Hedged portfolio return

[gonowpass]

I saw this example in reading 27.
Say we have a $5m portfolio and want to increase beta. We purchase 6 contracts for say $240,000 each = $1.44m (I have skipped the calculation).
If the unhedged portfolio is now worth $5.255m and each contract has increased in price by $12,240, the hedged portfolio ending value = 5.255m + (6 x 12,240) = $5.32844m.
So the hedged portfolio return = ($5.32844m/$5m) - 1 = 6.57%.
For hedged portfolio return, why is cost of the futures not included in the beginning portfolio value? So it would be: ($5.32844m/($5m+$1.44m)) - 1 = -17.2%.

 

[pokhim]

The gain/loss of the future is part of the profit / loss.
You essentially buy the futures for x and sell it for x + (6*12240). The profit you make is part of the return calculation and you don’t need to incorporate the capital to purchase the future.

 

[gonowpass]

I understand that the gain/loss of the future is part of the profit/loss.
Hedged portfolio return = (initial portfolio + gain on equity + gain/loss on future) / initial portfolio.
I don’t understand why the cost of the futures isn’t included in the denominator, so why not:
Hedged portfolio return = (initial portfolio + gain on equity + gain/loss on future) / (initial portfolio + cost of future)

 

[Would You Look]

They’re assuming that the portfolio was used as collateral on the futures and no expense, I suppose.