A five year bond pays a 6% annual coupon and trades at 95.00 per 100 of face. Estimate the yield to maturity by hand to within five basis points and show the iteration you used.

A five year bond pays a 6% annual coupon and trades at 95.00 per 100 of face. Estimate the yield to maturity by hand to within five basis points and show the iteration you used.

Approach: Start from the current yield plus the discount amortised over the remaining life as a first guess, then price the bond at two nearby yields and interpolate on price to converge.

7.23%. A first guess is the current yield of 6/95, which is 6.32%, plus the discount amortised over five years, 5/5 per year on an average price near 97.5, adding 1.03% for about 7.35%. Now price the bond at 7.10%: the discount factor is 1/1.071^5, or 0.7096, the annuity factor is (1 - 0.7096)/0.071, or 4.0895, and the price is 6 * 4.0895 + 100 * 0.7096, which is 95.50. The same calculation at 7.25% gives 94.91. Interpolating between 95.50 and 94.91 for a target of 95.00 puts the yield at 7.23%. Each basis point moves the price by about 0.039, so the interpolation is well inside five basis points because the price function is nearly linear across a 15 basis point window.

Follow-up: The same bond instead pays semiannual coupons of 3. What is the yield on a semiannual bond equivalent basis and why is it below the annual figure?

Key concepts: yield to maturity, annuity factor, current yield, interpolation.