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%.

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.

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)