● 郭志明 By Vincent Kok
There is a relationship between bond prices and interest
rates, and the maturity of a bond has an impact on its price
sensitivity to interest rates. This article examines the
relationship.
A dollar today is worth more than a dollar in the future,
simply because a dol-lar today can be deposited into a bank
ac-count to earn interest. If one-year interest rates are
5%, the $1 received today and deposited into the bank
account would be worth $1.05 in a year's time.
$1 today is also known as the present value of the $1.05
expected in a year, given the one-year interest rates of 5%.
The relationship between present value, future value and
interest rates is given by the simple discounting formula :-
Present Value = sum of future cashflows / (1 interest
rate)
In our earlier example, the present val-ue of $1 was
therefore obtained from:-
=$1.05/ (1 5%)
=$1.00
A bond holder receives a stream of interest, or coupons
for owning the bond and gets back his principal on maturity
of the bond. In order to receive these streams of future
cashflows, the pros-pective bond holder pays a price to the
issuer of the bond. The price paid upfront is the present
value of all the future cash-flows of coupons and principal
on matu-rity, discounted at the appropriate interest rate,
which is also known as the yield to maturity (YTM) of the
bond.
The YTM is the current market interest rates, which could
differ from the fixed interest or coupon rate paid by each
bond. The YTM is determined by (among other factors)
inflation, demand and supply of funds and Central Bank
policy. On the other hand, the bonds coupon or fixed
in-terest rate is determined at the launch of the bond and
stays fixed during the bond's lifetime.
The following examples will illustrate how changes in YTM
or market interest rates affect bond prices.
Let's calculate the price of a two-year bond, which pays
annual coupons of 8%, if the current interest rates or YTM
is 5%. Note that this bond pays a higher coupon than the
prevailing interest rates of 5%, which therefore makes the
bond attractive to investors. Applying the present value
formula to obtain the price of the bond:-
Present Value = 〔$8/(1 5%) 〕 〔$8 $100/(1 5%)2.〕
= $105.58
A very important point to note is the inverse relationship
between yield (deno-minator) and price. A rise in interest
rates will reduce the price, or present value of all the
future cashflows, of the bond. Conversely, a fall in
interest rates will in-crease the price, or present value of
all future cashflows of the bond. For in-stance, if the
interest rates or yields rise to 6%, the new price of the
bond will now only be:-
Present Value = 〔$8/(1 6%)〕 〔$8 $100/(1 6%)2.〕
= $103.67
Shorter maturity bonds are typically less price-sensitive
to interest rate changes than long maturity bonds. In
ge-neral, the price sensitivity of a two-year fixed income
bond is twice that of a one-year fixed income bond.
Likewise, a 10-year fixed income bond will be about 10 times
more sensitive to interest rates than a one-year fixed
income bond. The longer the maturity, the higher the price
sensitivity of the bond to interest rate changes.
A fixed income bond investor has to understand these two
concepts. For example, if an economy is undergoing a severe
recession, there is a greater chance for the Central Bank to
reduce interest rates. If interest rates fall, bond prices
will rise, as shown by our earlier exam-ples. The prices of
longer maturity fixed income bonds will rise more than
shorter maturity bonds. Hence, a fixed income investor who
expects market interest rates to fall should invest in
longer maturity fixed income bonds to maximise price
appreciation.
On the other hand, if the economy has been booming and
inflation is high, there is a greater chance that the
Central Bank will raise interest rates. If interest rates
do rise, bond prices will fall, according to the inverse
relationship between bond price and interest rates. The
fixed income investor should hold only shorter maturity
bonds to avoid heavier price falls from ri-sing interest
rates. When these shorter maturity bonds mature, the fixed
income investor can reinvest the proceeds in new higher
coupon bonds, assuming that in-terest rates do rise as
expected.
A good grasp of these two concepts enables a fixed income
investor to tailor the maturity profile of his portfolio to
his expectations of future interest rates. If the investor
expects interest rates to fall, he should invest in longer
maturity bonds which have higher price sensitivity to
in-terest rates in order to maximise his re-turns. On the
other hand, if the investor expects interest rates to rise,
he should keep his bond portfolio short in maturity to
lessen price falls in his portfolio.
(The writer is Associate Director, Portfolio Management of
Morgan Grenfell (Asia) Limited. This column has the support
of the Investment Management Association of Singa-pore and
the Stock Exchange of Sin-gapore.)
2007-12-06
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