1. A 20-year 10% corporate bond was issued 10 years ago. You purchased this bond today, when it was trading to yield 12%. Next day, the yield decreased to 7% and remained at this level indefinitely. Disregarding the possibility of default, if you decide to sell the bond just before its maturity date, you will have incurred a capital loss.

2. A 30-year 8% corporate bond was issued exactly 10 years ago. You purchased this bond today, when it was trading to yield 6%. Tomorrow, the yield decreased down to 5%, only to increase to 8% after 10 years. At maturity, the bond's realized return must be equal to 7%.

3. You purchased a 10% corporate bond when it was trading to yield 8% and calculated its duration to be 16.5 years. Next day, your bond's YTM changed and remained at this new level indefinitely. When you sold your bond after 17.8 years and calculated the realized return over the holding period, you discovered the realized return was higher than the yield to maturity at which you purchased the bond. Based on this information, we can conclude that the YTM had must have decreased after you had acquired the bond.

4. When the YTM increases, the duration of a zero-coupon bond will decrease.

5. Second order approximation produces asymmetric volatility of a bond's price in response to positive/negative changes in the YTM.

7. The invoice price as of the settlement day is equivalent to the dirty price as of the purchase date plus 2 days' worth of accrued interest.

8. For a bond with a positive coupon rate, which is to pay at least one coupon before its maturity date, the value of duration must be smaller than the time to maturity.

explain the TF problem