# Duration problem

An 8%, semiannual pay, option-free corporate bond that is selling at par has ten years to maturity. What is the effective duration of the bond based on a 75 basis point change (up or down) in rates? A. 5.6 B. 6.8 C. 7.2 D. 10.0 A little help here? Thanks

I get 5.833 S

i would calculate the price for i = 8.75 and i = 7.25 and get the difference from 1000 of each. i don’t know what to do with the two values. the 8.75 answer will be further from 1000 than 7.25. maybe just average the differences? i know this is wrong because duration is %change due to 100bps change in yield. great help aren’t i?

Ans is B. 6.81% Use the Bond function on your TI BA II Plus Calc. Use down arrow between each of these options SDT=1.0100 --> Translates to 1-01-2000 CPN=8 RDT=1.0110 --> becomes 1-01-2010 RV=100 ACT 2/Y YLD=8 initially PRI CPT ==> gives you 100 Now up arrow. Change YLD to 7.25 Down arrow. CPT PRI ==> 105.27 Now up arrow. Change YLD = 8.75 Down Arrow. Cpt PRI ==> 95.06 Now plug into Duration formula (105.27 - 95.06) / 2 * 100 * .075 = 6.81 --> (P- - p+) / (2*p0 * delta r) Ans

If you do it manually, will you take i/y as 8.75/2 and 7.25/2 and calculate the bond value? Can somebody do this way? S

I got B, 6.8012

saurya --> you would do the following N=20 i/y=4.375 PMT=4 FV=100 CPT PV ==> 95.07 i/y = 3.625 CPT PV–> 105.27 You know P0=100

Yup realized my mistake, I put n = 16, don’t know why? Cpk123, If I am following your bond worksheet, why I am getting error 6, when i ask it to compute Pri? man need to learn this? Is there a quick tutorial on Bond worksheet. S

Can you show me how you got i/y=4.375 cpk123?

Up shock of 8.75 and divide this by 2.

If you have a BAII Plus professional, it calculates your duration for the initial bond. This is the duration of the bond, no matter the change in price (on a range of 10bp to, say 120bp). It is the price that varies, not the duration. It is quite enough to calculate it fr the bond at 8, no need to plug values into the duration formula.

map, can you tell how do you that? S

CPK explained it, i suppose for a BAII Plus. With a BA II Plus professional you don’t need to shock the rates, the calculator does it for you calculating duration:) That’s why I love my BAII Plus professional:) SDT=1.0100 --> Translates to 1-01-2000 CPN=8 RDT=1.0110 --> becomes 1-01-2010 RV=100 ACT 2/Y YLD=8 initially PRI CPT ==> gives you 100 At about 2 arrows down, you get the duration. 6.7952

WOW !! I needed this post

Fantastic mate, time saver. So the interest change is 20 bp to 120bp?

Duration can be thought of, besides as the % change in price at 100bp change in interest rate, as the period of time necessary to recover the cost of a bond (PV of all coupons and of principal received in the future). It is going to be the same, no matter the shock in the interest rate (up or down at 50 or at 100 or at 120). The problem is that for very low shocks, like say 2 bp, duration gives no meaningful information, the shock is too small for a true reaction. A reasonable shock would be somewhere between 10bp and 120bp. And once you discovered what’s the % change in price for a certain shock, other than 100bp, the calculus of the % change in price is symmetrical.

i thought convexity said that a price move up will be more than down. e.g. in this example, for 100bp change in yield down - 66 (1000-934.96) up - 71 (1071-100)

This is a par, option free bond.

ryan – we are talking duration here, not Convexity.

map, they are asking the effective duration. the weighted average time to get your money is mcauley’s duration which is a different formula