Question

Ann purchased a treasury bond with exactly six years until maturity, which pays coupon annually. The bond has a par value of $1,000, a 5% annual coupon rate, and a current yield to maturity (YTM) of 6%. After exactly three years Ann sold the bond to another investor, with the yield to maturity of 4%.  She was always able to re-invest all her coupon income at a return of 3%. All rates are annual. What is her ANNUALIZED holding period return over the 3-year period?

Answer 1

Pr value of Bond= $1000

Annual coupon Payment = $1000*5% = $50

Current YTM = 6%

n= no of years to maturity = 6

Calculating the Current price:-

Price = $ 245.865 +$ 704.96

Price = $ 950.83

Now, after 3 years the YTM is 4%

& n will be 3 years

Calculating the Price after 3 years :-

Price = $ 138.755 +$ 889

So, Price after 3 years= $ 1027.76

- During the 3 year period all coupon will be re-invested at 3%:-

Calculating the future accumulated value of Coupon payment with interest after 3 years:-

Where, C= Periodic Payments = $50

r = Periodic Interest rate = 0.03

n= no of periods=3

Future value = $ 154.55

Now, we will Calculate the Annualized Holding period Return(AHPR):-

where, n= no of years = 3

Income = $ 154.55

P0 =Current price = $ 950.83

P1 =Price after 3 years= $ 1027.76

So, AHPR over 3 years is 7.53%