Bond prices and the yield curve

The table below shows the term structure of the zero-coupon, risk-free, interest rates.

-----------------------------------------------------------

Term Zero

(years) yield (%)

-----------------------------------------------------------------

1 5.50

2 5.70

3 5.85

4 6.40

5 6.95

-----------------------------------------------------------

The table below shows the term, in years, the annual coupon rate and the price of 5 risk-free bonds.

All bonds have a face falue F = 1000 and all bonds with a positive coupon rate make one annual coupon payment.

-----------------------------------------------------------

Term Coupon Price

Bond (years) rate (%) ($)

-----------------------------------------------------------------

A 1 0.00 947.87

B 2 3.50 1009.56

C 3 8.00 1108.08

D 4 7.00 1022.90

E 5 6.00 915.52

-----------------------------------------------------------

Are some of these bonds mispriced with respect to the arbitrage-free prices we obtain using the yield curve?

An overvalued bond is a bond for which the posted price is at least $5 greater than the price obtained with the yield curve.

An undervalued bond is a bond for which the posted price is at least $5 smaller than the price obtained with the yield curve.

Otherwise, a bond is considered as correctly priced.

• A.

  Bond A is correctly priced, Bond B is overvalued compared to its arbitrage-free price, Bond C is overvalued compared to its arbitrage-free price, Bond D is correctly priced, Bond E is undervalued compared to its arbitrage-free price.

• B.

  Bond A is overvalued compared to its arbitrage-free price, Bond B is correctly priced, Bond C is correctly priced, Bond D is overvalued compared to its arbitrage-free price, Bond E is undervalued compared to its arbitrage-free price.

• C.

  Bond A is overvalued compared to its arbitrage-free price, Bond B is undervalued compared to its arbitrage-free price, Bond C is undervalued compared to its arbitrage-free price, Bond D is overvalued compared to its arbitrage-free price, Bond E is correctly priced.

• D.

  Bond A is undervalued compared to its arbitrage-free price, Bond B is correctly priced, Bond C is correctly priced, Bond D is undervalued compared to its arbitrage-free price, Bond E is overvalued compared to its arbitrage-free price.