CFA CFA Level 1 Change in basis points clarification…

# Change in basis points clarification…

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What’s the rule to find the change in basis points in decimals for the duration calculation?

D = ( P if yields down – P if yields up ) / (2*initial price* change in yield in decimals)

In one question, the change in basis points was 100 and the change in yield in decimals was said to be : 0.001
In another, the basis point change was 60, and the answer in the formula used 0.006 as change in yield in decimal.
As far as I’m concerned, they didn’t do the same conversion there…… yet the answers work ( I checked their calculations)….

so what’s the deal? how do I turn basis point change into decimal yield change in order to use that formula??

thanks!

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Current price of bond 108.00
10 bp increase makes price 106.50
10 bp decrease makes price 110.00.
portfolio value = \$2 million.

The expected change in the market value of this holding for a 100 basis point change in interest rates will be closest to:
a- \$124,000. b-\$322,600. c-\$645,200. second exec:

price now 92.733
if price becomes 94.474 for a 60 bp drop and price becomes 91.041 for a 60 bp increase, the effective duration of the bond is:
a- 1.85. b-3.09. c-6.17. • 5  • 4

can you see the images? @graemea

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oh … maybe they did 0.001 in the first exec because the situation said TEN bp??
i thought they were using the HUNDRED bp that was in the actual question portion of the exec…

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I guess ill type

first exec calculation is:
(110-106.5 ) / (2*108.5*0.001) = 16.13 = duration

second exec calculation is:
(94.474-91.041)/(2*92.733*0.006) = 3.09

I did the execs in another way (not using this precise formula) and got the same answers

but if I were to use their formula, then I’m not sure whats happening

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it would mean that if its 10 bp then you divide 10 by 10,000

or whichever bp –> divide by 10,000 to get percentage yield change??

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Hey Lulu123,

The first question seems to be erroneous because 100bps is 1% or 0.01… so you’re correct in that they didn’t do the same conversion. May you post the question so I can see and attempt to interpret what was done?

Graeme

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Yes that is correct Lulu123….you’re duration calculation is also correct….16.13%*1.0*2,000,000=322,600 … since the example didn’t specify the direction of the rate change and all are negative… the answer is B … the 10bps change had to be used in the denominator of your duration calculation since that was the change used to compute the prices in the numerator….. the 100bps change came into play when you were estimating the change in market value

10bps (or 0.1%) was the hypothetical change used to calculate the duration
100bps (or 1.0%)was the actual change used to estimate the change in the value of the portfolio