Fixed Income Markets
Price a bond
Why does a fixed coupon lose value when market yields rise?
Higher yields discount fixed future payments more heavily.
Price = Σ coupon / (1 + y)ᵗ + face / (1 + y)ⁿ
Discount each coupon and the final principal at the market yield y. The one-year payment is $1,000 + $50 = $1,050, which is $954.55 today at a 10% yield.
A one-year $1,000 bond with a 5% coupon is worth $1,050 ÷ 1.10 = $954.55 at a 10% yield.
Discount each coupon and the final principal at the market yield y. The one-year payment is $1,000 + $50 = $1,050, which is $954.55 today at a 10% yield.
If yield falls to 5%, what is the same bond worth?