Mata kuliah
: F0922 - Pengantar Analisis Pendapatan Tetap
Dan Ekuitas
Tahun
: 2010
YIELD MEASURED, SPOT RATES,
AND FORWARD RATES
Pertemuan 5
-mupo-
YIELD MEASURED SPOT RATE AND FORWARD
RATES
Materi:
1.
Traditional yield measured
2.
Spot rates
3.
Forward rates
Bina Nusantara University
3
1.
Traditional yield measured
Yield measures cite in the bond market include Current Yield,
Yield to Maturity, Yield to Call, Yield to Put, Yield to Worst and
Cash flow Yield.
1.1 Current Yield.
Current Yield = annual dollar coupon interest
Price
Example: the Current Yield for 7% 8-year bond whose price is
$ 94.17 is 7.43% as show bellow:
annual dollar coupon interest = 0.07 x $ 100 = $ 7
price = $94.17
Current Yield = $ 7 = 0.0743 = 7.43%
$94.17
The Current Yield will be greater than the coupon rate when
the bond sells at a discount; the reverse is true for a bond
selling at a premium. For a bond selling at par, the Current
Yield will be equql to the coupon rate.
1.2 Yield to Maturity
The most popular measure of yield in the bond market is the
yield to maturity. The yield to maturity is the interest rate
that will make the present value of bond’s cash flow equal
to its market price plus accrued interest.
Example: consider a 7% 8 years bond selling for $ 94.17. The
cash flows for this bond are (1) 16 payments every 6 months
of $ 3.50 and (2) a payment sixteen 6 month period from
now of $ 100. The present value using various semiannual
discount (interest) rates is:
Semiannual interest rate 3.5% 3.6% 3.7% 3.8% 3.9% 4%
Present value
100.00 98.80 97.62 96.45 95.30 94.17
When a 4% interest rate is used, the present value of cash flow is
equal to $ 94.17, which is the price of bond. Hence, 4.0% is the
semiannual yield to maturity
The relationship between the price of bond, coupon rate, current
yield, and yield to maturity:
Bond selling at
Relationship
par
coupon rate = current yield = yield to maturity
discount
coupon rate < current yield < yield to maturity
premium
coupon rate > current yield > yield to maturity
1.3 Yield to call.
When a bond is callable, the practise has been to calculate
a yield to call as well as a yield to maturity. A callable
bond may have a call schedule. The yield to call assumes
the issuer will call a bond on on some assumed call date
and that the call price is the price specified in the call
schedule. Typically, investors calculate a yield to first call,
a yield to first par call, and a yield to refunding. The yield
to first call is computed for an issue that is not currently
callable, while the yield to next call is computed for an
issue that is currently callable.
1.4 Yield to Put
When a bond is putable, the yield to the first put date is
calculated. The yield to put is the the interest rate that will
make the present value of the cash flows to the first put
date equal to the price plus accrued interest.
Example: Suppose a 6,2% coupon bond maturing in 8 years is
putable at par in 3 years. The price of this bond is $ 102.19.
The cash flows for this bond if it is put in three years are:
(1) a total of 6 coupon payment of $ 3.10 each paid every 6
months
(2) the $ 100 put price in 6 month period from now
The semiannual interest rate that will make the present
value of each cashflows equal to the price of $ 102.19 is
2.7%. Therefor, 2.7% is semiannual yield to put and 5.4% is
the yield to put on a bond equivalen basis
1.5 Yield to worst
A yield can be calculated for every possible call date. In
addition, a yield to matury can be calculated. The lowest
of all these possible yields is called the yield to worst.
Example: suppose that there are only 4 possible call dates for
a callable bond, that the yield to call assuming each possible
call date is 6%, 6,2%, 5.8% and 5.7%, and that the yield to
maturity in 7.5%. Then the yield to worst is the minimum of
this yields, 5.7%
1.6 Cash flow yield
Mortgagebacked securities and assets backed securities are
backed by a pool of laoans or receivables. The cash flow for
these securities include priciple payment as well as interest.
The complication that arises is that the individual borrowers
whose loans make up the pool typically can prepay their loan
in whole or in part prior to scheduled principal payment dates.
Because of pricipal prepayments, in order to project cash
flows it is necessary to make an assumption about the rate at
which which principal prepayments will accur. This rate is
called prepayment rate or prepayment speed.
2. Spot rate
The theoritical spot rate for Treasury securities represent the
appropriate set of interst rates that should be used to value
default free cash flows. A default free theoretical spot rate can be
constracted from the observed Treasury yield curve. There are
several approaches that are used in practice.
2.1 Bootstrapping.
Bootstrapping begins with the yield for the on the run Treasury
issues because there is no credit risk and no liquidity risk.
2.2 Yield spread measures relative to a spot rate curve.
Traditional analysis of the yield spread for a non Treasury
involes calculating the difference between the bond’s yield and
the yield to maturity of a benchmark Treasury coupon security.
The latter is obtained from the Treasury yield curve