nle 1618 Problem Set 6 classpdf I Prices and yields A 10year

.nl????e) 16:18 Problem Set 6 class.pdf I. Prices and yields A 10-year bond is issued with a face valuc of $1,000, paying inlerest of 560 a year, IE market yields increase shortly after the T-bond is issued what happens to the bonds a Coupon rate? No change) b. Price? No change c. Yield to maturityNo chanpet a Does not change Price falls Yield rises. 2. Prices and yields Constnact some simple examples to illustrate your answers to the following a If interest rates rise, do boed b. If the bond yield is greater than the coupon, is the price of the bond greater or less than 100 c. If the price of a bond exceeds 100, is the yield greater or less than the coupon? d. Do high-coupon bonds sell at higher or lower prices than low-coupon bonds prices rise or fall? a. Fall ie.g.. 1-year 10% bond is wortb110/1.1-100 ifr-10% and is worth 1101.15 -9565 ifr-15%). b Less (cg. See Sa) c.Less (c.g. with r-5%, 1-year 10% bond is worth 1 101.05-104.76). d.Higher (eg. ifr-105, 1-year 10% beed is worth 110,1.1-100, while 1-year 8% bond is werth 108/1.1 -9818)

Solution

1.

A.

Coupon rate does not change, because it is fixed w.r.t. the face value when the bond is issued.

B.

Price of the bond decreases, because yield increases. There is an inverse relationship between bond price and yield rate.

C.

Yield to maturity increases, because price of the bond decreases. There is an inverse relationship between the YTM and the bond price.

2.

A.

With rise in interest rate, bond price will fall.

For example,

Price of 2 year bond with face value of $1000 , coupon rate of 10% and interest rate of 8% is P1.

P1 = 100*(1-1/1.08^2)/.08 + 1000/1.08^2 = $1035.67

Price of 2 year bond with face value of $1000 , coupon rate of 10% and interest rate of 11% is P2.

P2 = 100*(1-1/1.11^2)/.11 + 1000/1.11^2 = $982.87

It can be seen that, with increase in interest rate, bond price is decreasing.

B.

If yield rate is greater than the coupon rate, then bond price will be less than $100.

For example,

Price of 2 year bond with face value of $100, coupon rate of 10% and interest rate of 11% is P. Here, yield rate is bigger than the coupon rate.

P = 10*(1-1/1.11^2)/.11 + 100/1.11^2 = $98.28

Now, it can be seen that price is lower than the $100.

C.

Yield is less than the coupon, when the price exceeds $100.

For example,

Price of 2 year bond with face value of $100 , coupon rate of 10% and interest rate of 8% is P.

P = 10*(1-1/1.08^2)/.08 + 100/1.08^2 = $103.56

Here, bond price is more than $100, when coupon rate is higher than yield.

D.

High coupon bonds sell at higher prices than the low coupon bonds.