Money and Banking

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Lesson 14
YIELD TO MATURIRY
Yield to Maturity
Current Yield
Holding Period Returns
Bond Supply & Demand
Factors affecting Bond Supply
Factors affecting Bond Demand
Yield to Maturity: General Relationships
General Relationships
If the yield to maturity equals the coupon rate, the price of the bond is the same as its face value.
If the yield is greater than the coupon rate, the price is lower;
if the yield is below the coupon rate, the price is greater
If you buy a bond at a price less than its face value you will receive its interest and a capital
gain, which is the difference between the price and the face value.
As a result you have a higher return than the coupon rate
When the price is above the face value, the bondholder incurs a capital loss and the bond's yield
to maturity falls below its coupon rate.
Table: Relationship between Price and Yield to Maturity
YTM on a 10% Coupon rate bond maturing in ten years (Face Value = \$1,000)
Price of Bond (\$)
Yield to Maturity (%)
1,200
7.13
1,100
8.48
1,000
10.00
900
11.75
800
13.81
Three Interesting Facts in the above Table
1. When bond is at par, yield equals coupon rate
2. Price and yield are negatively related
3. Yield greater than coupon rate when bond price is below par value
Current Yield
Current yield is a commonly used, easy-to-compute measure of the proceeds the bondholder
It is the yearly coupon payment divided by the price
Yearly Coupon Payment
Yield =
Current
Price Paid
The current yield measures that part of the return from buying the bond that arises solely from
the coupon payments;
It ignores the capital gain or loss that arises when the bond's price differs from its face value
Let's return to 1-year 5% coupon bond assuming that it is selling for \$99.
Current yield is 5/99 = 0.0505 or 5.05%
YTM for this bond is calculated to be 6.06% through the following calculations
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\$5
\$100
+
= \$99
(1 + i)  (1 + i)
If you buy the bond for \$99, one year later you get not only the \$5 coupon payment but also a
guaranteed \$1 capital gain, totaling to \$6
Repeating this process for the bond selling for \$101, current yield is 4.95% and YTM is 3.96%
The current yield moves inversely to the price;
If the price is above the face value, the current yield falls below the coupon rate.
When the price falls below the face value, the current yield rises above the coupon rate.
If the price and the face value are equal the current yield and the coupon rate are equal.
Since the yield to maturity takes account of capital gains (and losses),
When the bond price is less than its face value the yield to maturity is higher than the current
yield,
If the price is greater than face value, the yield to maturity is lower than the current yield, which
is lower than the coupon rate
Relationship between a Bond's Price and its Coupon Rate, Current Yield and Yield to Maturity
Bond Price < Face Value:
Coupon Rate < Current Yield < Yield to Maturity
Bond Price = Face Value:
Coupon Rate = Current Yield = Yield to Maturity
Bond Price > Face Value:
Coupon Rate > Current Yield > Yield to Maturity
Holding Period Returns
The investor's return from holding a bond need not be the coupon rate
Most holders of long-term bonds plan to sell them well before they mature, and because the
price of the bond may change in the time since its purchase, the return can differ from the yield
to maturity
The holding period return ­ the return to holding a bond and selling it before maturity.
The holding period return can differ from the yield to maturity
The longer the term of the bond, the greater the price movements and associated risk can be
Examples:
You pay for \$100 for a 10-year 6% coupon bond with a face value of \$100, you intend to hold
the bond for one year, i.e. buy a 10 year bond and sell a 9 year bond an year later
If interest rate does not change your return will be \$6/100 = 0.06 = 6%
If interest rate falls to 5% over the year then through using bond pricing formula we can see that
You bought a 10-year bond for \$100 and sold a 9-year bond for \$107.11
Now the one year holding return has two parts
\$6 coupon payment and
\$7.11 capital gain
So now, one year holding Period return =
\$107 .11 - \$100  \$13.11
\$6
+
=
= .1311
\$100
\$100
\$100
Or 13.11%
If the interest rate in one year is 7%...
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One year holding Period return =
\$93.48 - \$100  - \$.52
\$6
+
=
= -.0052
\$100
\$100
\$100
Or -0.52%
Generalizing, 1-year holding return is
Yearly Coupon Payment  Change in Price of the Bond
=
+
Price Paid
Price of the Bond
= Current Yield + Capital Gain (as a %)
Bond Market and Interest Rates
To find out how bond prices are determined and why they change we need to look at the supply
and demand in the bond market.
Let's consider the market for existing bonds at a particular time (the stock of bonds) and
consider prices and not interest rates.
One Year Zero-coupon (discount) Bond
- P
\$ 100
\$ 100
P =
i =
or
1 + i
P
Bond Supply, Demand and Equilibrium
Bond Supply
The Bond supply curve is the relationship between the price and the quantity of bonds people
are willing to sell, all other things being equal.
