A bond with an 8% semi-annual coupon and 10-year maturity is currently priced at $904.52 to yield 9.5%. If the yield declines to 9%, the bond’s price will increase to $934.96, and if the yield increases to 10%, the bond’s price will decrease to $875.38. Estimate the percentage price change for a 100 basis point change in rates. A) 4.35%. B) 6.58%. C) 2.13%. Your answer: A was incorrect. The correct answer was B) 6.58%. The formula for the percentage price change is: (price when yields fall – price when yields rise) / 2 × (initial price) × 0.005 = ($934.96 – 875.38) / 2($904.52)(0.005) = $59.58 / $9.05 = 6.58%. Note that this formula is also referred to as the bond’s effective duration. tell me what im missing - i guessed at the answer coz i had 3.29…arent they asking for a 100BP change in rates not 50???
Effective Duration is an approximation of a price change for 100 bp change in rate… so the question is just another way to asking you to calculate the effective duration. delta y in that formula is the change in yield which in this question is 50 bp.
Do not get caught up on that final sentence, it got me once too. Look at the relationship between prices and yields to see what basis point change they are using, in this case its (50 BPS*.0001) = .005 The percentage price change for a 100 basis point change in yield (1%) is the definition of duration. So instead of saying “hey, whats the duration”, they are trying to f with you by giving you the definition.
Look below, it’s a more intuitive way of reading effective duration: Increase-decrease/ 2 * 1/ (price * change in yield) The first term is simply the average change in price for an increase or decrease in the price. You divide by two because it is an increase PLUS the decrease amounts. The second term standardizes the change. By dividing it by the price you’re essentially making the difference a percentage value, and dividing it by the change in yield gives you the amount for a 1% change. If it was a 25 basis point change, the increase and decrease amounts would be half that of the 50 basis point change (roughly), but because you divide the 50 BP change by twice as much, it all evens out. Not very clear, I know, but hopefully it’s not too convoluted.
gotcha, thanks all