Jana, I’m far from the sharpest student of risk management, but to me the text seems pretty clear in stating the beta either has to be matched or its difference accounted for. It’s right there on p363, and every example up to that point in the reading supports this.
not any example with the synthesized cash or equity position, it does not.
so I am not convinced. Even when they solved it in the mock exam they did not use the beta. so I would go with that.
Middle of page 363 - first paragraph below the box:
“In the example here, we sell the precise number of futures to completely hedge the stock portfolio. The stock portfolio, however, has to be identical to the index. It cannot have a different beta. The other formula, which reduces the beta to zero, is more general and can be used to eliminate the systemic risk of any portfolio.”
I rarely understand these things through and through, so I must be wrong somewhere. I just don’t know where.
I read that too. However - whereas every other formula is written out in black and white - if this were so important - why wouldn’t they provide it?
I don’t know – it looks pretty clear to me, and it’s consistent with the rest of the reading. In any event, given a conflict between 2012 curriculum and a 2009 mock, I side with the curriculum.
Please help me in interpreting this on P.No 363
"If we apply that formula to a portfolio that is iden- tical to the index on which the futures is based, the two formulas are the same and the number of futures contracts to sell is the same in both cases.29
29 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."
After rereading also, I tend to believe that in synthetic cash from futures or synthetic index from cash, both the beta i.e. of the index & future should be identical otherwise the text says the two formula (i.e. the one where we alter the beta of the portfolio & here when create synthetic position) will be same.
How you Guys dealing with it? Memorizing & moving forward with a view that if there is question of creating synthetic position, will ignore betas.
I would ignore betas for a synthetic cash/equity postition.
That seems to be the CFA way for this type of question.
To the OP, I’m glad this whole question was raised – I could have easily overlooked one simple paragraph in 2,500 pages of text. Still, I think we assume that both betas are the same. If they aren’t, then the portfolio has residual risk.
I suggest you to send an inquiry to CFAI to clarify it !
To me, it looks completely clear. What am I missing?
To convert equity portfoio to synthetic cash you just need to bring beta of the portfolio to zero and eventually earn risk free rate.
(0 - 1.2) 75,000,000 / (1.29 * 235,000) = - 297
You dont care about the risk free rate. To create synthetic cash today you sell 297 3-month futures and for 3 months your protfolio will grow at risk free rate. See practice problem 5A. If you ignore beta, it would mean you need to buy 322 futures of any instrument irrespective of beta, either 1.29 or 1.5 or 2 or 3. Does not make sense.
a. aren’t you missing the “synthetic” part (so risk free rate should figure in).
b. Show me one solved problem in the book on Synthetic equity where beta has been used.
c. if you had done the problem like you did above - you would have gotten it wrong.
Volume 5 Page 365 Exhibit 6 shows how to convert stock to cash.
Page 360 3.4, “Creating cash out of Equity” formula, however, does not use betas. I believe the difference here is whether you want to convert stock to cash to use now or convert into cash equivalent (risk-free bond). When you want to convert to a risk-free bond you dont care of betas anymore and just sell futures that fetch you risk-free return at the end of time-horizon.
I think ignoring beta of futures derivative does not makes sense. As Hank mentioned if betas are not specifically mentioned we can assume that they are same. But, if they are specifically mentioned I think we should take that into consideration.
Even if they mentioning about beta we need to ignore them, these are basically distractors to induce to pick wrong answers.
I watched SCH video as well to check how have they explained this formula. They have said that both the formula (i.e. alteration of beta one & to synthetize equity/cash) are same.
Though while creating synthetic position, we assume that systematic risk of index & future are identical & our target beta is zero so the formula does not include beta values.
Did anyone else think it was strange that there we so few EOC questions for readings 36 and 37? With so much material it seems like there should have been more practice questions.
Volume 5 page 363 specifically mentions the beta concern. “In Section 3.2, we gave a different formula to reduce the portfolio beta to zero. These formulas do not appear to be the same. Would they give the same value of Nf? In the example here, we sell the precise number of futures to completely hedge the stock portfolio. The stock portfolio, however, has to be identical to the index. It cannot have a different beta.”…" If we apply that formula to a portfolio that is identical to the index on which the futures is based, the two formulas are the same and the number of futures contracts to sell is the same in both cases." Also see footnote 29.
Implicitly the beta is assumed to be 1 for both the portfolio and futures.
Beta of futures/index and the portfolio does not have to be “1” but equal whatever the actual value is.
But then as cited in question in the starting of thread - where betas are given for both futures & index not used, why the answer is (322) instead of 300 (using given betas)?
I think beta values should not be used even if given & should assumed to be identical.
Yes , that is the appropriate thing to do , since we do not know how to incorporate beta into a synthetic cash or synthetic index calculation.
Ignore betas or write that calculation assumes betas are identical.
Thanks for stressing this point