I was just going through random stuff, and realized I cant even do this! Can someone help? 1) Estimate the percentage price change for this 5-year $1,000 par value bond, with a 6% coupon, if the yield rises from 8% to 8.5%. Interest is paid semiannually. Modified duration is 8.38 years. a) 2.1% b) –2.1% c) 4.4% d) –4.4% e) None of the above 2) Consider a bond with a duration of 6 years having a yield to maturity of 8% and interest rates are expected to rise by 50 basis points. What is the percentage change in the price of the bond? a) 2.88% b) 3.45% c) -3.89% d) -3.45% e) -2.88%
1 -> B? 2 -> no clue
- b 2. e
wait…can someone show the work for this? i thought #2 was just -6x(.0050) but it’s not. what am i missing? that does not bode well for me…and fixed income was one of my stronger subjects
You don’t need a calc for number 2. Since duration is 6 (for a 100 basis point move) you know that it will move about 3%. Because the interest rates are going up the bond will move down. Positive covexity will make it slightly less than the 3% move (as positive convexity always helps). So -2.88% is the best answer.
- effective duration = - % change in price / change in yield % price change = -0.419 must be d 2) % price change = -3% based on effective duration formula. I guess its either d or e. i am guessing e.
thanks! i wasn’t completely crazy with #2!
Remember that duration is only calculation the linear move on the price/yield function…so unless you take convexity into account it will always be off a little bit. For small moves this isn’t really a big deal. For big moves it becomes move important.
Yea, I understood this logic when I took the test. However, the CFAI decided to throw in that bond question where the duration and convexity were both given, and the convexity number was negative…so the price would have been adjusted downward…apparently because it was a callable bond? But, for this one, indeed upward! -1 for me. Thanks CFAI 