Question

You purchase a bond today for $900 that has a 5% coupon rate, paid semi-annually, and has 10 years to maturity. The face value of the bond is

$1,000. One year later you sell the bond for $1,020

a) Calculate the Holding Period Return (HPR) (in %) over the one year that you held the bond. (8)

b) Do you think interest rates increased or decreased over the one year period that you held the bond? Explain briefly. (5)

Answer 1

a) Price of bond today = P0 = $900, Face value of bond = $1000, Years to maturity = 10, Coupon rate = 5%

First we need to find the yield to maturity of bond today. As the coupons are paid semi annually

Semi annual coupon payment = (Coupon rate x par value) / 2 = (5% x 1000) / 2 = 50 / 2 = $25

No of half years to maturity = 2 x no of years to maturity = 2 x 10 = 20

Now we will find the semi annual yield to maturity of bond. We can find the semi annual yield to maturity of bond using RATE function in excel.

Formula to be used in excel: =RATE(nper,-pmt,pv,-fv)

Using RATE function in excel we get semi annual yield to maturity of bond = 3.1836%

Now we will find the future value of. reinvestment of coupons of bond assuming coupons are reinvested at current semi annual yield to maturity

Future value after 1 year of reinvestment of coupons of bond = FV = Coupon received in 6 months(1+semi annual yield to maturity of bond) + Coupon received in one year = 25(1+3.1836%) + 25 = 25.7959 + 25 = 50.7959

Price of bond after 1 year = P1 = 1020

Holding Period Return over one year = [(P1 + FV) / P0] - 1 = [(1020 + 50.7959)/900} - 1 = [1070.7959 / 900] - 1 = 1.189773 - 1 = 0.189773 = 18.9773% = 18.98% (rounded to two decimal places)

Hence Holding Period Return over one year = 18.98%

b) It is know that interest rate(yield to maturity) and price of bond are inversely proportional.Increase(decrease) in yield to maturity will result in decrease(increase) in price of bond. Also it is know that if price of bond is greater than face value of bond, then yield to maturity is less than coupon rate of bond. Or if price of bond is less than face value of bond, then yield to maturity is greater than coupon rate of bond.

At present price of bond equal $900 is less than face value. So yield to maturity = 2 x semi annual yield to matuirty = 2 x 3.1836% = 6.3672% is greater than coupon rate. After 1 year price of bond is greater than face value, so yield to maturity must be less than coupon rate of 5%. So yield to maturity or interest over the year.

Hence Interest rate or yield to maturity has decreased over one year period.