YIELD TO MATURIRY:Current Yield, Holding Period Returns

<< BONDS & BONDS PRICING:Zero-Coupon Bonds, Fixed Payment Loans

SHIFTS IN EQUILIBRIUM IN THE BOND MARKET & RISK >>

Money & Banking MGT411

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

receives for making a loan

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

Money & Banking MGT411

$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

= .1311

$100

Or 13.11%

If the interest rate in one year is 7%...

Money & Banking MGT411

One year holding Period return =

$93.48 - $100 - $.52

= -.0052

$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

P =

i =

1 + i

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.

Money & Banking MGT411

Figure: Supply, demand and equilibrium in the bond market

The supply of bonds from

the borrowers slopes up

and the demand for bonds

from the lenders slopes

down. Equilibrium in the

bond

market

determined

the

interaction of supply and

demand.

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.

Changes in business conditions

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

Money & Banking MGT411

Figure: A shift in the supply of bonds

When borrower's desire for

funds increases, the bond

supply curve shifts to the

right, lowering bond prices

and raising interest rates.

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