From the point of view of investors, the higher the price, the more tempting it is to sell a bond
they currently hold.
From the point of view of companies seeking finance for new projects, the higher the price at
which they can sell bonds, the more advantageous it is to do so.
For a \$100 one-year zero-coupon bond, the supply will be higher at \$95 than it will be at \$90,
all other things being equal.
Bond Demand
The bond demand curve is the relationship between the price and quantity of bonds that
investors demand, all other things being equal.
As the price falls, the reward for holding the bond rises, so the demand goes up
The lower the price potential bondholders must pay for a fixed-dollar payment on a future date,
the more likely they are to buy a bond
The zero-coupon bond promising to pay \$100 in one year will be more attractive at \$90 than it
will at \$95, all other things being equal.
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Figure: Supply, demand and equilibrium in the bond market
The supply of bonds from
the borrowers slopes up
S
and the demand for bonds
from the lenders slopes
down. Equilibrium in the
E
Po
bond
market
is
determined
by
the
interaction of supply and
demand.
D
Qo
Quantity of Bonds
Equilibrium in the bond market is the point at which supply equals demand.
If the price is too high (above equilibrium) the excess supply of bonds will push the price back
down.
If the price is too low (below equilibrium) the excess demand for bonds will push it up
Over time the supply and demand curves can shift, leading to changes in the equilibrium price
Factors that shift Bond Supply
Changes in government borrowing
Any increase in the government's borrowing needs increases the quantity of bonds outstanding,
shifting the bond supply curve to the right.
This reduces price and increases the interest rate on the bond.
Business-cycle expansions mean more investment opportunities, prompting firms to increase
their borrowing and increasing the supply of bonds
As business conditions improve, the bond supply curve shifts to the right.
This reduces price and increases the interest rate on the bond.
By the same logic, weak economic growth can lead to rising bond prices and lower interest rates
Changes in expected inflation
Bond issuers care about the real cost of borrowing,
So if inflation is expected to increase then the real cost falls and the desire to borrow rises,
resulting in the bond supply curve shifting to the right
This reduces price and increases the interest rate on the bond.
Table: Factors that increase Bond Supply, lower Bond Prices, and Raise Interest Rates
Change
Effect on Bond Supply, Bond Prices, and
Interest Rates
An increase in the government's desired
Bond Supply shifts to the right, Bond prices
expenditure relative to its revenue
decrease and interest rates increase
An improvement in general business conditions
Bond Supply shifts to the right, Bond prices
decrease and interest rates increase
An increase in expected inflation, reducing the real Bond Supply shifts to the right, Bond prices
cost of repayment
decrease and interest rates increase
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Figure: A shift in the supply of bonds
So
S1
Eo
When borrower's desire for
Po
funds increases, the bond
E1
supply curve shifts to the
P1
right, lowering bond prices
and raising interest rates.
D
Qo
Quantity of Bonds
Factors that shift Bond Demand
Wealth
An increase in wealth shifts the demand for bonds to the right as wealthier people invest more.
This will happen as the economy grows during an expansion.
This will increase Bond Prices and lower yields.
Expected inflation
A fall in expected inflation shifts the bond demand curve to the right, increasing demand at each
price and lowering the yield and increasing the Bond's price.
Expected return on stocks and other assets
If the return on bonds rises relative to the return on alternative investments, the demand for
bonds will rise.
This will increase bond prices and lower yields.
Risk relative to alternatives
If a bond becomes less risky relative to alternative investments, the demand for the bond shifts
to the right.
Liquidity of bonds relative to alternatives
When a bond becomes more liquid relative to alternatives, the demand curve shifts to the right
Table: Factors that increase Bond demand, raise Bond Prices, and lower Interest Rates
Change
Effect on Bond demand
An increase in wealth increases demand for all assets,
Bond demand shifts to the right, Bond prices
including bonds
increase and interest rates decrease
A reduction in expected inflation makes bonds with
Bond demand shifts to the right, Bond prices
fixed nominal payments more desirable
increase and interest rates decrease
An increase in expected return on the bond relative to
Bond demand shifts to the right, Bond prices
the expected return on alternatives makes bonds more
increase and interest rates decrease
attractive
A decrease in the expected future interest rate makes
Bond demand shifts to the right, Bond prices
bonds more attractive
increase and interest rates decrease
A fall in the riskiness of the bond relative to the
Bond demand shifts to the right, Bond prices
riskiness of alternatives makes bonds more attractive.
increase and interest rates decrease
An increase in the liquidity of the bond relative to the
Bond demand shifts to the right, Bond prices
liquidity of alternatives makes bonds more attractive
increase and interest rates decrease
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Figure: A shift in Bond Demand
S
When there is an increase in
E1
investor's willingness to hold
P1
bonds, the bond demand curve
Eo
Po
shifts to the right, increasing bond
prices and reducing interest rates.
D1
Do
Qo
Quantity of Bonds
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