Yield to Maturity, Study notes of Financial Economics

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Financial Economics

Yield to Maturity

The

(^) yield to maturity

(^) is the rate of return obtained by buying a

bond at the

(^) current market price

(^) and holding it to maturity.

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Financial Economics

No Default

less than the yield to maturity.If there is default, then the rate of return actually achieved ispromised.there will be no default: all payments will be made as In the calculation of the yield to maturity, one assumes that

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Financial Economics

Example

maturity?If the current market price is $1000, then what is the yield tomaturity value $1000 in ten years. Consider a bond with a coupon payment of $80 per year and

4

Financial Economics $80 per year on a $1000 investment.The yield to maturity must be 8%, since one receives a profit of

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Financial Economics

Yield to Maturity

Current Yield

One might say that the yield to maturity is the

(^) current yield

, the

coupon payment divided by the current market price,

current yield

coupon price

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Financial Economics

Understatement

The current yield

(^) understates

(^) the yield to maturity. The

price.maturity, the $1000 maturity value less the $900 purchaseinvestor also receives a $100 profit by holding the bond to

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Financial Economics

Overstatement

This figure

(^) overstates

(^) the yield to maturity. The calculation

$10 received each year for ten years.A payment of $100 in ten years has a lower present value thanthe total $100 profit is received only at maturity.supposes that a $10 profit is received each year, whereas in fact

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Financial Economics

Inverse Relation of Price and Yield

one receives the same payments for a smaller initial investment. A lower current market price raises the yield to maturity, since

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Financial Economics

Yield to Maturity

Calculating the Yield to Maturity

rate Hence one calculates the yield to maturity as the discount

R

(^) that makes the current bond price equal to the present

For a bond with current market pricevalue of the payments.

P

, coupon payment

C

and maturity value 1000 after

(^) n (^) years, one solves

P

C

R

C

R

2

(^) · · ·

(^) +

C

R

n − 1

(^) C (^) +

(^1000)

R

n

for

(^) R .

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Financial Economics

Yield to Maturity

Inverse Relation of Price and Yield

As As the interest rate increases, the present value falls (figure 1).

(^) R (^) goes to infinity, the present value goes to zero. As

R

(^) goes

goes up, then the yield to maturity goes down.factor that makes the present value equal the price. If the priceGiven the price, one finds the yield to maturity as the discountto minus one, the present value goes to infinity.

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Financial Economics If the price

P

(^) 1000, then the yield to maturity is

R

C

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