CFAI curriculum, Vol. 5 P330, top paragraph.
For creating cash out of equity, it says the value of the overall position (long stock plus short futures) will be [(V/S)(1 + δ)^T]St + qNf*St – qNf*f. shouldn’t this be [(V/S)(1 + δ)^T]St _ – _ qNf*St + qNf*f since we’re short futures? i.e. the futures payoff should be –qNf*ST + qNf*f as we receive qNf*f and deliver qNf*ST?
If I knew what all of those letters abbreviated, I could probably answer the question.
Thank you sir S2000, V = amount of money to be invested, f = futures price, T = time to expiration of futures, δ = dividend yield on the index, r = risk-free rate, q = multiplier, Nf=number of contracts shorted, S=price of each unit of index @ t=0, St=price of each unit of index at contract expiration. --> (V/S)(1 + δ)^T =# of units we are effectively converting to cash.
so [(V/S)(1 + δ)^T]St is the long equity position, and qNf*St – qNf*f is the payoff on the futures position according to the CFAI text.
pay off should also be equal to multiplier x number of shares sold x (new price - old price).
Yes. In this case, it’s negative correct? i.e payoff on your short futures position is (-) [multiplier x number of shares sold x (new price - old price).]