are evolved on the basis of three factors:

(i) coupon rate (ii) years to maturity (iii) expected rate of return.

The five bond value theorems are as follows:

Theorem 1: If the bonds market price increases then its yield declines

and vice versa. Theorem 2: If the bonds yield remains constant over its life, then the

discount or premium depends on the maturity period.

Theorem 3: If the yield remains constant over its life, the discount andpremium on bonds will decline at an increasing rate as its life gets

shorter. Theorem 4: A raise in the bonds price for a decline in the bonds yield

is greater than the fall in the bonds price for a raise in the yield.

Theorem 5: The percentage change in the bonds price owing tochange in its yield will be small if the coupon rate is high.


17/19

Duration It measures the time structure and interest rate risk of

the bond.

The formula for calculating the duration is as follows:

where D = DurationC = Cashflow

R = Current yield to maturity

T = Number of years

Pv(ct) = Present value of the cashflow

P0 = Sum of the present value of cashflow

Tv t

t =1 0

P (C )

D = tP


18/19

Immunisation

It is a technique that makes a bondholder relatively

certain about the promised cash stream.

An immunisation can be achieved by reinvesting the

coupons in the bonds that offer higher interest rate.


19/19

Chapter Summary

By now, you should have:

Understood the basics of bond

Understood the concept of bond return and valuation

Learnt about the types of bond risks

Understood the various bond value theorems

Learnt the concept of immunisation

Bond Return and Valuation

Documents

Transcript of Bond Return and Valuation