# Duration

According to my knowledge, this is the formula for duration: (Price if yield declines - Price if yield increases) / (2 * Initial Price * change in yield in BP) For this reason, I am a little bit troubled by this question: Nicole Diver, CFA, owns a Debstar Industries Bond with a market value of \$9,600,000. She estimates the bond’s duration is 4.4. Following a 40 basis point increase in yield, what is the approximate change in value of the bond? A -\$32,128 B - \$98,284 C -\$168,960 Answer is C I keep getting the wrong number. Any thoughts? Here’s how I solved it: 4.4 = Difference / (2 * 9,600,000* 0.4) This gives me achange in value of \$33,792,000 (which is coincidentally two times the correct answer value which makes me think that duration was calculated without the * 2 in the denominator)

Your equation should be: 4.4 = Difference / (2 * 9,600,000* 0.004)

The difference according to you is \$33,792,000. Assuming x to be the value which changes for 40bp ; So (9,600,000 + x) - (9,600,000 - x) = -33,792,000 Thus x = -\$168,960

One basis point is one hundredth of a percent so if you just divide the basis points by 10000 all the time and get the ratio, you can’t go wrong: 40/10.000=0.004 I think this is the fastest way to deal with basis points in the exam, you can work out the percentage - 0.4% in this case - after that and only if you need it

i haven’t adjusted the zeroes in the solution…just copy pasted your figures…feeling too lazy

another way to do this question very quick Duration = change in value for 1%, we know Duration is 4.4 and interest rate shock is 4/10 of 1%. So do (4/10)(4.4)(9,600,000) = -\$168,960 (you know price down b/c int rate shock up)

Thanks! I saw that in the book after I posted this question: The formula is Approximate price change: - duration x change in yield in basis points x 100 Thanks for all your input!