Question

cover her retirement needs. What amount does she have to deposit? Q-2. (Bond Valuation) The YTM on a bond is the interest rate you earn on your investment if interest rates don't change. If you actually sell the bond before it matures, your realized return is known as the holding period yield (HPY). a) Suppose that today you buy a bond for $1,150. The bond has a face value of $1,000, 10 years to maturity, a 9 percent coupon rate, and the coupons are paid annually. What rate of return do you expect to earn on your investment? b) Two years from now, the YTM on your bond has declined by 1 percent, and you decide to sell. What price will your bond sell for? What is the HPY on your investment? Compare this yield to the YTM when you first bought the bond. Why are they different?

Answer 1

a) Rate of return expected on bond

The bond is bought at $1150 and 10 years from now the bond will mature at Face value of $1000.. The YTM is the rate at which the PV of all flows from the bond will equate to the purchase price of $1150. The yearly coupon payments are $90.

C= 90 ( 9% of $1000 Face value)

N=10 years

r = YTM

P =1150

F=1000

We will derive the YTM as below

Price of Bond= C x ((1-(1/(1+r)^n))/r)+F/(1+r)^n

1150 =90*((1-(1/(1+r)^10))/r)+1000/(1+r)^10

Through trial and error method, the YTM derived will be 6.90% approximately. This is the rate at which PV of all outflows from the bond will equal the price of $1150.

b) Two years from now the YTM will reduce by 1% i.e YTM will be 6.9%-1% = 5.9%. The price of the bond will be as follows:

Price of Bond= C x ((1-(1/(1+r)^n))/r)+F/(1+r)^n

=90*((1-1/(1+5.9%)^10)/5.9%)+1000/(1+5.9%)^10

=90*((1-0.56369)/5.9%)+1000/1.774024

=90*((0.43631)/5.9%)+563.6901

=90*7.395085+563.6901

= 665.5577+563.6901

= 1229.248

=1229.25

Holding period yield = ((Coupon payments received+(End of period value - Original Purchase Value))/Original Value) %

=((90*2+(1229.25-1150))/1150)

=(180+79.25)/1150

=259.25/1150

=22.5435% =22.54%

YTM is the yield received in terms of annual percentage till the bond matures, whereas holding period yield is absolute percentage return, depicting the return received over the holding period of the bond.