# Creating Cash out of Equity

Say you have a Large-cap Fund that has a beta of 0.9. And you have a large cap futures contract which has a price of 100,000 = 0.1M and a *different* beta say 1.2. And say you are trying to convert 75M of the fund to cash,… should you be selling 75*(1+rfr)/0.1 contracts or 75*(1+rfr)/0.1 * (0.9/1.2) contracts ? CFAI says you don’t factor the beta in that calculation.i.e., use the first formula above. Now, if you do that, are the two positions - long equity fund and short futures - not going to move by different amounts when the underlying market(large-cap) moves ? What am I missing here ?

# Contracts = -[V§ * (1+Rf)^t] / P(f) where: V§ = current value of equity position P(f) = total futures price Rf = Risk free rate t = designated time period (for example 6 months = 0.5) the negative sign is there because you are reducing the beta to zero (even though you aren’t using it to calculate) thus you need to go short contracts (sell futures). So in your case, assuming 75M is 75 million # Contracts = -(75,000,000 * (1 + Rfr)^t) / 100,000

I think you need to do something with beta. Personally, I think we should get beta of the fund to the futures contract underlying index and use that but if we’re too lazy, I’d go with the two betas.

"Say you have a Large-cap Fund that has a beta of 0.9. And you have a large cap futures contract which has a price of 100,000 = 0.1M and a *different* beta say 1.2. And say you are trying to convert 75M of the fund to cash,… should you be selling " Now if you have a LC fund that you are trying to “Equitize” you want to reduce the funds Beta to 0 b/c by reducing the funds beta to zero you should “in effect” be market neutral and earn the Risk-free rate of return. So you Need to use the Betas so I would Short/Sell 562.5 or 563 Futures. Based on the above. If you don’t go Beta Neutral you will still have an effect Beta of 0.3 which is not beta neutral and thus are still exposed to systematic risks and will require a return greater than the Risk-free rate.

Thanks guys. So, CFAI is wrong in this case. Both in its text and its answer to the last question on the CFAI sample exam - 2.

I dont know if they are necessarily wrong, b/c I do remember the other equation also, but it might depend on the circumstances…

bigwilly Wrote: ------------------------------------------------------- > I dont know if they are necessarily wrong, b/c I > do remember the other equation also, but it might > depend on the circumstances… Both the approaches will give you the same result if the betas are equal. So, that formula is right when(and I think only when) the betas are the same.

Beta wouldnt matter if you try to equitize. You have a stock at S and you want to sell it at S*e^rt, so obviously you need to buy futures that would give you that amount so S*e^rt/(n*f) Now, if you have a beta of 1 and you want to reduce it to 0.5, it is different then trying to equitize part of your portfolio as you are interested that your portfolio would move at beta 0.5 and not produce Rfr

But you are not trying to Equitize it in the above quesiton, you are trying to turn it into Cash…Well “cash-like”

That is the point, sample exam asked about equitizing in one question and adjusting beta in another

I think there are two ways to do it, # Contracts = -[V§ * (1+Rf)^t] / P(f) or # Contracts = Bp/Bf *V§/P(f) Both should earn you Rf rate. Can anybody comment on that?

Tanyusha i agree in theory and i need to think more about it

1st one won’t earn you the Risk-free rate if the Beta of the Futures and the Beta fo your portfolio are different.

CSK, so are you saying the original question is wacked? FSA-sucka states that they asked to convert to cash, but didnt factor in Beta which they should have… Now if they were Equitizing the Cash into S&P futures then you dont need the beta…

they were equitizing, i took this test and scored 83% on this question (i dont remember which one i got wrong, need to double check)

Alrighty then…

comp_sci_kid Wrote: ------------------------------------------------------- > Beta wouldnt matter if you try to equitize. > > You have a stock at S and you want to sell it at > S*e^rt, so obviously you need to buy futures that > would give you that amount so S*e^rt/(n*f) You are right. When you have a stock and a stock future…both have the same beta with respect to any index. So, it doesn’t matter which of the 2 formulaes you use. However, if you are managing a LC fund it’s likely that your fund has a different beta than S&P500 because of different weightings, security selection, etc. If you want to cash out a part of the fund for the next few months, you are going to be short the future for that time duration…and that future contract could possibly(most likely) have a different beta. What do you do in that situation ? Which formula do you use ?

FSA-sucker, CSK stated that your original problem was that they were Equitizing Cash that they had into Stock futures, not converting Stock into Cash… Or I am just confused as all HE!! as to what was “supposed” to be asked

ok enough confsuion, i will double check tonite!

fsa-sucker Wrote: ------------------------------------------------------- > And say you are trying to convert 75M of the fund > to cash,… should you be selling >