# futures and fwds

if we want to convert equity to cash… we have two options 1. set the target beta =0 and the solve (beta target- beta eq / beta futures) 2. use the other formula where we go long the stock and short the futures … and use risk free bonds i’m not sure when to use what. CFAI explains the diff on pg 111 , volume . 5 but i can’t understand it anyone please ?

use #2. Why the diff i dont really know, i will read up on it as i am curios myself

there was a post yesterday … they tested this in one of the sample exams apparently and yes there is a difference…

Long Stock = Long Futures + Long Rf Debt Right? Also, if you are going to convert equity to Cash: Use Nf = V(1+r)^t / Qf Where V = value of Equity r = Rf rate Qf = Futures price x multiplier Nf = # of Futures If the Beta is not equal then you ahve to multiply the equation by (Target Beta - Current Beta)/(Futures Beta).

bigwilly Wrote: ------------------------------------------------------- > Long Stock = Long Futures + Long Rf Debt > Right? > > Also, if you are going to convert equity to Cash: > > Use Nf = V(1+r)^t / Qf > > Where V = value of Equity > r = Rf rate > Qf = Futures price x multiplier > Nf = # of Futures > > If the Beta is not equal then you ahve to multiply > the equation by > > (Target Beta - Current Beta)/(Futures Beta). >> If the Beta is not equal then you ahve to multiply the equation by (Target Beta - Current Beta)/(Futures Beta). That is not what happens in sample exam…

bigwilly Wrote: ------------------------------------------------------- > Long Stock = Long Futures + Long Rf Debt > Right? > > Also, if you are going to convert equity to Cash: > > Use Nf = V(1+r)^t / Qf > > Where V = value of Equity > r = Rf rate > Qf = Futures price x multiplier > Nf = # of Futures > > If the Beta is not equal then you ahve to multiply > the equation by > > (Target Beta - Current Beta)/(Futures Beta). i got the equations, i am just not getting which two betas have to be equal to use the formula and why ?

i think when they use the word “synthetically” creat cash or equity , you must use that FV formula. for simple allocation changes use the target beta formula. there sholud be slight difference coz target beta formula uses PV. as for why? who cares or better yet who knows

The whole point is then you ‘equitizing’ something in the future you will get shares by buying long futures, so beta of futures CANNOT be different then beta of equitized index. if Beta is different you cannot ‘equitize’ That is how i see it

CSK - I totally agree that the Sample Exam doesnt do that, and I think the Sample Exam is WRONG! B/c the Betas of the two were different and hence I got the Question wrong b/c they didnt adjust for the Beta…it was something like 422 which I got and then I mulitplied it by I think .095 and got like 399 or 400 and the answer was 422 if I recall b/c they didnt adjust.

Will, the point is that when u equitize it doesn’t matter what beta is cause in the future u will get predetermined number of shares and that is all u care about.

CSK, I don’t believe that’s entirely true from my readings in Stalla and CFAI. The Equation ONLY holds if the Betas are the Same. If they are different then the equation becomes the normal one with the differences in Beta taken into consideration… Please prove me wrong, as if CFAI states that its always the equation without the Beta adjustment then it will make my mind at ease, but I don’t believe that’s the case.

I think the key is equitize. I never saw equiti2 equation with different betas

Probably b/c they said in the question assume the portfolio trackst he futures very closely or something like that… But if my portfolio has a Beta of 0.8 and the futures Beta is 1.1, then I’m going to have tracking error.

I gotta agree with bigwilly here. For the exam though, they implicitly make the assumption that beta of the portfolio and beta of the index future are the same or very close, so we won’t have to invoke the difference in beta’s, but if they are drastically different you would do an ajustment of [beta§/beta(f)]

I want my 3.33% back on my sample exam . I guess on the exam I will not adjust for Beta unless there is a big discrepancy.

I suggest dont take V*(1+r) if betas are different as you cannot equitize per se using futures on underliers which is different from underlier which you are trying to equitize

or atleast i am not going to do as it adds additional level of complexity i dont understand

I’m with Willy and Volkovv. If you’ve got some portfolio different from any futures contract, you do what you gotta do and short the closest futures contract. The best you’re going to do easily is to use the ratio of the betas for your hedge ratio.