convexity scaling

[sachin_patel]

schweser’s notes say convexity should be scaled to duration squared.
in below answer they mention
With duration of 9.5, duration squared is 90.25, which implies that the reported convexity of 107.2 is scaled appropriately.
I scaled the duration to 10.7 and got my answer wrong.
What’s the rule for scaling?
is it number of decimals or the difference between duration and convexity?

A UK 12-year corporate bond with a 4.25% coupon is priced at £107.30. This bond’s duration and convexity are 9.5 and 107.2. If credit spreads narrow by 125 basis points, the estimated price of the bond is closest to:
A)
£120.95.
B)
£112.72.
C)
£121.84.
The correct answer was A.
With duration of 9.5, duration squared is 90.25, which implies that the reported convexity of 107.2 is scaled appropriately.
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Return impact
≈ −(Duration × ΔSpread) + (1/2) × Convexity × (ΔSpread)2

≈ −(9.5 × −0.0125) + (1/2)× (107.2) × (−0.0125)2

≈ 0.1188 + 0.0084

≈ 0.1272 or 12.72%
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Estimated price of bond
= (1 + 0.1272) × 107.30

= 120.95

 

[sachin_patel]

anyone?

 

[S2000magician]

All they’re saying is that the convexity number should be of about the same order of magnitude (power of 10) as the square of the duration. If they give you a convexity number that is off by one or two decimal places, move the decimal. Don’t mess with the duration; apparently they won’t foul up the decimal place on duration.
Frankly, I have no idea why anyone would give you a convexity of 10.7 when it should be 107; that just seems stupid to me. Nevertheless, CFA Institute says that they may do this, so be careful.
(Also, because this is in the credit analysis section, remember to include the factor of ½ in the convexity adjustment. Another stupidity of the finance profession.)

 

[sachin_patel]

I am sorry I messed up the question..
I meant to say
I scaled the convexity to 10.72 and got my answer wrong. (instead of 107.2 as schweser suggested)
I look at the duration and i think convexity should be 2 decimal places. but schweser kept the convexity at 3 decimal places. (even though duration squared is 2 decimal places)
Whats the logic?

 

[S2000magician]

sachin_patel wrote:I am sorry I messed up the question..
I meant to say
I scaled the convexity to 10.72 and got my answer wrong. (instead of 107.2 as schweser suggested)
I look at the duration and i think convexity should be 2 decimal places. but schweser kept the convexity at 3 decimal places. (even though duration squared is 2 decimal places)

It’s not the number of decimal places; it’s the magnitude of the of number. Here, you want a convexity number around 100.

sachin_patel wrote:Whats the logic?

The logic is that duration is multiplied by Δy, and convexity is multiplied by (Δy)², so they figure that the convexity value should be roughly on the order of the duration squared.
As I say, it’s stupid that they don’t give you the correct convexity number. Sorry.

 

[Viraj Dalal]

i am also confused with this part.. but what this is what ive understood so far.
If the modified duration of an option free bond is 6.0 and convexity is 0.562, than we need to correct the scaling. Hence, we square the modified duration as 36.0 (modified duration squared) and multiply 0.562*100 = 56.20. This is done to get both the numbers on same line, ie 36 & 56.20.
Please have a look at page 170 study session 16.
Caution: as you saw, i multiplied the convexity with 100. In some cases, we may even multiply it with 10.
It all depends on the scale, the squared duration would be on. But still, for calculations we would use the duration mentioned, and not the squared duration.
I hope this helps.

 

[Viraj Dalal]

to further support my claim, please have a look at page 171, study session 16 in kaplan notes.
The question mentions: duration as 6.4 and convexity as 0.5 Calculate the return impact.
Solution: we cannot use the convexity mentioned in the problem, as it does not have the same scaling as the duration. So in order to get the right scaling, we need to square the duration: 6.4^2 = 40.96.
We need to get convexity in the same scale as the squared duration, ie 0.5*100 = 50.00
Did you notice the thing out here? We now have the convexity and squared duration on same scale, and so now we can calculate the return impact using duration as 6.4 and convexity as 50.00