Your company has purchased (invested) 2 (one of each A and B) annual-coupon paying bonds. Bond A is a 2-year, 6% coupon with a $1,000 face value and bond B is a 3-year, 16% coupon with a $1,000 face value. The YTM for both these bonds is 8%. Which of the following statements are true? A. The duration of portfolio investment in A and B is equal to 2.33 years. B. Bond A is a premium bond and Bond B is a discount bond. C. Bond A has lower default risk, but higher interest rate risk than bond B. D. The duration of portfolio investment in A and B is equal to 2.29 years. E. Selling a single bond with a face value of $1,000, a YTM of 8%, and a duration equal to that of the portfolio investment, creates a dollar-for-dollar hedge of the companys investment in A and B.

Show your work explaining each statement why it is true or false, thank you!