Query regarding formula for creating synthetic equity position

CFA Level III Derivatives
#1

Hi,

I had a query regarding creating synthetic equity.

The formula for creating synthetic equity position from a Treasury position is:

no. of contracts = (Bt - Bp)/Bf * [Theld * (1+Rf)^t] / Vf

where,

Bt = target Beta = Bf & Bp= Beta of existing portfolio = 0 ; Hence (Bt - Bp)/Bf = 1

Theld = Value of Treasuries held Rf = Yield on Treasuries (ie risk free rate) Vf = Value of futures contract

My issue is with the " [Theld * (1+Rf)^t] " term. Earlier in the reading, it was mentioned that this portion of the formula is Vp - current value of the portfolio. However, here it seems to suggest that it is the future value of the portfolio (due to multiplication with (1+Rf)^t ).

Is there any explanation as to why it is this way?

#2

First, do not assume that βt = βf; they will give you these numbers.

Second, you’re correct, you’re converting the future value of the portfolio. You do this _ only _ when you’re converting a cash position to equity, not when you’re converting a fixed-income position to equity. (You can argue that cash is fixed income - and I would agree with you - but of you treat it this way you’ll fail this topic. CFA Institute says that when you’re converting cash to equity, use the future value of the cash. [Cue Yul Brynner’s voice.] “So let it be said; so let it be done.”)

#3

There is way too much handwaving at Level III.

CFAI textbook writers = “Those who can, do. Those who cannot, teach.”

#4

So, to conclude: the CFAI arbitrarily uses the future value of portfolio for converting cash to synthetic equity (and equity to synthetic cash) while using current value of portfolio for manipulating portfolio beta otherwise.

Can’t argue with CFAI’s diktat.

Thanks a ton for your help, S2000magician

#5

Yup.

Do so at your peril.

My pleasure.