Question

(C) An investor is investing in a bond with a 6-year maturity with 6% annual coupon at PAR. The investor plans to invest the bond for 4 years before selling it off. Assume further that in the following years interest rates follow a downtrend, so that the coupon received in year 1 is invested for three years at 4.5%; the coupon received in year 2 is reinvested for two years at 3%, and the coupon received in year 3 is reinvested for 1 year at 2%. 4 years later, the YTM of the bond is expected to increase to 8%. What’s the realized compound yield (RCY) in year 4. (10 Marks)

Answer 1

Assume a par value of 1,000 so purchase price of the bond is 1,000

Annual coupon

==> coupon rate*par value

==>6%*1,000

==>60

Coupon earnings in Year 4:

Coupon in Year 1 reinvested for 3 years at 4.5%: earnings

==> 60*(1+4.5%)^3

==>68.47

Coupon in Year 2 reinvested for 2 years at 3%:

earnings

==> 60*(1+3%)^2

==>63.65

Coupon in Year 3 reinvested for 1 year at 2%:

earnings

==>60*(1+2%)

==>61.20

Total coupon earnings in Year 4

==>68.47 + 63.65 + 61.20 + 60

==>253.32

Selling price of the bond in Year 4: FV (par value) ==>1,000; PMT (annual coupon) = 60; N (number of remaining coupons) ==>2; rate ==>8%, solve for PV.

Bond price ==>964.33

Total earnings ==>total coupon earnings + selling price of the bond

==>253.32 + 964.33 ==>1,217.66

Realized compound yield ==>[(total earnings/amount invested)^(1/4)] -1

==>[(1,217.66/1,000)^(1/4)] -1

==>5.05%

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