# Synthetic Cash position with Equity Futures

Scratching my head at this one….

There is a formula to temporarily reduce equity by using futures. That formula to find out how many futures contracts to do this synthetic cash position :

Formula 1: N_{f}=((β_{T}−β_{S})/β_{f})x(S/f)

Set β_{T }= 0

And then there’s another formula that says:

Formula 2: N_{f}= S(1+ R_{f})^{n}/(f x multiplier)

Then I run into a practice problem that uses Formula #2: [*An investment management firm has a client who would like to temporarily reduce his exposure to equities by converting a $25 million equity position to cash for a period of four months. The client would like this reduction to take place without liquidating his equity position. The investment management firm plans to create a synthetic cash position using an equity futures contract.] *

And then a few questions later, I run into another problem that uses Formula #1 rather than Formula #2: [*Create a synthetic cash position by temporarily converting the US equity exposure in the fund into cash for a period of three months.]*

Which formula is the right one, and why didn’t formula #2 work for the 2nd question? I tried formula #2 for the 2nd question and it was way off compared to formula #1

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Figured this out… They’re essentially the same formulas. Formula 2 assumes beta of 1 while formula 1 lets you plug in the betas. Schweser notes was helpful in this explaining this part.

Under what circumstance does one use each formula? What if all data for the two formulas are given in a problem.

It's a long shot, gotta make it.

bump

It's a long shot, gotta make it.

You are referring to Question *, page 267 of Reading 32. I do not quite understand the logic as well. It has to do with whether you want to track the performance of the index or eplicate exactly the performance of the index. To me itis still unclear. The book tries to give an explantation on page 240, but still dont get it.

Bringing the portfolio beta to zero (as per the first formula) is not a 100% “cashization”. A synthetic cash position means that you slice and dice your portfolio so that you create a synthetic cash position that earns the RFR with a probability of 1.

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Was going to ask the exact same question as I was working on this last night. It doesn’t seem to be consistent some questions require you to use the rf rate and dividend yield to PV the exposure you need when creating synthetic cash whilst others just seem to use the plug and chug beta formula and set the target beta to 0. I don’t want to rely on using the rf rate and div yield method if the data is provided as could be a red herring so any insights appreciated.

There is a logic behind both formulas. Guess not enough people have understood what we are talking about as I do not see much participation to an otherwise extremely tricky/testable point.

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It has nothing to do with the beta of the index. It has something to do with time and cash. Cash is Rf of course.

back against the wall. no retreat no surrender.

You sound clueless and confused. If you can explain the point, we are listening carefully.

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I am not confused. Only the Synthetic Equity and the Equitizing of Cash are meant for a specified time. If it is for specified time the factor (1+R

_{f})^{T}will invariably come into picture. Either monetizing or cashing out the R_{f}is again unavoidable (hope this is understood).The only other factor to consider why the Beta=1. You tell me. Easy enough again I think. Unless you are equitizing (or cashing out) in an overseas market the Beta will always be 1.

I am hopeful nobody should be confused about this anymore.

back against the wall. no retreat no surrender.

I’m still confused about this. Looking at MM mock #3 PM Q46: The question asks to create a synthetic equity position for 6 months in a different currency/market. The currency part is easy enough, however I calculated the number of futures adjusted for the foreign risk free rate. The correct answer is to simply calculate the number of futures using the same ol’ formula (Bt-Bp/Bf) X ($Port/$Futures), with no adjustment for time/risk free rate. I used (V0 (1+rf)(Time adjustment))/$Futures. And of course the answer I got was an option, meaning this is likely a common mistake.

Under what circumstances do we adjust for time/interest? Maybe I’m just having a brain freeze… but this mock is really getting the best of me. Scratching the surface on 60% overall…

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Ask Bill or Mark about that one. I think the answer may be wrong but maybe I’m wrong. I did ponder this one a while back.

Maybe it was a trick question, because the question did not mention he would invest in risk free bonds. if he does not, then you don’t multiple it by (1+rf). The whole thing about the risk free rate assumes the investor takes a larger contract size but also uses his cash to invest in risk free bonds. By the end of the time period, he will have the right amount of cash to pay for the contract.

Thanks 125. But isn’t that the point? You have cash today and you don’t need to settle the futures contract for 6 months… seems reasonabe that you’d invest this cash at the risk free rate for the 6 month duration.

A little cheeky if this is a trick questions. But at the very least it’s forcing me to spend some serious time learning this.

I looked at the question and I agree: the risk-free rate is missing.

Simplify the complicated side; don't complify the simplicated side.

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Thanks, Bill for taking a look. Pleasantly surprised to hear that.

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pleasantly relieved to hear that.

To my understanding, the two formulas are different.

The first one is used to adjust the systematic risk of a portfolio that already has equity. Therefore, it takes into consideration the Beta of both stocks and options.

The second one is for a synthetic position. It means that the portfolio never includes stocks in reality. As a result, it does not concern Beta.