# Synthetically Altering Equity to Bonds

No issues setting up the bonds to get the target duration. But, when shifting the Equity position to synthetic cash, which formula to we use (beta t - beta p)/ beta f x (Vp/Pf) where beta t = 0 or Vp(1+Rf)^t / Pf or theoretically should they yield the same result?

I would go with the second one. I have been looking for an example is which the inputs for both were given so I could test if they both come out the same and I couldn’t find one. Looking at them, I don’t think you will get the same result.

I don’t think you use the beta for synthetic cash. And I don’t think it gets you to the same place.

So it’s safe to say, only use the beta formula if we are swapping an equity to equity position?

Big Babbu Wrote: ------------------------------------------------------- > So it’s safe to say, only use the beta formula if > we are swapping an equity to equity position? Or just altering the beta exposure of our current position.

(beta t - beta p)/ beta f x (Vp/Pf) = (0-1)/1 X (Vp/Pf) = -Vp/Pf -Vp/Pf <> Vp(1+Rf)^t / Pf Your results will be different.

i am pretty sure that when it’s synthetic cash or synthetic equity you use the second equation using the future value…

I would use the first one, Vp(1+Rf)^t / Pf, as that’s what’s in the CFAI text. Plus, with cash involved it’s tricky as to whether you use a beta of 0.25 or 0.0.

bhill020 Wrote: ------------------------------------------------------- > I would use the first one, Vp(1+Rf)^t / Pf, as > that’s what’s in the CFAI text. > > Plus, with cash involved it’s tricky as to whether > you use a beta of 0.25 or 0.0. You’re thinking 0 or .25 duration with bonds and cash

I did this today and based on Qns from the Mock this is what i concluded: 1) I want to change from equity to cash or cash to equity for the next three months — I need to use syntheic in both cases. Ref: Q44 and Q47 of the Mock. reasoning the cash will grow at the risk free rate and that “grown” amount needs to be short or long 2) If given a cash equivalent T-bill, use it for intermediate transactions… like from equity to cash to bonds (Q 45. they use the T-bill cash equivalent instead of cash for the intermediate cash position) they never specify so if given use the cash equivalent for cash positions Also per page 337 of the CFAI text … if you move from bonds to cash use cash duration as 0.25 even if not given … this is when you plan to remain in cash

There’s an example CFA Volume 5 pgs 339-340 that uses the beta formula to convert equity index to a cash position. I knew I had seen this before. At this point I’m guessing you will know by what they put in the question.

Yeah, the CFAi text says they’re both feasable, but the beta one is an approximation whereas the other one is exact. I’ve seen problem sets both ways in the EOC q’s so it just depends on what they give you.

Black Swan Wrote: ------------------------------------------------------- > Yeah, the CFAi text says they’re both feasable, > but the beta one is an approximation whereas the > other one is exact. I’ve seen problem sets both > ways in the EOC q’s so it just depends on what > they give you. The mock gives you the information to do it both ways.

Fanfrickentastic mwvt. So what did the answer give as the more viable way to do it?

Right and I knew that, so not sure why I said it! Thanks ng. Sorry BB. ng30 Wrote: ------------------------------------------------------- > bhill020 Wrote: > -------------------------------------------------- > ----- > > I would use the first one, Vp(1+Rf)^t / Pf, as > > that’s what’s in the CFAI text. > > > > Plus, with cash involved it’s tricky as to > whether > > you use a beta of 0.25 or 0.0. > > > You’re thinking 0 or .25 duration with bonds and > cash

The mock answer is the second way. I choose the beta way and missed it. I just looked back at it though and I don’t think the beta way gave you one of the three options. I just couldn’t remember the other way. Edit: Didn’t mean to shake anybody’s confidence here!

B@stards!! Thanks.

mwvt9 Wrote: ------------------------------------------------------- > Black Swan Wrote: > -------------------------------------------------- > ----- > > Yeah, the CFAi text says they’re both feasable, > > but the beta one is an approximation whereas > the > > other one is exact. I’ve seen problem sets > both > > ways in the EOC q’s so it just depends on what > > they give you. > > The mock gives you the information to do it both > ways. I was refering to page 333 of CFAi volume 5. I was going to type it but it’s too long. I haven’t done the mock yet, is it possible being graded AM that either was acceptable? Although the CFAi did express a preference for the second.

Not sure. This was the PM section.

Read page 333 Black Swan…thanks. That clears it up pretty good…I think