Illustration of Bond Price Volatility by J.D. Han
Assumption:
1. No liquidity premium
2. No expectation of changing business cycle.
Principle 1: In so far as their risk characterstics are the same, market competition
ensures that the two financial assets give the same rate of returns.
Suppose there are two bonds with the same risk characteristics except for the term of
maturity, and that suppose that the liquidity risk premium does not exist:
YTM2= YTM1
What will happen to the bond market if the rate of return on stocks rises in the
financial market due to an increase in dividend rates?
Market competition ensures that YTM for Bond2(bond with 2-year term) and
Bond1(bond with 1-year term) should go up as well.
In order for YTM to go up, the market price of bond should go down as shown in the
formula:
100  Market Pr ice
Term period
Average Pr ice
CouponPayment 
YTM =
Solving the above for Market Price, we get:
Market Price of Bond =
2 xCouponPamymentxN  200  100 xYTMxN
YTMxN  2
Let's take some numerical example:
Suppose that the competitive rate of return on bonds in the financial market rise from
5% to 6% (we ignore the liquidity risk premium here)
The prices of a one-year bond and a two-year bond will change as follows:
Bond 1
Coupon Payment =
10
Term or Maturity Period =
1
Suppose that the market determined YTM for this borrower rises from 5% for 6% for some
reason. What will happen to the prices of bonds of different terms for this borrower?
before
i)YTM1
Market Price of Bond 1
after
5%(0.05)
6%(0.06)
104.9
103.9
% change in Market Price
-0.9(0.009)
ii) Bond 2
Coupon Payment =
Before
YTM2
Market Price of Bond2
Maturity
10
Period or Term
=
2
After
5%
6%
109.5
107.5
% change in Market Price
-1.8%
iii) Bond 3
Coupon Payment =
Before
YTM3
Market Price of Bond2
Maturity
10
Period or Term
=
3
After
5
6
114.0
111.0
% change in Market Price
-2.6
iii)Bond 10, say
Coupon Payment =
Before
YTM4
Market Price of Bond 4
Maturity
10
=
After
5%
6
140.0
130.8
Period or Term
10
% change in Market Price
-6.6%
The following table is the same as the above, except that it is in the Excel format, and
thus you can see the original worksheet that I have worked on.
For instance, you
can go into the Excel worksheet and see the formula for each market price.
Bond 1
Coupon Payment =
YTM1
Market Price of Bond 1
change in Market Price
Bond 2
Coupon Payment =
YTM2
Market Price of Bond2
change in Market Price
Bond 3
Coupon Payment =
YTM3
Market Price of Bond2
change in Market Price
Bond 4
Coupon Payment =
YTM10
Market Price of Bond2
change in Market Price
at t period at t+1 period
10
Term or Maturity Period =
before
after
0.05
0.06
104.9
103.9
-0.01
10
Before
After
0.05
109.5
10
Before
After
0.05
114.0
10
Before
After
0.05
140.0
1
Maturity Period or Term =
2
Maturity Period or Term =
3
Maturity Period or Term =
10
0.06
107.5
-0.02
0.06
111.0
-0.03
0.06
130.8
-0.07
Principe 2 When the YTM rises, the bond price should fall, This signifies the inverse
relationship between the broad spectrum of interest rates and the bond prices.
Principle 3 When the YTM or market interest rates changes (that is the given one year
average rate of return; in the above case it is a 1% increase), the long term bond will
show more (market) price fluctuations than the short term bond.
Investment strategy:
If you hold the bonds for the entire maturity period, it really does not matter. Your
YTMs of all different term bond go up all by 1% or 0.01.
However, if you are going to be a short-term investor – you do not wish to hold the
bond until maturity. You may invest on this bond for only one term: Expecting this
big change in prices(drop) between t and t+1, you may short-sell the long-term bond
between t and t+1. You are capturing all the capital gains within one year.
What is the rate of return for this short term investor?
Net Return = (5 + 10-5)
At the time point of t, This investor is paid $5 for his coupon for one period.
He borrows one unit of bond and has to return it next period. He sells it at time t for
140.0.
At time t+1, he buys one unit of bond at the market price of 130.8, and returns it to the
lender.
His revenue is 5 + (140-130.8); his cost would be the money he has to pay to the
lender, which should be in fact 5%.
If this is measured against a possible margin of 130 dollars, the rate of retun should be
around 7-8%.