# AND Mock Question 47 -- ANOTHER CFAI ERROR?

On question #47, we are creating synthetic cash from an equity portfolio with a known and different beta than the futures contract we are going to use. In this case, the guideline answer ignores the difference in beta (1.20 vs. 1.29). Now… again in book V, on page 333, the curriculum discusses this situation and says that there is another formula from section 3.2 of the chapter which adjusts for the difference in beta. In the example from the text, the curriculum notes that “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.[emphasis added] The other formula, which reduces the beta to zero, is more general and can be used to eliminate the systematic risk on any portfolio” Of course, because if the underlying stock portfolio is different from the index, there will remain some non-systematic risk. But that’s a red herring and doesn’t change the fact that the appropriate adjustment should take into account the difference in betas. I appreciate any feedback.

I completely agree with you. I used the target beta- port beta formula and I got it wrong. I do not know - if it comes on the exam-which way to go ?

I had this same question & looked through the books for the answer. I don’t have the text in front of me, but I remember it saying something about using the risk free rate to compound the beta (I’ve never heard of this but I think it’s what they said). One of the footnotes said they will not go into the mathematical derivation of it, but to accept it. Apparently they are assuming some relationship between the beta of the portfolio (even if it’s not the same as the index represented by the futures contract) and the beta of the futures used to synthetically convert to cash. I spent a lot of time trying to get to the REAL answer here, but concluded that it’s beyond the scope of the curriculum. I’m just going to use this formula if asked on the exam: Number of Futures= - (Value to convert to cash x (1+rfr)^t) / futures price x multiplier. I’m sure it’s not the answer any of us want, but that’s what the text said. I’ll send the page number of the footnote when I have my books.

vanz1212 Wrote: ------------------------------------------------------- > I’m sure it’s not the answer any of us want, but > that’s what the text said. I’ll send the page > number of the footnote when I have my books. Well, until I see the quote in the text, I’m going to use the actual cited quote from page 333 above. Let me know if you can find the section you are talking about. It does not sound correct to me.

This is footnote #29 on p. 333 “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” It’s not clear to me if this same principle would apply to the portfolio beta, but since that is what they did in question 47, I’m going to go with it. It doesn’t sound right to me either, because what if the portfolio beta was 2x the futures beta? The number of contracts would have to be adjusted accordingly otherwise the returns diverge and you’re NOT left with the return on cash. Take a look and see if you can make better sense of it than I could.

Yes… I can make sense of the footnote. I cannot make any sense of why you think it justifies the CFA answer. Or even how it suggests that we do NOT take into account the difference between the portfolio and futures beta. It’s just not talking about that. The point of the footnote is to clarify the statement in the text. The statement being clarified is the fact that, “IF WE APPLY THAT FORMULA [the formula that takes into account differences in beta] TO A PORTFOLIO THAT IS IDENTICAL TO THE INDEX ON WHICH THE FUTURES IS BASED, THE TWO FORMULAS ARE THE SAME…” Well, duh. If there is no difference in the betas (which is not our case here), then you don’t have to use a formula that accounts for the difference in beta. Got it? The footnote tells us that this, of course, assumes that the futures beta is in fact the same and the beta of the underlying index multiplied …etc. That’s all well and good, but it does nothing to negate the fact that in our little example, we do in fact have different betas and should use the more precise formula.

basically, the way i think about it (and i missed it too bc of this)—anytime going from equities to cash or cash to equities—ignore the beta method and use the t-bill method.

Beta Tbill is zero. Therefore if you beta in the numerator, the whole thing will be zero. From equity to cash, you looking, there is no risk, tehrefore no need for beta. The problem is when going from cash to equity.Again this is synthetic, NOT real, you still have your cash, i guess no beta. I think CFAI could have done a bette job.

Now guys, I’m getting worried that we (collectively, including me) are not able to answer this kind of simple question… I believe this whole vignette is BS - hope we won’t have a similar one at the real. My question : Why are we given the beta of the equity futures? Why not using the following formula to adjust the beta of a portfolio: nb of contracts = (Beta_target - Beta_ptf) / Beta_futures * Value_ptf / (Value_future * Multiplier) MH

mhannebert, I have the same question as you. Why do we not divide by the 0.8 futures beta? It looks necessary to get the right amount of contracts. Otherwise you are assuming futures beta is 1, but its not. The vignette tells you its 0.8.

Typo on my part. The vignette tells you its 1.29. Why do we not divide by it?

Now, I realy believe this vignette is crap. For equity futures, - either they give us the beta and we should be able to use it with the beta formulas. - or they give the RFR and we use the (1+r)^t formula. Have you had a look at the duration and beta of the Fund D. I don’t have it here but they gave the duration and beta to the fixed income and equity parts of Fund D, not the average duration / beta for the fund as a whole! I hope we won’t have such crappy vignette on Saturday. MH

I think any time we see convert to synthetic cash or synthetic equity index, and they give you a time period like 3 months…you should use the RFR eqtn since it compounds the RFR by # of months / 12?

Did anyone write to CFAi on this? I got it wrong too, seems counter to everything I studied.

Any resolution on this? Looking at No.44 and this one, it looks like when they are talking about SYNTHETIC cash or Equity, use Nf= V(1+r)^t/QF but completely ignoring the beta of the mid-cap equities does not make sense at all.

So everyone agrees that ignoring the futures beta does not make sense? They did it in questions 44 and 47, so maybe there some logic to it that I am not seeing… Thanks

I guess all has been said. I hope it doesn’t show up in PM. If they want to test it then i rather have it in AM session - to get the credit for the formula and presentation i suppose.

This is a mistake on CFAI’s part right?

I believe so. Not the first none. Not the last. We all make mistakes. So does the CFAI. MH