Mata kuliah
: F0922 - Pengantar Analisis Pendapatan Tetap
Dan Ekuitas
Tahun
: 2010
VALUING BONDS
Pertemuan 7
-mupo-
VALUING BONDS
Materi:
1.
Bond valuing model and Bond valuing process
2.
Valuing a Bond with an Embedded Option
3.
Valuation and analysing Callable Bond
4.
Valuing a putable bond
5.
Analysis of convertible bond
Bina Nusantara University
3
1.
Bond valuing model and Bond valuing process
The valuation process begins with determining
benchmark interest rates.
There are 3 potential markets where benchmark interest rate
can be obtined:
- the Treasury market
- a sector of bond market
- the market for the issuer’s securities
In building a model to value bonds with embedded option is that the
future cash flows will depend on what happen to interst rate in the
future.
For a given interest rate volatility, there are several interest rate
models that have been used in practice to construct an interest rate
tree. An interst model is probabilistic description of how interest can
change over life of the bond. An interest rate model does this by
making an assumption about the relationship between the level of
short term rates and the interest rate volatility as measured by the
standart deviation.
Bond valuing model and Bond valuing process (cont’)
The building of a model to value bonds with embedded option is more
Complex than building a model to value option free bonds, the basic
Principles are the same. In the case of valuing an option free bond,
the model that is built is simply a set of spot rates that are used to
value cash flows.
BOND VALUATION PROCESS
If a bond has an ambedded option, the following can we done:
- Given a required yield to maturity, we can compute the value of a
bond.
Exp: If required yield to maturity of a 9 year, 8% coupon bond the
pays interest semiannualy is 7%, its price is 106.59
- Given the observed market price of a bond we can calculate its
yield to maturity.
exp: if the price of a 5 Year, 6% coupon bond that pays interest
semiannualy is 93.84, its yield maturity is 7.5%
- Given yield to maturity, a yield spread can be computeed.
exp: if the yield to maturity for a 5 yer, 6% coupon bond that pays
Bond valuation process (cont’)
interest semiannualy is 7.5% and its yield is compared to
benchmark yield of 6.5%, then the yield spread is 100 basis points
(7.5% minus 6.5%)
2. Valuing a bond with an embedded Option
There are various models that have been developed to value a
bond with embedded options. The one that we usu to illustrate
the issues and assumptions options is the binomial model. The
interest rates there are used in the valuation process are
obtained from a binomial interest rate tree.
3. Valuation and analysing Callable bond
The valuation process proceeds in the same fashion as in the
case of an option free bond, but with one exception: when the
call option may be exercise by the issuer, the bond value at a
node must be changed to reflect the lesser of its values if it is
not called and the call price.
4. Valuing a Putable bond
A putable bond is one in which the bondholder has right to force
the issuer to pay off the bond prior to the maturity date.
The value of putable bond, is grater thn the value of the
corresponding option free bond:
valuable of putable bond = value of an option+ value of the put
option
Suppose that a bond is both putable and callable. The procedure
for valuing such a structure is to adjust the value at each node to
refect whether the issue would be put or called.
At each node there are 2 decisions about the exercising of an
option that must be made.
First, given the valuation from the backward induction method at
a node, the call rule is invoked to determine whether the issue
will called. If it is called, the value at the node is replaced by the
call price. The valuation prosedure then continues using the call
price at the node.
Valuing a Putable bond (cont’)
Second, if the call option is not exercised at anode, it must be
determined whether or not the put option is exercised. If it is
exercised, then the value from the backward induction method is
overriden and the put price is substituted at that node and is
used in subsequent calculations
5. Analysis of Convertible bonds
Convertible bond is a security that can be converted into
common stock at the option of investor. It is a bond with an
embedded option is granted to the investor. Morever, since a
convertible bond may be callable and putable, it is a complex
bond because the value of the bond will depend on both how
interest rates change (which affects the value of the call and any
put option) and how changes in the market price of the stock
affects the value of the option to convert to common stock.
Analysis of Convertible bonds (cont’)
The conversion provision of a convertible security grant the
securityholder the right to convert the security into
predetermined number of shares of the common stock of the
issuer. An exchangeable security grants the securityholder the
right to exchange the security for common stock of a firm other
than the issuer of the security.
The number of shares of common stock that the securityholder
will receive from exercising the call option of a convertible
security is called the conversion ratio.
Exp: assume the conversion ratio is 20. If investor converts the
bond for stock the investor will receive 20 shares of common
stock. Suppose that the par value for comvertible bond is $ 1000
at issuance, investors are purchasing the common stock for $ 50
per share ($ 1000/20 shares). This price is reffered to in the
prospectus as the conversion price and some investors refer
Analysis of Convertible bonds (cont’)
to it as the stated conversion price.
5.1 Traditional analysis
Traditinal analysis of convertible bonds relies on measures
that do not directly value the embedded cal, put, or
common stock option
5.1.1 Minimum value of a Convertible security
The conversion value or parity value of a convertible
security is the value of secrity if it is converted
immidiately:
Conversion value = market price of common stock x conversion ratio
Exp: The ADC convertible issue, the straight values, of
the bond is $ 98.19 per $ 100 of par value. Since the
market price per share of common stock is $ 33,
conversion ratio 25.32; theconversion value $ 1,000 of
par value is:
conversion value = $ 33 x 25.32 = $ 835.56
Analysis of Convertible bonds (cont’)
The conversion value is 83.556% of par value. Per
$ 100 of par value the conversion value is $ 83.556.
5.1.2 Market conversion price
The price that an investor effektifly pays for the
common stock if the convertible is purchased and
then converted into the common stock is called
the market conversion price or conversion
parity price :
market conversion price = market price of convertible security
conversion ratio
An investor who purchases a convertible bond
rather than the underlying stock, effectively pays
a premium over the current market price of stock.
This premium per share is equal to the different
between the market conversion price and
Analysis of Convertible bonds (cont’)
the current market price of common stock :
market conversion premium per share =
market conversion price – current market price
The market conversion premium per share is ussualy
expressed as a precentage of the current market
price as follows:
market conversion premium ratio =
market conversion premium per share
market price of common stock
5.2 Investment characteristics of Convertible bond
depend on the comman stock price. If the price low,
The straight value is considerably higher than the
conversion value the security will trade much like
a straight security, is reffed to as a fixed income
equivalent or busted convertible.
Analysis of Convertible bonds (cont’)
When the conversion value is considerably higher than
straight value, it said to be a comman stock equivalen.
The market conversion premium per share will be small.
Between these two cases, fixed income equivalent and
comman stock equivalent, the covertible security trade
as a hybrid security,having the characteristic of both
a fixed income security and comman stock instrument.
5.3 An option based valuation approach
5.3.1 Approximation to the value of a convertible bond,
the formula :
convertible security value =
straight value + value of the option on the stock
5.3.2 The value of a convertible bond that is callable is
equal to:
convertible bond value =
straight value + value of the call option on stock – value of
the call option on the bond
Analysis of Convertible bonds (cont’)
5.3.3 The callable convertible bond is also putable, the
value of such a convertible would be equal to:
convertible bond value =
straight value + value of the call option on the stock
- value of the call option on the bond
+ value of the putoption on the bond