# Hedged portfolio return

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)

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