2015 Schweser mock - beta adjustment (Q8A)

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Carni

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Here’s the question
Company wants to use derivative contracts to hedge bond and stock positions. Five-month S&P500 futures contracts are trading at 1112.50, and the current level of the index is 1098.23. The multiplier for the contract is 250. The beta of the futures contract is 1.04. Risk-free rate is 5.2%
Company has a portfolio of 270 day T-bills valued at $52.83m. Calculate the number of contracts that company should use to create a synthetic equity position for a period of five months with risk similar to the futures index.
My answer
Compound the $52.83m forward by 1.052^(5/12), to get $53 957 751. Schweser agrees.
Divide that amount by the price of the contract (1112.50 x 250), multiplied by the beta of the futures contract 1.04.
Schweser disagree and don’t think you use the 1.04 anywhere in the answer. Can they be right?
I think they did this because the question says “with risk similar to the futures index” and maybe they’re saying that the futures index has beta risk of 1.04, but that was the risk of the contract, not necessarily the index?
Any ideas?
 
correct, beta doesn’t come in to play: #contractsUNrounded = (Theld)(1 + RF)t/(Pf)(multiplier)
 
Why doesn’t beta come into play? We are trying to increase beta to 1, but the futures contract is for 1.04. We have to adjust the number of contracts right? Or are you saying we’re trying to adjust to 1.04?
 
that is a red herring, for this question use the formula above and NOT #contacts = (Dtarget - Dp)/Dfut x V/(futprice x multiplier)
 
Well, you’re right. That’s what the formula is. But it’s not at all clear to me why the beta value of the forward contract is not relevant.
If we wanted to get beta exposure of 2 from cash, and the beta of the forward contract was 1.2, don’t we somehow need to take this into account?
 
Just looked it up in CFAI and its addressed in a footnote (footnote 29 on p240) of reading 27.
That says that to use the formula cohiba42 says you should use “a key element in this statement is that the futures beta is the beta of the underlying index, multiplied by the present value interest factor using the risk-free rate. This is a complex and subtle point, however, that we simply state without going into the mathematical proof”.
Basically, the only way Schweser is right is if we are trying to adjust the beta to 1.04. If we are trying to adjust it to 1.0, I am right.
Comes down to what “with risk similar to the futures index” means. I think the futures index on the S&P500 should have a beta of 1. But the contract has a beta of 1.04. I the S&P500 has a beta of 1.04, I’m wrong.
 
I wish I never get a girlfriend like Schweser ” when I said a symbolic gift I meant a diamond ring not flowers”
 
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