sample 2 questions synthetic cash & synthetic stock index

Question 27 asks you to create a synthetic stock index fund for Carly Dungan. You accomplish this by finding out how much cash she will have in 3 months and then dividing by the sum of the contract price and multiplier. This is all easy enough; however, doesn’t an index by definition have a beta of 1? Because that contract had a beta of 0.8 and adjusting for that gives you a “wrong” answer. Question 30 asks you to create synthetic cash. Once again CFA’s answer does not adjust for the difference between the Beta of Fund A and the futures contract that is being used to hedge it. obviously I’m missing something here because it looks to me that CFA got it’s own questions wron. Can someone point out the error in my ways?

Can I get some love here? I got burned on the same technicality on 2 questions. Do we adjust for Beta discrepancies between the underlying and the contract when creating synthetic cash or synthetic index investments?

#27 is correct, b/c she has her money in Eurodollar deposits ~ t-bills. You dont have to adjust for Beta on this one. #30 I totally agree and there have been numerous discussions about this. They should adjust by Beta b/c the Betas arent the same. I remember them being different. I think CFAI goofed here, but they could come back with the Betas are only slightly different… BOOO!

Thanks for the response Willy. However, if she invests all her cash in futures with Beta of 0.8, she is not getting true index exposure. I’m still at a loss on this one.

I just checked the actual CFAI text. It states that a simplifying assumption is that the beta of the futures contract equals the Beta of the index, which in this case the Beta does not equal one. In the CFAI text examples there is no adjustment for Beta because of this simplification.