Synthetic cash from bonds - Past CFA paper

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broadex

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A U.S.-based portfolio manager manages an $800 million portfolio ($600 million in stocks and $200 million in bonds). In reaction to anticipated short-term market events, she wishes to adjust the allocation to 50 percent stock and 50 percent bonds through the use of futures. Her position will be held only until “the time is right to restore the original asset allocation.” The stock futures index multiplier is 250 and the denomination of the bond futures contract is $100,000.
  • Bond portfolio modified duration 5 years
  • Bond portfolio yield to maturity 7%
  • Basis Point Value (BPV) of bond futures $97.85
  • Stock Index Futures Price $1378
  • Stock Portfolio Beta 1.0
Compute the number of Bond futures contracts to implement the asset allocation strategy.
 
Thanks Magician. But i tried following your article. In the question above - which is 2000 exam, there is duration of the fugure contracts.
 
assumed as same as the existing portfolio component. if not available,
so if you did $ Duration of existing portfolio / $ Duration of future - the duration cancels out.
 
Bond futures always have duration; you can get that from the BPV of the futures contract ($97.85).
 
Still perplexed by the answer from the exam:
5 × $200,000,000 × 0.0001 / 97.85 = 1,022 contracts
 
How much of the portfolio does she wish to change from equity to fixed income?
$400,000,000 − $200,000,000 = $200,000,000.
What’s the target dollar duration of the synthetic fixed income portfolio?
$200,000,000 × 5 years = 1,000,000,000 dollar-years.
What’s the existing dollar duration of the synthetic fixed income portfolio?
0 dollar-years.
What’s the dollar duration of a bond futures contract?
$97.85 ÷ 0.0001 = 978,500 dollar-years.
How many contracts are necessary (and does she take the long position or the short position)?
(1,000,000,000 − 0) / 978,500 = 1,021.97.
So she uses 1,022 contracts, and, because the number is positive, she takes the long position.
 
With changes in the curriculum I think you might confuse things a little of you are looking at papers from before 2005-6.
 
Hey Magician. Thanks for the answer but i dont get it as well.
1) Explain the dollar duration of a bond futures contract of $97.85 ÷ 0.0001 = 978,500 dollar-years. Where is this fomula i nthe curriculum and whats the intuition here.
2) The question provides the denomination of the bond futures contract which is $100,000.I thought you would further divide the calculation by 100,0000 (just like the multiplier in stocks). Was this information not useful??
My answer would have been:
[MDt – MDc]/MDf X CASH/future price = [5-0]x200,000,000/97.85/100,000
 
patso wrote:Hey Magician. Thanks for the answer but i dont get it as well.
1) Explain the dollar duration of a bond futures contract of $97.85 ÷ 0.0001 = 978,500 dollar-years. Where is this fomula i nthe curriculum and whats the intuition here.
Click to expand...
That’s from Level I.
patso wrote:2) The question provides the denomination of the bond futures contract which is $100,000.I thought you would further divide the calculation by 100,0000 (just like the multiplier in stocks). Was this information not useful??
Click to expand...
That’s included in the BPV.
You may know it as the price value of a basis point (PVBP) = portfolio value × duration × 0.0001.
patso wrote:[MDt – MDc]/MDf X CASH/future price = [5-0]x200,000,000/97.85/100,000
Click to expand...
MDf = BVP ÷ (portfolio value × 0.0001) = $97.85 ÷ ($100,000 × 0.0001) = 9.785 years.
When you put that into your formula, you got it!
 
Hey Magician.Thanks once again. But im somehow not getting the CFAI answer using the Mduf you have computed. Maybe im having a brain freeze here. Could you please put the numbers in into the formula below that ties to the CFAI answer. My comp is below.
=’[MDt – MDc]/MDf X CASH/future price = [5-0]x200,000,000/97.85/100,000

=[5 – 0]/9.785] X $200m/[97.85] ??????????
 
$800 million portfolio ($600 million in stocks and $200 million in bonds). In reaction to anticipated short-term market events, she wishes to adjust the allocation to 50 percent stock and 50 percent bonds through the use of futures. Her position will be held only until “the time is right to restore the original asset allocation.” The stock futures index multiplier is 250 and the denomination of the bond futures contract is $100,000.
  • Bond portfolio modified duration 5 years
  • Bond portfolio yield to maturity 7%
  • Basis Point Value (BPV) of bond futures $97.85
  • Stock Index Futures Price $1378
  • Stock Portfolio Beta 1.0
needs to sell $200 M in Stocks, buy $200 M in Bonds.
For the Bond side, calculation follows:
PVBP of Portfolio = 5 (Duration) * 200000000 (Portfolio) * 0.0001 = = 100000
PVBP = Price Value of Basis Point
PVBP of Portfolio / PVBP of Bond Futures = # of Bond Futures = 100000/97.85 = 1021.97 = 1022 rounded.
BUY. (since it is a positive number).
 
patso wrote:Hey Magician.Thanks once again. But im somehow not getting the CFAI answer using the Mduf you have computed. Maybe im having a brain freeze here. Could you please put the numbers in into the formula below that ties to the CFAI answer. My comp is below.
=’[MDt – MDc]/MDf X CASH/future price = [5-0]x200,000,000/97.85/100,000

=[5 – 0]/9.785] X $200m/[97.85] ??????????
Click to expand...
=[5 – 0]/9.785] X $200m/[$100,000] = 1,022
 
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