 # Question about bond yields

Deep discount bonds have: A) less call protection than bonds selling at par. B) greater reinvestment risk than bonds selling at par. C) less coupon protection than bonds selling at par. D) greater price volatility than bonds selling at par. ANSWER: Your answer: B was incorrect. The correct answer was D) greater price volatility than bonds selling at par. A deep discount bond is a bond selling at a discount of at least 20%. This means that a \$1000 face value bond will be selling at \$800. Using the duration method to show risk, a deep discount bond will have a significantly greater duration than the bond selling at par. Thus having a duration higher than the face value duration means there is more price volatility for the deep discount bond. ***** My question: My argument against (D) is that if you have two otherwise identical bonds (e.g. same coupon rate, same maturity, same face value), but one is issued at par and the other at discount, the discount bond should offer a higher YTM than the par bond. Given a positively convex price to yield curve, a movement left or right by the same yield amount should result in a smaller price fluctuation than a similar movement around a lower yield point. Hence, a deep discount bond should have less price volatility than a bond selling at par. And on (B), if a bond is at discount it should have a higher required YTM. Doesn’t this pose greater reinvestment risk for the investor, since it’s less likely that investor will be able to reinvest coupons at a rate = this high YTM, compared to the lower YTM a par bond will require? What is wrong with my logic? Thanks so much!

is D the answer? cuz bond that is priced lower than otherwise same bond, will move more as a % if any of the factors that affect price of a bond are changed. Reinvestment risk has nothing to do with price ofthe bond, so eliminate B Coupon does not affect on price, so eliminate C. Also eliminate A, cuz deep discount bond are UNLIKELY to be called.

“is that if you have two otherwise identical bonds (e.g. same coupon rate, same maturity, same face value), but one is issued at par and the other at discount,” That would be a nice arbitrage. Let me know when you find that. I will short the discount bonds buy the coupon bonds and move to the Riviera.

LOL. nice.